nd - icomaa 2019...a note on approximating finite hilbert transform and quadrature formula.....39...

2nd International Conference on Mathematical Advances and Applications, May 3-5, 2019,

Istanbul / TURKEY

http://icomaa2019.com/

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2nd INTERNATIONAL CONFERENCE ON MATHEMATICAL

ADVANCES AND ITS APPLICATIONS

MAY, 3-5, 2019, ISTANBUL / TURKEY

Abstract Book

Editors:

Assoc.Prof. Dr. Yusuf ZEREN Prof. Dr. Necip ŞİMŞEK Yıldız Technical University İstanbul Commerce University

İstanbul, TURKEY İstanbul, TURKEY

Prof. Dr. Bilal BILALOV Azerbaijan National Academy of Sciences

Baku, AZERBAIJAN

ISBN: 978-605-245-207-3 Yıldız Technical University, Istanbul, TURKEY – 2019


http://websiteyonetimi.ahievran.edu.tr/_Dosyalar/Genel/8bf368fe-87d8-49f6-af18-4aa29d3ad5b4-9f763441-54c9-4597-a1bb-3f5477ba3df9.pdf

http://www.amu.ac.in/dshowfacultydata.jsp?did=6&eid=605

http://www.amu.ac.in/dshowfacultydata.jsp?did=6&eid=601


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FOREWORDS

Dear Conference Participant, Welcome to the 2nd International Conference on Mathematical Development and Applications (ICOMAA-2019) we organized the second. The aim of our conferences is to bring together scientists and young researchers from all over the world and their work on the fields of mathematics and mathematics, to exchange ideas, to collaborate and to add new ideas to mathematics in a discussion environment. With this interaction, functional analysis, approach theory, differential equations and partial differential equations and the results of applications in the field of Mathematics Education are discussed with our valuable academics, and in mathematical developments both science and young researchers are opened. We expect the participation of many prominent experts from different countries who will present the state-of-the-art in real analysis, complex analysis, harmonic and non-harmonic analysis, operator theory and spectral analysis, applied analysis.

The conference brings together about 100 participants from 10 countries (Algeria, Azerbaijan, Canada, Czech Republic, Indonesia, Iran, Italy, Kuwait, Lebanon, Turkey) and 8 invited talks.

It is also an aim of the conference to encourage opportunities for collaboration and networking between senior

academics and graduate students to advance their new perspective. Additional emphasis on ICOMAA-2019 applies

to other areas of science, such as natural sciences, economics, computer science, and various engineering

sciences, as well as applications in related fields. The articles submitted to this conference will be addressed on the

conference web sites and in the journals listed below:

Azerbaijan Journal of Mathematics,

Sigma Journal of Engineering and Natural Sciences,

Istanbul Commerce University Journal of Sciences,

Transactions Issue Mathematics.

This booklet contains the titles and abstracts of almost all invited and contributed talks at the 2nd International Conference on Mathematical Advances and Applications. Only some abstracts were not available at the time of printing the booklet. They will be made available on the conference website http://icomaa2019.com/ when the organizers receive them.

We wish everyone a fruitful conference and pleasant memories in Istanbul, Turkey.

Assoc. Prof. Yusuf ZEREN

On Behalf of Organizing Committee Chairman


http://www.advancesindifferenceequations.com/

http://carpathian.ubm.ro/

http://www.ybook.co.jp/jnca.html

http://www.journalofinequalitiesandapplications.com/



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It was a big excitement moment when Assoc. Prof. Yusuf ZEREN discussed with me on the issue of "2nd

International Mathematical Developments and Applications Conference" (ICOMAA-2019) in Yıldız Technical

University, Istanbul. It is a great pleasure that this conference is going to take place now. As one of the organizers

of the conference, I am delighted with all the delegates, distinguished mathematicians, speakers and young

researchers in this international event. It is expected that delegates and participants will benefit from this conference

experience and the legacy of information dissemination will continue.

I wish all of you to have a nice and enjoyable participation in the conference.

Prof. Necip SIMSEK



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SCIENTIFIC COMMITTEE

Abdel-Aty, M., Egypt

Abdullayev, F., Turkey

Ahlatcioglu, M., Turkey

Akarsu, M., Turkey

Akbas, M., Turkey

Akin, L., Turkey

Aktosun, T., USA

Basarir, M., Turkey

Bilalov, B., Azerbaijan

Bouhamidi, A., France

Burenkov, V. I., U.K.

Celik, E., Turkey

Chalabi, A., France

Colak, R., Turkey

Cruz-Uribe, D., U.S.A.

Diening, L., Germany

Dogan, M., Turkey

Duman, O., Turkey

Duru, A., Turkey

Ekincioglu, I., Turkey

Ersoy, B. A., Turkey

Gogatishvili, A., Czech

Gok, O., Turkey

Guliyev, V. S., Azerbaijan

Guzel, N., Turkey

Huseynli, A., Azerbaijan

Isgenderoglu, M., Turkey

Jbilou, K., France

Kalantarov, V., Turkey

Kara, E. E., Turkey

Karakaya, V., Turkey

Kaya, D., Turkey

Klingler, B., France

Kokilashvili, V., Georgia

Kucuk, I., Turkey

Loeser, F., France

Mamedov, F., Azerbaijan

Mardanow, M. J., Azerbaijan

Monsurro, S., Italy

Mursaleen, M., India

Nuray, F., Turkey

Ocal, F., Turkey

Oleg, R., Russia

Ozdemir, A. S., Turkey

Ozdemir, M. E., Turkey

Palagacheva, L. S., Italy

Pascu, M., Romania

Phong, D. H., USA

Piskin, E., Turkey

Polat, H., Turkey

Samko, S., Portugal

Sari, M., Turkey

Savas, E., Turkey

Secer, A., Turkey

Serbetci, A., Turkey

Sevli, H., Turkey

Simsek, N., Turkey

Tabachnikov, S., USA

Tok, I., Turkey

Transirico, M., Italy

Ugur, T., Turkey

Wang, W., China

Zeren, Y., Turkey



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ORGANIZING

COMMITTEE

Yusuf ZEREN (Chairman)(Turkey)

Misir J. MARDANOV (Azerbaijan)

Necip SIMSEK (Turkey)

Lutfi AKIN (Turkey)

Murat AKARSU (Turkey)

Fatih SIRIN (Turkey)

LOCAL ORGANIZING

COMMITTEE

Erdoğan Mehmet Ozkan, Yildiz Technical University,

Turkey

Selmahan Selim, Yildiz Technical University, Turkey

Selim Yavuz, Yildiz Technical University, Turkey

Hulya Burhanzade, Yildiz Technical University, Turkey

Adem Cengiz Cevikel, Yildiz Technical University,

Turkey

Ozgur Yildirim, Yildiz Technical University, Turkey

Emirhan Hacioglu, Yildiz Technical University, Turkey

Ibrahim Murat Turhan, Yildiz Technical University,

Turkey

Melih Cinar, Yildiz Technical University, Turkey

Ibrahim Demir, Yildiz Technical University, Turkey

Mustafa Bayram Gucen, Yildiz Technical University,

Turkey

Murat Kirisci, Istanbul University, Turkey

Harun Baldemir, Cankiri Karatekin University, Turkey

Yunus Atalan, Aksaray University, Turkey

Cemil Karacam, Yildiz Technical University, Turkey

Kader Simsir, Yildiz Technical University, Turkey

Seyma Cetin, Yildiz Technical University, Turkey

Hande Uslu, Yildiz Technical University, Turkey

Elif Deniz, Yildiz Technical University, Turkey

Kubra Aksoy, Yildiz Technical University, Turkey

Arshed Adham Ahmad, Yildiz Technical University,

Turkey

Faruk Dusunceli, Mardin Artuklu University, Turkey

Ruken Celik, Istanbul Commerce University, Turkey

Zhamile Askerova, Istanbul Commerce University, Turkey

Faik Gursoy, Adiyaman University, Turkey

Kadri Dogan, Artvin Coruh University, Turkey

Suayip Toprakseven, Artvin Coruh University, Turkey

Muzeyyen Erturk, Adiyaman University, Turkey

Mustafa Gezek, Namik Kemal University, Turkey

Hasan Kurban, Siirt University, Turkey


http://avesis.yildiz.edu.tr/mozkan/

http://avesis.yildiz.edu.tr/mozkan/


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FOREWORDS..................................................................................................................................................................2

SCIENTIFIC COMMITTEE .................................................................................................................................................4

ORGANIZING COMMITTEE .............................................................................................................................................5

LOCAL ORGANIZING COMMITTEE ..................................................................................................................................5

INVITED TALKS

CHARACTERİZATİON OF EMBEDDİNGS OF SOBOLEV-TYPE SPACES İNTO GENERALİZED HOLDER SPACES..................... 12

AMIRAN GOGATISHVILI

ON THE RIEMANN PROBLEM IN WEIGHTED SMIRNOV CLASSES WITH POWER WEIGHT CLOSE TO 𝑳𝟏(𝑻) ................... 13

BILAL BILALOV

A NEW SEQUENCE SPACE AND (A, 𝝋)- STATISTICAL ALMOST CONVERGENCE OF ORDER 𝜶 ......................................... 14

EKREM SAVAS

ON HARNACK’S INEQUALITY FOR SOME CLASS OF NON-UNIFORMLY DEGENERATED ELLIPTIC EQUATIONS ................ 15

NARMIN AMANOVA AND FARMAN MAMEDOV

SURVEY ON GRADİENT ESTİMATES FOR NONLİNEAR ELLİPTİC EQUATİONS İN VARİOUS FUNCTİON SPACES ............... 16

LYOUBOMIRA SOFTOVA

ON THE FORMALİZATİON OF MATHEMATİCS İN HİGHER-ORDER LOGİC FOR ENGİNEERİNG APPLİCATİONS ................ 17

SOFIÈNE TAHAR

ON SOME PROPERTIES OF FUNCTIONS FROM GRAND-HARDY SPACE .......................................................................... 18

YUSUF ZEREN , MIGDAD ISMAILOV AND FATIH SIRIN

FİNİTE-PARAMETER FEEDBACK STABİLİZATİON OF ORİGİNAL BURGERS' EQUATİONS AND BURGERS' EQUATİON WİTH NONLOCAL NONLİNEARİTİES ....................................................................................................................................... 19

VARGA K. KALANTAROV

CONTRIBUTED TALKS

DETECTION OF ASYMTOTIC CRITICAL VALUES OF POLYNOMIAL MAPPING .................................................................. 20

SUSUMU TANABE , BAYRAM ALI ERSOY AND ABUZER GUNDUZ

ON (𝑷, 𝑸) −LUCAS POLYNOMIAL COEFFICIENTS FOR A NEW CLASS OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH 𝒒 −RUSCHEWEYH DIFFERENTIAL OPERATOR ............................................................................................................... 21

ARZU AKGUL

REPRESENTATION OF Z-TENSOR ON PSEUDO CONCIRCULAR RICCI SYMMETRIC MANIFOLD ....................................... 22

AYSE YAVUZ TASCI AND FUSUN OZEN ZENGIN

ON µ- STRONG CESARO SUMMABILITY AT INFINITY AND ITS APPLICATIONS TO THE FOURIER-STIELTJIES .................. 23

YUSUF ZEREN AND CEMIL KARACAM



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KOROVKIN TYPE APPROXIMATION BY POSITIVE LINEER OPERATOR IN SOME LEBESGUE SPACES .............................. 24

YUSUF ZEREN AND CEMIL KARACAM

ON SOME PROPERTIES OF GRAND LORENTZ SPACES ................................................................................................... 25

CIHAN UNAL AND ISMAIL AYDIN

THE CO-EXPRESSION MEASURES' EFFECT ON THE INTEGRATION OF PROTEOMIC AND GENE EXPRESSION DATA FOR GENE REGULATORY NETWORK INFERENCE METHODS ................................................................................................. 26

CIHAT ERDOGAN, ZEYNEB KURT AND BANU DIRI

SPATIAL CRITICAL POINTS OF THE SOLUTIONS OF A NONLINEAR HEAT EQUATION WITH DYNAMIC BOUNDARY CONDITIONS ................................................................................................................................................................ 27

DENIZ DEMIRCANLI AND MANSUR I. ISMAILOV

CUSTOMIZED SAMPLE EXAM REVIEWS: EFFECTS ON STUDENT PERFORMANCE IN MATHEMATICS ............................. 28

DIANA M. AUDI

GAUSSIAN BALANCING AND GAUSSIAN COBALANCING POLYNOMIALS ...................................................................... 29

MUSTAFA ASCI AND DILEK KAYACELIK

ON THE BITSADZE SAMARSKII TYPE NONLOCAL BOUNDARY VALUE PROBLEM WITH THE INTEGRAL CONDITION FOR AN ELLIPTIC EQUATION ............................................................................................................................................... 30

ELIF OZTURK

USING HOL4 FOR THE RELIABILITY VERIFICATION OF PARITY CHECKING CIRCUIT ........................................................ 31

ELIF DENIZ, KUBRA AKSOY, SOFIÈNE TAHAR AND YUSUF ZEREN

SOME QUESTIONS OF APPROXIMATION THEORY IN REARRANGEMENT INVARIANT BANACH FUNCTION SPACES ...... 32

ELIF DENIZ AND YUSUF ZEREN

TRANSLATION–FACTORABLE SURFACES IN 4-DIMENSIONAL EUCLIDEAN SPACE .......................................................... 33

E. AYDAN PAMUK AND BETUL BULCA

NONEXISTENCE OF GLOBAL SOLUTIONS FOR A CLASS OF HIGHER-ORDER WAVE EQUATION WITH VARIABLE EXPONENTS ................................................................................................................................................................. 34

ERHAN PISKIN

STABILITY OF AN ITERATIVE ALGORITHM .................................................................................................................... 35

FAIK GURSOY

ON SPEKTRAL PROPERTIES OF DISCONTINUOUS DIFFERENTIAL OPERATORS WITH SECOND ORDER ........................... 36

YUSUF ZEREN AND FATIH SIRIN

REVERSIBLE DNA CODES OVER A NON-CHAIN RING VIA SKEW CYCLIC CODES ............................................................. 37

FATMANUR GURSOY AND AYTEN OZKAN

AN EVALUATING OF MATHEMATICS EDUCATION PROGRAMS BASED ON STEM TRAINING APPLICATION FOR GIFTED AND TALENTED STUDENTS .......................................................................................................................................... 38

FILIZ SECKIN

A NOTE ON APPROXIMATING FINITE HILBERT TRANSFORM AND QUADRATURE FORMULA ........................................ 39

FUAT USTA

COMPLETE LIFT PROBLEMS OF PROJECTABLE LINEAR CONNECTION IN SEMI-TANGENT BUNDLE ................................ 40

FURKAN YILDIRIM AND MURAT POLAT



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ADAPTED FRAMES IN THE SEMI-TENSOR BUNDLE ....................................................................................................... 41

FURKAN YILDIRIM

INVESTIGATION OF THE SUBORBITAL GRAPHS ............................................................................................................ 42

MURAT BESENK AND GIZEM DEMIRBAS

A NOTE ON PRIMALITY TESTING: ALGORITHMS AND ANALYSES .................................................................................. 43

GOZDE SARIKAYA AND ENVER OZDEMIR

ON LIE GROUP ANALYSIS OF BOUNDARY VALUE PROBLEM WITH CAPUTO FRACTIONAL DERIVATIVE ......................... 44

GULİSTAN ISKENDEROGLU AND DOGAN KAYA

A STOCHASTIC APPROACH FOR THE NONLINEAR DUFFING OSCILLATOR WITH DAMPING TERM ................................. 45

HANDE USLU AND MURAT SARI

A CONVERGENCE RESULT FOR A THREE-STEP ITERATIVE ALGORITHM ........................................................................ 46

HARUN POLAT AND FAIK GURSOY

INVOLUTIONS IN ELLIPTIC BIQUATERNIONS ................................................................................................................ 47

HASAN ES AND MURAT BEKAR

INVOLUTIONS IN ELLIPTIC QUATERNIONS ................................................................................................................... 48

HASAN ES AND MURAT BEKAR

NEGATIVE COEFFICIENT OF STARLIKE FUNCTIONS OF ORDER 𝟏𝟐 ................................................................................ 49

HASAN SAHIN, ISMET YILDIZ AND UMRAN MENEK

ON THE CONVERSION OF CONVEX FUNCTIONS TO CERTAIN WITHIN THE UNIT DISK .................................................. 50

HASAN SAHIN, ISMET YILDIZ AND UMRAN MENEK

SIMPLE UNDIRECTED GRAPHS TOPOLOGY ................................................................................................................... 51

HATICE KUBRA SARI AND ABDULLAH KOPUZLU

A STUDY ON THE ROLE OF DRAMA IN LEARNING MATHEMATICS ................................................................................ 52

ILKNUR YILMAZ AND ADEM CEVIKEL

EXACT SOLUTIONS FOR GENERALIZED (3+1) SHALLOW WATER-LIKE (SWL) EQUATION................................................ 53

FARUK DUSUNCELI

A CHARACTERIZATION OF HOMOGENEOUS FRACTIONAL HARDY-TYPE INTEGRALS ON VARIABLE EXPONENT SPACES 54

LUTFI AKIN

NEW EXACT SOLUTIONS FOR ABLOWITZ-KAUP-NEWELL-SEGUR WAVE EQUATION VIA BERNOULLI SUB-EQUATION FUNCTION METHOD .................................................................................................................................................... 55

FARUK DUSUNCELI

STRONG CONVERGENCE RESULT FOR THE FASTER ITERATIVE SCHEME ........................................................................ 56

YUNUS ATALAN AND FAIK GURSOY

SOME PROPERTIES FOR HIGHER ORDER COMMUTATORS OF HARDY-TYPE INTEGRAL OPERATOR ON HERZ–MORREY SPACES WITH VARIABLE EXPONENT ............................................................................................................................ 57

YUSUF ZEREN AND LUTFI AKIN

SOME FIXED POINT THEOREMS WITH 𝒘-𝜶-DISTANCE METHOD .................................................................................. 58

FATMA POLAT AND GULCAN ATICI TURAN



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AMALGAM SPACES WITH VARIABLE EXPONENT .......................................................................................................... 59

ISMAIL AYDIN AND CIHAN UNAL

THE RATE OF CONVERGENCE OF TWO FIXED POINT ITERATIVE SCHEMES FOR CONTINUOUS FUNCTIONS ON CLOSED INTERVALS ................................................................................................................................................................... 60

KADRI DOGAN AND FAIK GURSOY

INTRODUCTION TO HOL THEOREM PROVING .............................................................................................................. 61

KUBRA AKSOY, SOFIÈNE TAHAR AND YUSUF ZEREN

WEAK TYPE ESTİMATES OF HARDY INTEGRAL OPERATORS ON MORREY SPACES WİTH VARİABLE EXPONENT LEBESGUE SPACES ........................................................................................................................................................................ 62

LUTFI AKIN

NECESSARY CONDITIONS FOR THE OPTİMAL CONTROL OF THE PLATES UNDER MOVİNG MASS ................................. 63

MELIH CINAR AND AYDIN SECER

A NUMERICAL APPROACH TO ACTIVE DAMPING OF BEAM-STRING SYSTEM ............................................................... 64

MELIH CINAR AND AYDIN SECER

PERTURBATION SOLUTIONS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS .............................................. 65

MELIKE KELES, SERDAL PAMUK

CYCLIC CODES OVER A SPECIAL NON-CHAIN RING WITH RESPECT TO THE HOMOGENEOUS WEIGHT .......................... 66

MERVE BULUT YILGOR, ELIF SEGAH OZTAS AND FATIH DEMIRKALE

ON WEAK BIHARMONIC GENERALIZED ROTATION SURFACE IN E4 ............................................................................... 67

MERVE HARMANLI, KADRI ARSLAN AND BETUL BULCA

SOME GEOMETRIC PROPERTIES OF EULER TOTIENT SEQUENCE SPACE ........................................................................ 68

MERVE ILKHAN AND EMRAH EVREN KARA

EULER TOTIENT SEQUENCE SPACES IN GENERALIZED ORLICZ SPACE ............................................................................ 69

MERVE ILKHAN AND EMRAH EVREN KARA

ON SOME SUBSPACE OF GRAND-LEBESGUE SPACE ...................................................................................................... 70

YUSUF ZEREN, MIGDAD ISMAILOV AND SELIM YAVUZ

ON SPECTRAL PROPERTIES OF SECOND ORDER DISCONTINUOUS DIFFERENTIAL OPERATOR IN 𝑳𝒑)⊕ ℂ .................... 71

YUSUF ZEREN, MIGDAD ISMAILOV AND FATIH SIRIN

INTERVAL ANALYSİS OF NATURAL FREQUENCY OF COMPOSİTE BEAM OF WHİCH MATERİAL HAVİNG LOCAL CURVATURE ................................................................................................................................................................. 72

MUHAMMED FURKAN SİMSEK, ZAFER KUTUG AND AYSE ERDOLEN

DEVELOPING A STEM MODULE WITH AN ENGINEERING DESIGN PROCESS .................................................................. 73

MURAT AKARSU

IN-SERVICE TEACHERS’ UNDERSTANDING OF GEOMETRIC REFLECTIONS: MOTION AND MAPPING VIEW ................... 74

MURAT AKARSU, SELIM YAVUZ, FATIH SIRIN

A BILINEAR HIROTA-KIMURA DISCRETIZATION OF THE MOTION OF A RIGID BODY IN AN IDEAL FLUID ....................... 75

ZERRIN OZCUBUKCU, MURAT TURHAN, SERPIL USLU AND OYA BAYKAL UNAL



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MATHEMATICAL BEHAVIOR OF SOLUTIONS OF P-LAPLACIAN EQUATION WITH LOGARITHMIC SOURCE TERM ........... 76

ERHAN PISKIN AND NAZLI IRKIL

MATHEMATICAL BEHAVIOR OF SOLUTIONS OF FOURTH-ORDER HYPERBOLIC EQUATION WITH LOGARITHMIC SOURCE TERM ........................................................................................................................................................................... 77

ERHAN PISKIN AND NAZLI IRKIL

SOLUTIONS OF SOME GENERALIZED PELL EQUATIONS WITH RECURRENCE RELATIONS .............................................. 78

NAZLIHAN ERTEN AND MURAT ALAN

HEALTH EFFICIENCY MEASUREMENT IN TURKEY BY USING DATA ENVELOPMENT ANALYSIS ....................................... 79

NEDIM ERTUGAY, ZULAL TUZUNER AND HASAN BAL

ON THE CONTROL OF THE SEVEN-MODE TRUNCATION SYSTEM OF THE 2-D NAVIER-SOKES EQUATIONS .................... 80

NEJIB SMAOUI, ALAA EL-KHADRI AND MOHAMED ZRIBI

ON GENERALIZATION SISTER CELINE’S POLYNOMIALS ................................................................................................. 81

NEJLA OZMEN

A NOTE ON SHIVELY’S PSEUDO-LAGUERRE POLYNOMIALS .......................................................................................... 82

NEJLA OZMEN

ANALYSIS OF SOME FEATURES OF DAILY TRANSPORTATION MOVEMENTS IN ISTANBUL BY SPATIAL STATISTICS ....... 83

NURAN KOSE CERCI AND IBRAHIM DEMIR

INTERVAL ANALYSİS OF NATURAL FREQUENCY OF COMPOSİTE BEAM OF WHİCH MATERİAL HAVİNG PERİODİCAL CURVİNGS .................................................................................................................................................................... 84

ORHAN SENYENER, ZAFER KUTUG AND AYSE ERDOLEN

LİE POİNT SYMMETRİES OF DİFFERENCE EQUATİON .................................................................................................... 85

OZGUR YILDIRIM AND SUMEYRA CAGLAK

SOME PASCAL SPACES OF DIFFERENCE SEQUENCES SPACES OF ORDER M ................................................................... 86

SAADETTIN AYDIN AND HARUN POLAT

COEFFICIENT BOUNDS FOR A SUBCLASS OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS INVOLVING HADAMARD PRODUCT AND DIFFERENTIAL OPERATOR.................................................................................................................... 87

F. MUGE SAKAR, S. MELIKE AYDOGAN AND SAHSENE ALTINKAYA

A STUDY ON BALANCE STATES, STEP COUNTS FOR STATE CHANGE AND ABSORPTIVE SITUATIONS IN STOCHASTIC PROCESSES .................................................................................................................................................................. 88

SERVET ES

A METHOD FOR CREATING MORTALITY TABLES IN THE ACTUARY. .............................................................................. 89

SERVET ES

MOTORCYCLE ACCIDENT MODEL PREDICTION BY APPROACHING GENERALIZED LINEAR MODEL ................................ 90

SOBRI ABUSINI

THE EXİSTENCE OF POSİTİVE SOLUTİONS AND A LYAPUNOV TYPE INEQUALİTY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTİONAL CAPUTO-FABRİZİO Dİ_ERENTİAL EQUATİONS .................................................................................. 91

SUAYIP TOPRAKSEVEN

A PADÉ-LEGENDRE RECONSTRUCTION FOR DIFFERENCE SOLUTIONS OF SHOCK BEHAVIOUR ...................................... 92

HUSEYIN TUNC, MURAT SARI, SUFII HAMAD MUSSA



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ON THE INCLUSIIN PROPERTIES OF COPSON-TYPE FUNCTION SPACES ......................................................................... 93

TUGCE UNVER YILDIZ

A VARIABLE EXPONENT BOUNDEDNESS OF THE STEKLOV OPERATOR ......................................................................... 94

YUSUF ZEREN, FARMAN MAMEDOV AND FATIH SIRIN

POSTER SESSION

IMPACT OF NON-LINEAR EFFECTS ON PROPAGATION ................................................................................................. 95

BOUTHEINA BOUTABIA-CHÉRAITIA AND HOURIA TRIKI

MATRICIAL SDE OF THE DERIVATIVE OF THE SOLUTION OF SDE IN THE NON LINEAR FRAMEWORK ............................ 96

HACÈNE BOUTABIA

VECTOR LATTICES OF WEAKLY COMPACT OPERATORS ON BANACH LATTICES............................................................. 97

SEMRA KIRIS AND OMER GOK

ON SPECTRAL PROPERTIES AND FUNDAMENTAL SOLUTIONS OF A DISCONTINUOUS ONE-POINT BOUNDARY VALUE PROBLEM..................................................................................................................................................................... 98

SEDA KIZILBUDAK CALISKAN, SUKRU OYNAR

INDEX .......................................................................................................................................................................... 99



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INVITED TALKS

Characterization of embeddings of Sobolev-type spaces into generalized Holder Spaces

Amiran Gogatishvili Institute of Mathemastics CAS, Prague, Czech Republic

[email protected]

Abstract

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a p-Lebesgue space, of a function f in

𝑊𝑘𝐿𝑝𝑛

𝑛+𝑘𝑝,𝑝+𝑊𝑘𝐿𝑝(Ω), where Ω is a domain with minimally smooth boundary and finite Lebesgue measure.This sharp

estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into

generalized Holder spaces defined by means of the k-modulus of smoothness. General results are illustrated with

examples. In particular, we obtain a generalization of the classical Jawerth embeddings.

References

1. A. Gogatishvili, J.S. Neves and B.Opic. Characterization of embeddings of Sobolev-type spaces into generalized Holder

spaces defined by Lp-modulus of smoothness, J. Funct. Anal. 276 (2019), no 2, 636 - 657.


mailto:[email protected]


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On the Riemann Problem in Weighted Smirnov Classes with Power Weight close to 𝑳𝟏(𝑻)

Bilal Bilalov

Department of Non-harmonic Analysis,

Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

[email protected]

Abstract

Weighted Smirnov classes with power weight in bounded and unbounded domains are defined in this work.

Homogeneous and nonhomogeneous Riemann problems with a measurable coefficient whose argument is a piecewise

continuous function are considered in these classes. In case of homogeneous problem, a sufficient condition on general

weight function is found which is satisfied by Muckenhoupt class weights, and the general solution of this problem is

constructed. In case of nonhomogeneous problem, a Muckenhoupt type condition is imposed on the power type weight

function and the orthogonality condition is found for the solvability of nonhomogeneous problem in weighted Smirnov

classes, and the formula for the index of the problem is derived. Some special cases with power type weight function

are also considered, and conditions on degeneration order are found.

Keywords: weighted Smirnov classes, Riemann problem, Muckenhoupt condition

References

1. B.T. Bilalov, Basis properties of some exponential, sine and cosine systems. Sibirski matem. Jurnal, 45(2)

(2004), 264-273 (in Russian).

2. B.T. Bilalov, Basis properties of power systems in pL . Sibirski matem. Jurnal, 47(1) (2006), 1-12 (in Russian).

3. B.T. Bilalov, On solution of the Kostyuchenko problem. Siberian Mathematical Journal, 53:3 (2012), 509-526.

4. T.I. Najafov, N.P. Nasibova, On the Noetherness of the Riemann problem in a generalized weighted Hardy

classes. Azerbaijan Journal of Mathematics, 5(2) (2015), 109-139.

5. B.T. Bilalov, T.B. Gasymov, A.A. Guliyeva, On solvability of Riemann boundary value problem in Morrey-

Hardy classes. Turk. J. of Math., 40(50) (2016), 1085-1101.

6. Z. Meshveliani, The Riemann-Hilbert problem in weighted Smirnov classes of analytic functions. Proc.

Razmadze Math. Inst., 137 (2005), 65-86.

7. S.R. Sadigova, A.E. Guliyeva, On the Solvability of Riemann–Hilbert Problem in the Weighted Smirnov

Classes. Analysis Mathematica, 44(4) (2018), 587–603




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A new sequence space and (A, 𝝋)- statistical almost convergence of order 𝜶

Ekrem SavasHata! Yer işareti tanımlanmamış.

Department of Mathematics, Uşak University, Uşak, Turkey

[email protected]

Abstract

In this paper we introduce and study some properties of the new sequence space of order 𝜶 which 𝑽𝝀𝜶((𝑨,𝝋)) − is defined

using almost convergence and the modulus function. Further, some connections between ((A, ))- strong almost

summability of sequences and 𝝀- strong almost convergence of order 𝜶 with respect to a modulus are studied.

Keywords: Modulus function, strong almost convergence of order, matrix transformations, new sequence spaces.

References

1- R. Colak, and C. A. Bektas, 𝜆-statistical convergence of order 𝜶, Acta Math. Scientia, 31B (3) (2011), 953-959.

2- J. Connor, On strong matrix summability with respect to a modulus and statistical convergent, Canad. Math. Bull.

32(2),(1989), 194-198.

3- E. Malkowsksy and E. Savaş, Some 𝜆 - sequence spaces defined by a modulus, Archivum Math. 36, (2000), 219-228.

4- Mursaleen, 𝜆-statistical convergence}, Math. Slovaca, 50 (2000), 111 - 115.

5- F. Nuray and E. Savas, Some new sequence spaces defined by a modulus funcion, Indian J. Pure. Appl. Math. 24(11),

(1993), 657-663.

6- E. Savaş and R. Savaş Some 𝜆 -sequence spaces defined by Orlicz functions, Indian J. Pure. Appl. Math. 34(12), (2003),

1673-1680.

7- E. Savaş, On some generalized sequence spaces defined by a modulus, Indian J. Pur. Appl. Math. 30(5), (1999), 459-464.




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On Harnack’s inequality for some class of non-uniformly degenerated elliptic equations

Narmin Amanova 1 and Farman Mamedov 2

1Baku State University, Azerbaijan

[email protected] 2”OilGasscienceresearchproject” Institute of SOCAR company, Azerbaijan

[email protected],

Abstract

The Krylov-Safonov theorem says solutions of non-divergence uniformly elliptic equations with rougf coefficients

are Holder contious. Its proof directly follows from the Harnack inequality of positive solutions. In this study, it has

been proposed the Harnack inequality for a class of second order non-uniformly degenerating elliptic equations of non-

divergent structure. The N.V. Krylov and M.V. Safonov’s method is applied in order to proov the main result of the

study. Before, such a result was known for the power type non-uniformly degenerating equations.

Keywords: Holder continuity, elliptic equations, the Harnack inequality, non-uniformly degenetation.

References

1. V.A. Kondrativ and E.M. Landis, Qualitative theory of linear differential equations in partial diferential eqautions, Itoqi nauki

techniki, ser. Mathematics, Nauka, v. 32, 99-212, 1988.

2. E.M. Landis, Second order equations of elliptic and parabolic type, "Nauka", Moscow, 1971 (in Russian); English transl.:

Amer. Math. Soc., Providence, RI, 1997.





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16

Survey on gradient estimates for nonlinear elliptic equations in various function spaces

Lyoubomira Softova

in collaboration with Sun-Sig Byun and Dian Palagachev

Department of Mathematics

University of Salerno, Italy

[email protected]

Abstract

This survey addresses the regularity problem for very general nonvariational elliptic equations of p-Laplacian

type. Let 1 < 𝑝 < ∞ be a fixed number and Ω a bounded domain in ℝ𝑛 with 𝑛 ≥ 2. We suppose

𝒇 = (𝑓1, … , 𝑓𝑛) ∈ 𝐿𝑝(Ω, ℝ𝑛)

is a given vector-valued function. The problem under consideration is

{div 𝒂(𝐷𝑢, 𝑥) = div(|𝒇|𝑝−2𝒇) 𝑖𝑛 Ω𝑢 = 0 𝑜𝑛 𝜕Ω

where

𝒂(𝜉, 𝑥) = (𝑎1(𝜉, 𝑥), … , 𝑎𝑛(𝜉, 𝑥)): ℝ𝑛 × ℝ𝑛 → ℝ𝑛

is a given 𝐶1-Caratheodory vector-valued function, that is, a is measurable in 𝑥 for all 𝜉 and derivable with respect to 𝜉 ≠

0 for almost all fixed 𝑥. We discuss an optimal Calderon-Zygmund theory of such a nonlinear elliptic equation in

divergence form in the setting of various function spaces including the Lebesgue spaces, Orlicz spaces, weighted Orlicz

spaces and generalized Morrey spaces.

Reference:

1. S.-S. Byun, Gradient estimates in Orlicz spaces for nonlinear elliptic equations with BMO nonlinearity in

nonsmooth domains, Forum Math. 23 (2011) (4), 693-711.

2. S.-S. Byun, D. Palagachev, L. Softova, Survey on gradient estimates for nonlinear elliptic equations in various

function spaces, Algebra i Analiz, 31 (2019) (2), 10-35.

3. S.-S. Byun, S. Ryu, Global weighted estimates for the gradient of solutions to nonlinear elliptic equations, Ann.

Inst. H. Poincare Anal. Non Lineaire, 30 (2013) (2), 291-313.

4. S.-S. Byun, L. Softova, Asymptotically regular operators in generalized Morrey spaces, arXiv:1904.10713.

5. S.-S. Byun, L. Wang, Nonlinear gradient estimates for elliptic equations of general type, Calc. Var. Part. Di. Equ.,

45 (2012) (3-4), 403-419.

6. L.A. Caffarelli, I. Peral, On 𝑊1,𝑝 estimates for elliptic equations in divergence form, Comm. Pure Appl. Math.,

51 (1998) (1), 1-21.




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17

On the Formalization of Mathematics in Higher-Order Logic for Engineering Applications

Sofiène Tahar

Department of Electrical & Computer Engineering

Concordia University, Canada

[email protected]

Abstract

The formalization of classical mathematics is gaining importance in many areas of engineering applications. In

particular, probabilistic analysis is a mathematical tool of fundamental importance to virtually all scientists and engineers

as they often have to deal with systems that exhibit random or unpredictable elements. Traditionally, computer simulation

techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle large-

scale problems due to their enormous computer processing time requirements. To overcome these limitations, we propose

to perform formal probabilistic and statistical analysis using higher-order logic theorem proving. We provide a framework

for the formalization of both discrete and continuous random variables and the ability to formally verify system's

probabilistic and statistical properties. The analysis carried out in this way is free from any approximation or precision

issues due to the mathematical nature of the models and the inherent soundness of the theorem proving approach. In order

to illustrate the practical effectiveness of the proposed framework, we present the probabilistic analysis of four examples

across four application areas: the Coupon Collector's problem (software), the Stop-and-Wait protocol

(telecommunications), the reliability of memory arrays (microelectronics), and floating-point error analysis (computer

hardware).

Reference

1- O. Hasan and S. Tahar: Formal Verification Methods; In: Encyclopedia of Information Science and Technology,

pp. 7162-7170, IGI Global Pub., 2015.

2- M. Elleuch, O. Hasan,S. Tahar and M. Abid:Formal Probabilistic Analysis of Detection Properties in Wireless

Sensor Networks; Formal Aspects of Computing, Springer, Vol. 27, No. 1, January 2015, pp. 79-102.

3- T. Mhamdi, O. Hasan, and S. Tahar. Formalization of Measure and Lebesgue Integration for Probabilistic

Analysis in HOL; ACM Transactions on Embedded Computing Systems, Vol. 12, No. 1, January 2013, pp. 13.1-

13.23.

4- O. Hasan and S. Tahar: Reasoning about Conditional Probabilities in a Higher-order-Logic Theorem Prover;

Journal of Applied Logic, Vol. 9, No. 1, March 2011, Elsevier, pp. 23-40.

5- O. Hasan, S. Tahar,N. Abassi: Formal Reliability Analysis using Theorem Proving, IEEE Transactions on

Computers, Vol. 59, No. 5, May 2010, pp. 579-592.




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On Some Properties of Functions from Grand-Hardy Space

Yusuf Zeren 1, Migdad Ismailov 2 and Fatih Sirin 3

1Department of Mathematics, Yildiz TechnicalUniversity,

[email protected] 2Baku State University,

Institute of Mathematics and Mechanics of the NAS of Azerbaijan,

[email protected] 3Istanbul Aydin University

[email protected]

Abstract

Grand Hardy class 𝐻𝑝)+ , 𝑝 > 1, is defined and some properties of functions belonging to this class are studied in this

work. Namely, the analogs of the Riesz theorems as well as the Cauchy’s formula for representation of function are

proved.

Keywords: grand Lebesgue space, grand Hardy class, Riesz theorem, Cauchy's formula

Reference:

1- B.T. Bilalov, Basis properties of some exponential, sine and cosine systems. Sibirski matem. Jurnal, 45(2) (2004),

264-273 (in Russian).

2- T.I. Najafov, N.P. Nasibova, On the Noetherness of the Riemann problem in a generalized weighted Hardy classes.

Azerbaijan Journal of Mathematics, 5(2) (2015), 109-139.






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19

Finite-parameter feedback stabilization of original Burgers' equations and Burgers' equation

with nonlocal nonlinearities

Varga K. Kalantarov

Department of Mathematics, Koc University, Istanbul

Abstract

The talk is devoted to the problem of stabilization of solutions to Burgers' original equations and Burgers' equation

with nonlocal nonlinearities es via finite-dimensional feedback controllers. We prove local and global stabilization with

an exponential rate of a concrete solution to original Burgers' equations and the Burgers' equation with nonlocal

nonlinearities, introducing a feedback control terms that employ finitely many Fourier modes.



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20

CONTRIBUTED TALKS

Detection of Asymtotic Critical Values of Polynomial Mapping

Susumu Tanabe 1, Bayram Ali Ersoy 2 and Abuzer Gunduz 3 1Department of Mathematics, Galatasaray University,

[email protected]

2Department of Mathematics, Yildiz Technical University,

[email protected] 3Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract

The bifurcation value set of a polynomial map 𝑓: ℂ𝑛 → ℂ is the smallest subset 𝐵(𝑓) ⊆ ℂ𝑛 such that 𝑓 is a locally

trivial fibration over ℂ𝑛 ∖ 𝐵(𝑓). 𝐵(𝑓) is described as 𝐵(𝑓) = 𝑓(𝑆𝑖𝑛𝑔 𝑓) ∪ 𝐵∞(𝑓) where 𝑓(𝑆𝑖𝑛𝑔 𝑓) is the the cirital values

of 𝑓 associated to critical points within a bounded domain and 𝐵∞(𝑓) is the set of critical values of 𝑓 at infinity. To detect

𝐵∞(𝑓), one generally constructs larger sets which is easier to study. This is Asymptotic Critical Value Set and is defined

as

𝐾∞(𝑓) = {𝑡 ∈ ℂ: 𝑡ℎ𝑒𝑟𝑒 𝑒𝑥𝑖𝑠𝑡 𝑎 𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒 {𝑥𝑙} → ∞ 𝑠. 𝑡. ∥ 𝑥𝑙 ∥∥ 𝑔𝑟𝑎𝑑 𝑓(𝑥𝑙) ∥→ 0} We study detection of Asymptotic Critical Values of poynomial mapping by athe id of Toric Geometry tools.

Keywords: Büfurcation values, Asymptotical Citical Values, Locally Trivial Fibration, Toric Geometry

References:

1. Dias, L. R. G., Tanabé, S., & Tibăr, M. (2017). Toward effective detection of the bifurcation locus of real polynomial

maps. Foundations of Computational Mathematics, 17(3), 837-849.

2. Jelonek, Z., & Kurdyka, K. (2003). On asymptotic critical values of a complex polynomial. Journal Fur Die Reine Und

Angewandte Mathematik, 1-12.

3. Némethi, A., & Zaharia, A. (1990). On the bifurcation set of a polynomial function and Newton boundary. Publications of the

Research Institute for Mathematical Sciences, 26(4), 681-689.

4. Zaharia, A. (1996). On the bifurcation set of a polynomial function and Newton boundary, II. Kodai Mathematical

Journal, 19(2), 218-233.






Istanbul / TURKEY


21

On (𝑷,𝑸) −Lucas Polynomial coefficients for a New Class of Bi-Univalent Functions

Associated with 𝒒 −Ruscheweyh Differential Operator

Arzu Akgul

1Department of Mathematics, Kocaeli University,

[email protected]

Abstract

In this study, we aim at introducing a new class of bi-univalent functions by using the (p, q)-Lucas polynomials and

𝑞 −Ruscheweyh differential operator. Also, we derive coefficient inequalities for this new function class.

Keywords: (p,q)-Lucas polynomials, q-derivative, Coefficient bounds, Bi-Univalent functions.

References:

1. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA 259 (1983).

2. Filipponi, P., Horadam, A.F.: Derivative sequences of Fibonacci and Lucas polynomials. In: Bergum, G.E., Philippou, A.N.,

Horadam, A.F. (eds.) Applications of Fibonacci Numbers, vol. 4, pp. 99.108. Kluwer Academic Publishers, Dordrecht (1991)

3. Filipponi, P., Horadam, A.F., (1993), Second derivative sequences of Fibonacci and Lucas polynomials. Fibonacci Q. 31,

194.204

4. Lee, G.Y., Ascı, M. (2012), Some properties of the (p, q)-Fibonacci and (p, q)-Lucas polynomials. J. Appl. Math. 2012, 1.18

(Article ID 264842)

5. Lewin, M. (1967), On a coe¢ cient problem for bi-univalent functions. Proc.Am.Math. Soc. 18, 63.68

6. F. H. Jackson. (1908), On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46 253–281. 1

7. D. O. Jackson, T. Fukuda, O. Dunn, E. Majors. (1910), On q-definite integrals, Quart. J. Pure Appl. Math., 41 193–203. 1

8. S. Ruscheweyh. (1975), New criteria for univalent functions, Proc. Amer. Math. Soc., 49 109–115. 1.

9. T. M. Seoudy, M. K. Aouf. (2016), Coefficient estimates of new classes of q-starlike and q-convex functions of complex

order, J. Math. Inequal., 10, 135–145. 1.

H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010),

1188–1192. 1




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22

Representation of Z-Tensor on Pseudo Concircular Ricci Symmetric Manifold

Ayse Yavuz Tasci 1 and Fusun Ozen Zengin 2

1Istanbul Technical University,

[email protected] 2Department of Mathematics, Istanbul Technical University

[email protected]

Abstract

The object of the present paper is to study Z-tensor on a pseudo concircular Ricci symmetric manifold. Section 2

and 3 deal with the definitions and the properties of pseudo Ricci symmetric manifolds and Z-tensor, respectively. In

section 3, considering the Z-tensor on a pseudo concircular Ricci symmetric manifold, we prove theorems and we find

some properties about these manifolds.

Keywords: Z-tensor, concircular tensor, Ricci symmetric tensor.

Reference:

1. U. C. De and G. C. Ghosh, On weakly concircular Ricci symmetric manifolds, South East Asian J. Math. and

Math. Sci 3(2) (2005) 9-15.

2. A. L. Besse, Einstein Manifolds Springer (1987).

3. U. C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor (N.S) 56 (1995) 312-317.

4. R. S. Mishra, Structures on a differentiable manifold and their applications, Chandroma Prakoshan, Allahabad

(1984).

5. A. Derdzinski and C.L. Shen, Codazzi tensor fields, curvature and Pontryagin forms, Proc. Lond. Math. Soc. 47

(1983) 15-26.





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23

On µ- strong Cesaro summability at infinity and its applications to the Fourier-Stieltjies

Yusuf Zeren 1 and Cemil Karacam 2


[email protected] 2Yildiz Technical University [email protected]

Abstract

The concept of µ- strong Cesaro summability at infinity for alocally integrable function is introduced in this

work.The concept of µ-statistical convergence at infinity is also considered and the relationship between these two

concepts is established.The concept of µ[p]-strong convergence at infinity point, generated by the measure µ(.) is also

considered.similiar results are obtained in this case too.This approach is applied to study of convergence of Fourier-

Stieltjies transform.

Keywords: µ -statistical convergence, µ-strong Cesaro summability, Fourier-Stieltjies transform.

References:

1. Schoenberg I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly

66(1959), 361-375. MR0104946.

2. Macaj.M.Salat..T.Statistical.convergence,of.subsquences.of.given.sequence,Math.Bohem.126(2001). No.1. 191-

208sequence,Math.Bohem.126(2001). No.1. 191-208

3. Bilalov B.T ..Sadigova S.R On µ- statistical convergence,Proceeding of the American Mathematical

Society,Volume 143,Number 9, September 2015, Pages 3869-3878V. S.,

4. Bilalov B.T ..Sadigova S.R., Cemil Karacam, µ- statistical convergence and the space of functions µ- stat

continous on the segment.(submitted)





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24

Korovkin type Approximation by positive lineer operator in some Lebesgue Spaces

Yusuf Zeren 1 and Cemil Karacam 2


[email protected] 2Yildiz Technical University

[email protected]

Abstract

The concept of Korovkin type Approximation in some Lebesgue spaces introduced in this work.The concept of

convergence of Positive Linear operators is considered in 𝐿𝑃[𝑎, 𝑏] , 𝐺�̆�[𝑎,𝑏] 𝑎𝑛𝑑 𝐿�̆�[𝑎,𝑏] The concept of statistical

convergence considered.similiar results are obtained in this case too.

Keywords: Korovkin type Approximation, convergence and statistical convergence, Some Lebesgue Spaces,

References:

1. N.I Mahmudov, Korovkin -type theorems and aplications. Cent.Eur. J.Math.,7(2) (2009) 348-356

2. Francesco Altomore ,Korovkin-type Theorems and Approximation by Positive Linear Operators (2010) 108-109

3. Rene- Erlin-Castillo ,Humberto -Rafeiro, An İntroductory Course in Lebesgue Spaces (2016) 300-302





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25

On Some Properties of Grand Lorentz Spaces

Cihan Unal 1 and Ismail Aydin 2

1Department of Mathematics, Sinop University,

[email protected] 2Department of Mathematics, Sinop University

[email protected]

Abstract

In this work, we consider grand Lorentz spaces 𝐿𝑝,𝑞)(𝑋, 𝜇) and 𝛬𝑝),𝜔 with finite measure. Also, we give the

relationship between these spaces. Moreover, under some conditions on the weight function and the exponents, we study

some inclusion properties for these spaces.

Keywords: Grand Lorentz spaces, Inclusion, Approximate identity.

References:

1. M. Carro, L. Pick, J. Soria, V. D. Stepanov, On embeddings between classical Lorentz spaces. Math. Inequal. Appl. 4(3),

(2001), 397--428.

2. D. V. Cruz-Uribe, A. Fiorenza, Approximate identities in variable 𝐿𝑝 spaces. Math. Nach. 280, (2007), 256--270.

3. A. T. Gurkanli, On the inclusion of some Lorentz spaces. J. Math. Kyoto Univ., 44-2, (2004), 441--450.

4. P. Jain, S. Kumari, On grand Lorentz spaces and maximal operator. Georgian Math. J. 19, (2012), 235--246.

5. G. G. Lorentz, Some new functional spaces. Ann. of Math., 51(2), (1950), 37--55.





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26

The Co-expression measures' Effect on the Integration of Proteomic and Gene Expression Data

for Gene Regulatory Network Inference Methods

Cihat Erdogan 1, Zeyneb Kurt 2 and Banu Diri 3

1Department of Computer Technologies, Isparta University of Applied Sciences,

[email protected] 2, 3 Yildiz Technical University

[email protected], [email protected]

Abstract

The influences of various co-expression measures on the integration of different biological data types were

examined in this work. These measures have a significant effect on methods inferring gene regulatory or protein-protein

interaction networks. Gene expression and proteomic data of lung cancer leveraged in this study were taken from The

Cancer Genome Atlas (TCGA) and The Cancer Proteome Atlas (TCPA). A comprehensive comparison was conducted

between nine common co-expression measures that are based on either correlation or mutual information (MI) score. The

disease-gene association integration platform (DisGeNET), the Molecular Signature Database (MSigDB), and Pathway

Commons (PC) were used for measuring the performance of the co-expression measures. The MI-based co-expression

measures outperformed the Spearman or Pearson correlation approaches, which are the only available ones in the weighted

correlation network analysis (WGCNA) procedure, in estimating gene-gene or protein-protein networks. The integration

of Proteomics and Gene Expression Data was performed using networks formed by estimators with higher performance.

The MI-based shrink estimator had the highest precision score of 0.25, while Spearman and Pearson had scores of only

0.15, 0.17, respectively. Biologically meaningful modules and hub genes are given for the investigations of researchers and

biologists. For instance, as a result of integrating multi-omics data and using shrink estimator, EIF4G1 was revealed as one

of the hub genes identified in our subnetworks. DisGeNET has shown that EIF4G1 was found to be associated with lung

cancer in multiple studies, highlighting the strengths of our findings.

Keywords: Co-expression measures, network inference, omics data integration, cancer.

References:

1. Langfelder, P. ve Horvath, S., (2008). WGCNA: an R package for weighted correlation network analysis, BMC

Bioinformatics, 9: 559.

2. Li, J., Lu, Y., Akbani, R., Ju, Z., Roebuck, P.L., Liu, W., Yang, J.Y., Broom, B.M., Verhaak, R.G. ve Kane, D.W., (2013).

TCPA: a resource for cancer functional proteomics data, Nature Methods, 10: 1046

3. Altay, G., Kurt, Z., Altay, N. ve Aydin, N., (2017). DepEst: an R package of important dependency estimators for gene network

inference algorithms, BioRxiv, 3: 102871.

Erdoğan, C., Kurt, Z. ve Diri, B., (2017). Estimation of the proteomic cancer co-expression sub networks by using association

estimators, PLoS One, 12: e0188016.




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27

Spatial critical points of the solutions of a nonlinear heat equation with dynamic boundary

conditions

Deniz Demircanli 1 and Mansur I. Ismailov 2

1,2Gebze Technical University, Department of Mathematics,

41400 Gebze – Kocaeli, Turkey

[email protected]

Abstract In this work, the variation in time of the number of spatial critical points of the positive solution for a nonlinear

parabolic type problem with the dinamic boundary conditions is examined. The availability of the positive solution of

this problem is shown by applying the maximum-minimum principle and monotonicity of spatial critical points is shown

by applying Newton polygons method combined by Taylor series expansion. It is proved that the number of spatial

critical points has not increased in time in the case of simplicity of critical points.

Reference:

1- Turyn L., (1989), “Spatial critical points of solutions of a one-dimensional nonlinear parabolic problem”, Proc.

Amer. Math. Soc., 106 (4), 1003-1009.

2- Chow S. N., Hale J. K., (1982), “Methods of bifurcation theory”, Springer-Verlag, 1st Edition, New York.

3- Vainberg M. M., Trenogin V. A., (1962),“ The methods of Lyapunov and Schmidt in the theory of non-linear

equations and their further development”, Russian Math. Surveys, 17 (2),1-60.

4- Friedman A., (1958), “On the regularity of the solutions of nonlinear eliptic and parabolic systems of partial

differential equations”, J. Math. Mech., 7 (1), 43-59

5- Vladimirov V.S., (1983), “Equations of mathematical physics”, Pure and Applied Mathematics, 2nd Edition,

Moscow




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28

Customized Sample Exam Reviews: Effects on Student Performance in Mathematics

Diana M. Audi Faculty of Arts and Sciences, Mathematics Department

American University of Sharjah

[email protected]

Abstract

Having technology in higher education is dramatically developing and continuously presenting a

challenge to educators and institutions to provide an adequate level of innovation in technology to create an

interactive environment suitable for a digital native generation. It has been observed that the technological

advancement of Lecture Capture has a positive impact on student learning and satisfaction within higher

education institutions. This paper focuses on a recent study at the American University of Sharjah, Mathematics

Department of integrating the use of video review lectures based on online sample exams feedback highlighting

the adoption of customized video lecture capture focused on student weakness. The objectives of the evaluation

of introducing this new teaching methodology are to examine and assess students’ experiences in doing pre-

exam online sample exams followed by focused review sessions. Changes in the preparation and delivery of

lectures using the proposed methodologies will help determine whether they could become a common teaching

practice replacing the traditional ways of delivering video lectures and normal face-face lectures especially in

Mathematics.

Keywords: Lecture Capture, interactive lecture capturing, teaching and learning technology, innovative learning

technology

References:

1. M. Fredette, “6 Innovative Uses of Lecture Capture -,” Campus Technology, 20-Nov-2013. [Online]. Available:

https://campustechnology.com/articles/2013/11/20/6-innovative-uses-of-lecture-capture.aspx. [Accessed: 22-Jul-2016].

2. J. Kennedy, “5 Features a Good Lecture Capture System Needs to Deliver Content to Students.” [Online]. Available:

http://www.higheredtechdecisions.com/article/5_features_a_good_lecture_capture_system_needs_to_deliver_content_to_stu

den. [Accessed: 22-Jul-2018].

3. “5 Criteria to Consider When Selecting a Lecture Capture System,” Panopto Video Platform, 15-Jul-2014. [Online].

Available: https://www.panopto.com/blog/5-criteria-to-consider-when-selecting-a-lecture-capture-system/. [Accessed: 22-

Jul-2018].

4. “5 innovative ways to use lecture capture technology,” University Business Magazine. [Online]. Available:

https://www.universitybusiness.com/article/5-innovative-ways-use-lecture-capture-technology. [Accessed: 22-Jul-2016].

5. “Videoing lectures ‘has no impact’ on attendance, says study,” Times Higher Education (THE), 24-Sep-2015. [Online].

Available: https://www.timeshighereducation.com/news/videoing-lectures-has-no-impact-attendance-says-study. [Accessed:

22-Jul-2018].




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29

Gaussian Balancing and Gaussian Cobalancing Polynomials

Mustafa Asci 1 and Dilek Kayacelik 2

1,2Department of Mathematics, Pamukkale University,

[email protected]

[email protected]

Abstract

In this paper, we define and study the lucas balancing polynomials, cobalancing polynomials and Gaussian

balancing polynomials, Gaussian cobalancing polynomials with boundary conditions. We identify and prove Binet

formulas, matrix formulas and partial derivatives of these polynomials.

Keywords: Balancing numbers, Cobalancing numbers, balancing polynomials, Cobalancing polynomials.

References:

1. Asci M., Gurel E., "Bivariate Gaussian Fibonacci and Lucas polynomials", Ars Comb., 109(2013): 461-472.

2. Asci M., Gurel E.,"Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers", Ars Comb., 111(2013): 53-63.

3. Asci M., Gurel E., "Gaussian Fibonacci and Gaussian Lucas p-numbers", Ars Comb., 132(2017): 389-402.

4. A. Behera and G. K. Panda, "On the square roots of triangular numbers," Fibonacci Quart., 37 (1999), 98-105.

5. P.K.Ray, "Balancing polynomials and their derivatives" Ukrainian Mathematical Journal, 69 (2017), 646-663.

6. Horadam, A. F., "A Generalized Fibonacci sequence." American Math. Monthly, 68(1961): 455-459.

7. Jordan, J. H., "Gaussian Fibonacci and Lucas numbers". Fibonacci Quart., 3(1965) 315-318.

8. Kovacs, T., Liptai, K., Olajos, P., "On (a,b)-balancing numbers", Publ. Math. Debrecen, 77(2010), 485-498.

Panda, G. K., Ray, P. K., "Cobalancing numbers and cobalancers", Int. J. Math. Sci., 8(2005): 1189-1200.





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30

On the Bitsadze Samarskii Type Nonlocal Boundary Value Problem with the Integral

Condition for an Elliptic Equation

Elif Ozturk 1 1Department of Mathematics, Uludag University,

[email protected]

Abstract

Bitsadze Samarskii type nonlocal boundary value problem with the integral condition for an abstract elliptic

differential equation in a Hilbert space is studied. Theorem on well-posedness of this problem in Hölder spaces with a

weight is established. The nonlocal boundary value problem for multidimensional elliptic equations with the Dirichlet

condition is considered. The first order of accuracy difference scheme for the approximate solution of the Bitsadze

Samarskii type nonlocal boundary value problem is investigated. Theorem on well-posedness of this difference scheme in

difference analogue of Hölder space with a weight established.

Keywords: Elliptic equation, Well-posedness, Difference scheme, Stability.

References:

1. A.V. Bitsadze and A.A. Samarskii, Some elementary generalizations of linear elliptic boundary value problems, Doklady

Akademii Nauk SSSR 18 (1969) 739-740.

2. A.L. Skubachevskii, Elliptic functional differential equations and applications, Operator Theory: Advances and Applications

91 (1997) 1-209.

3. A. Ashyralyev and P.E. Sobolevskii, New difference schemes for partial differential equations, Operator Theory: Advances

and Applications 148 (2004) 1-311.

4. Ashyralyev A., Ozturk E. On Bitsadze-Samarskii type nonlocal boundary value problems for elliptic differential and difference

equations:Well-posedness. Apply Mathematics and Computation. Vol. 219, No. 3 (2012) 1093-1107.

Sapagovas M.P. A difference method of increased order of accuracy for the Poisson equation with nonlocal conditions.

Differentsial’nye Uravneniya. Vol. 44, No. 7 (2008) 988-998.




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Using HOL4 for the Reliability Verification of Parity Checking Circuit

Elif Deniz 1, Kubra Aksoy 2, Sofiène Tahar 3 and Yusuf Zeren 4

1Department of Mathematics, Yildiz Technical University, Turkey

[email protected] 2Department of Mathematics, Yildiz Technical University, Turkey

[email protected] 3Department of Electrical & Computer Engineering, Concordia University, Canada

[email protected] 4Department of Mathematics, Yildiz Technical University, Turkey

[email protected]

Abstract

A parity check is the process that ensures accurate data transmission between nodes during communication. In this paper,

we present the modelling and formal verification of parity checking circuit using Higher-Order Logic theorem proving.

We use the HOL4 theorem prover to mathematically describe the parity checking specification as well as mathematical

model of the circuit implementation. The formal verification of reliability shows that the circuit implementation satisfies

the parity checking specification for all inputs and outputs.

Keywords: Parity Checking, Formal Verification, Reliability, Higher-order Logic, Theorem Proving, HOL4

References:

[1] T.F. Melham. Higher Order Logic and Hardware Verification, Cambridge University Press,1993

[2] D. Burlyaev. Design, Optimization and Formal Verification of Circuit Fault-Tolerance Techniques, Université

Grenoble Alpes, France, 2015.

[3] V. Stavridou. Formal Methods in Circuit Design, Cambridge University Press, 1993.

[4] R.E. Ziemer and W.H. Tranter. Principles of Communication: Systems, Modulation, and Noise, Wiley, 2001.





mailto:r@


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32

Some Questions of Approximation Theory in Rearrangement Invariant Banach Function

Spaces

Elif Deniz 1 and Yusuf Zeren 2

1Department of Mathematics, Yildiz Technical University, Turkey

elifdeniz9592@gmailcom 2Department of Mathematics, Yildiz Technical University, Turkey

[email protected]

Abstract

Banach function spaces are banach spaces of measurable function in which the norm is related to the underlying measure

in an appropriate way. We consider the subspaces of banach function spaces in which the set of infinite differential

functions is dense. We present Korovkin type operator and some conditions of its accuracy and also statistical version of

this theorems in considered such subspaces.

Keywords: Rearrangement Banach Function Spaces, Korovkin Type Theorems, Statistical Convergence

References:

[1] C. Bennet, R. Sharpley, “Interpolation of Operators”, Academic Press, INC. Orlando, Florida,1988.

[2] F. Altomare,“Korovkin-type Theorems and Approximation by Positive Linear Operators”, Surveys in Approximation

Theory, Surveys in Approximation Theory, 5(13).

[3] F. Altomare, M. Campiti. “Korovkin-type Approximation Theory and its Applications”, de Gruyter Studies in

Mathematics, 17, Walter de Gruyter & Co., Berlin,




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33

Translation–Factorable Surfaces in 4-Dimensional Euclidean Space

E. Aydan Pamuk 1 and Betul Bulca 2

1Department of Mathematics, Institute of Natural and Applied Science, Bursa Uludağ University,

[email protected] 21Department of Mathematics, Arts and Science Faculty, Bursa Uludağ University

[email protected]

Abstract

In this study we consider translation-factorable (TF-type) surfaces in Euclidean 4-space E⁴. We have calculated

the Gaussian, mean and nornal curvature of the TF-type surfaces. Further, we give some sufficient conditons to become a

flat for these surfaces. Finally we give some examples of flat TF-type surfaces and plot the projection of the graphics into

the Euclidean 3-space.

Keywords: Translation surface, factorable surface, Gaussian curvature, mean curvature.

References:

1. K. Arslan, B. Bayram, B. Bulca and G. Öztürk, On Translation Surfaces in 4-dimensional Euclidean Space, Acta Comm. Univ.

Tartuensis Math. 20(2) (2016) 123–133.

2. S. Büyükkütük and G. Öztürk, A Characterization of Factorable Surfaces in Euclidean 4-Space E4, Koc. J. Sci. Eng. 1(1)

(2018) 15-20.

3. B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, (1973).

4. S. A. Difi, H. Ali and H. Zoubir, Translation-Factorable Surfaces in the 3-dimensional Euclidean and Lorentzian Spaces

Satisfying iii rr , EJMAA, 6(2) (2018) 227-236.





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34

Nonexistence of global solutions for a class of higher-order wave equation with variable

exponents

Erhan Piskin 1 1Department of Mathematics, Dicle University

[email protected]

Abstract

In this paper, we consider a class of nonlinear higher-order wave equation with variable exponents in a bounded domain Ω⊂Rⁿ. We prove a finite time blow up result for the solutions with negative initial energy. This improves earlier results in the literature [1, 2].

Keywords: Global nonexistence, wave equation, variable exponents.

References:

1. W. Chen, Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal. 70 (2009) 3203-

3208.

2. E. Pişkin, Sobolev Spaces, Seçkin Publishing, 2017. (in Turkish) 3. J. Zhou, X. Wang, X. Song, C. Mu, Global existence and blow up of solutions for a class of nonlinear higher-

order wave equations, Z. Angew. Math. Phys., 63(3) (2012) 461-473.




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35

Stability of an Iterative Algorithm

Faik Gursoy 1Department of Mathematics, Adıyaman University

[email protected]

Abstract

We prove that iterative algorithm (1.7) of [1] is weak 𝒘𝟐 −stable w.r.t an operator 𝑻 in the class of weak contraction

mappings.

Keywords: Fixed Point, Convergence, Iterative algorithm.

References:

1- Karakaya, V., Atalan, Y., Doğan, K. and El Houda Bouzara, N. Some fixed point results for a new three steps iteration

process in Banach spaces, Fixed Point Theory 18, 625-640 (2017).




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36

On Spektral Properties of Discontinuous Differential Operators With Second Order

Yusuf Zeren 1 and Fatih Sirin 2 1Department of Mathematics, Yildiz Technical University,

[email protected] 2Department of Computer Programming, Istanbul Aydin University

[email protected]

Abstract

In this work, we consider spectral problem for a second order discontinuous differential operator with spectral

parameter in the boundary condition in Grand Lebesgue Spaces. We study on a method for establishing the basicity of

eigenfunctions of this problem.

Keywords: Spectral problem, eigenfucntions, basicsity, grand lebesgue space.

References:

1. OGLU, Bilalov Bilal Telman; GASYMOV, Tel'man Benser oglu. On basicity of eigenfunctions of second order discontinuous

differential operator. Уфимский математический журнал, 2017, 9.1.

2. Gasymov, Telman B., and Shakhrizad J. Mammadova. "On convergence of spectral expansions for one discontinuous problem

with spectral parameter in the boundary condition." Trans. NAS Azerb 26.4 (2006): 103-116.

3. A.N. Tikhonov, A.A. Samarskii. Equations of mathematical physics. Izd. Mosc. univ., Moscow (1999). [Int. Ser. Monog. Pure

Appl. Mathe. 39, Pregamon Press, Oxford (1963)].

4. F.V. Atkinson. Discrete and continuous boundary problems. Mir, Moscow (1968). (in Russian).





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37

Reversible DNA Codes over a Non-chain Ring via Skew Cyclic Codes

Fatmanur Gursoy 1 and Ayten Ozkan 2

1,2Department of Mathematics, Yildiz Technical University, Turkey

[email protected]

[email protected]

Abstract

The idea of using DNA strings as a computational tool has started with the study of Adleman in 1994. He solved

the Hamiltonian path problem by DNA strings. Then, many researchers focus on associating DNA codes with different

mathematical structures. In this study, we define skew cyclic codes over 2 2 2

16[ , , ] , ,R F u v w u u v v w w ,

which is a non-chain ring. We obtain reversible DNA codes from skew cyclic codes over R by defining a special Gray

map.

Keywords: DNA codes, Reversible codes, Linear codes, Skew cyclic codes, Skew polynomial rings

References:

1. Adleman, L.M., (1994). “Molecular Computation of Solutions to Combinatorial Problems”, Science, 266: 1021-1024.

2. Öztaş, E.S. ve Şiap, İ., (2013). “Lifted Polynomials Over 16F and Their Applications to DNA Codes”, Filomat, 27(3): 459–

466.

3. Boucher, D., Geiselmann, W. ve Ulmer, F., (2007). “Skew Cyclic Codes”, Applicable Algebra in Engineering, Communication

and Computing, 18(4):379-389.

4. Abualrub, T., Ghrayeb, A. ve Nian Zeng, X., (2006). “Construction of Cyclic Codes Over GF(4) for DNA Computing”,

Journal of the Franklin Institute, 343: 448-457.

5. Yıldız, B. ve Şiap, İ., (2012). “Cyclic Codes Over 4

2[ ] / ( 1)F u u and Applications to DNA Codes”, Computers &

Mathematics with Applications, 63: 1169-1176.

6. Gürsoy, F., Öztaş, E. S. ve Şiap, İ., (2017). “Reversible DNA codes over 16 16 16 16F uF vF uvF ”, Advances in

Mathematics of Communications, 11(2):307–312.





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38

An Evaluating of Mathematics Education Programs Based on Stem Training Application for

Gifted and Talented Students

Filiz Seckin 1Department of Math, Bahcelievler ITO Bilim ve Sanat Merkezi

[email protected]

Abstract

Gifted and talented children means whose potential is distinctly above average and show high performance

capability in different areas. Such as evidence in specific academic fields, leadership capacity ,creativity ,artistic,

intellectual.There are different main issues for gifted education and talent development.Such as different levels of math

giftedness , need to understand unique needs of mathematicly, the learning characteristic and identify their preferences

regarding learning. As known gifted children need special education. The education that is needed by the gifted children

in our country is currently being carried out by the Science and Art Centers in Turkey. Admission to the entrance exam is

not individual, but the students are recommended by their teachers in primary school. Students firstly take tablet test, then

take exams in three categories of general talent, music talent and art talent.Finally students who pass these stages are

beginning to study outside school hours at Science and Art Centers. It is aimed for gifted and talented students to become

aware of their own potentials, specialize in their developments and skills.

This study includes activities and their evaluations used in the integration of STEM trainings into the curriculum within

the scope of curriculum enrichment and differentiation in curricula applied to gifted students during the mathematics

education given at the Science and Art Center. As a result of this study, positive feedback was obtained from the talented

students in terms of the acquisition of upper gains, motivation against the course and motivation against the course. Some

STEM activities are described in detail.

Keywords: STEM, Gifted and Talented Students, Science and Art Center, Mathematic Education Programs

References:

[1] David, H.(1997B).Mathematical Giftedness.Talpiot College Yearbook, T, 147-169.

[2]Lappan, G. March 1999. “Mathematics for All’ Must Include High-Ability and Highly Motivated Students.”NCTM News

Bulletin 35(8):3.(Available online at http://www.nctm.org/news- bulletin/1999/03/1999-03. president.html)

[3] Haury, D L. (1999). Mathematics Education for Gifted and Talented Children, V 6 Issue 2, 48-50

Lappan, G. March 1999. “Mathematics for All’ Must Include High-Ability and Highly Motivated Students.” NCTM News Bulletin 35

(8): 3. (Available online at http://www.nctm.org/news- bulletin/1999/03/1999-03. president.html)

[4] David, H (2002). Differences Between Genders in Math studies in Seventh- Twelfth Grades. Part II: Gender differences in

matriculation exams and the psychometric test in mathematics. J.O.M - Journal of Mathematics education at High School, 28, 35-51.



http://www.nctm.org/news-%20bulletin/1999/03/1999-03

http://www.nctm.org/news-%20bulletin/1999/03/1999-03


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A note on approximating finite Hilbert transform and quadrature formula

Fuat Usta 1

1Department of Mathematics, Düzce University,

[email protected]

Abstract

In this presentation, approximations for the finite Hilbert transform are given utilizing the fundamental integral

identity for absolutely continuous mappings. Then, a numerical integrations for this transform are obtained. Finally some

numerical experiments have been presented. Keywords: Finite Hilbert Transform, CPV (Cauchy Principal Value), Absolutely Continuous Mappings.

References:

1. N. M. Dragomir, S. S. Dragomir, P. M. Farrell and G. W. Baxter, A quadrature rule for the finite Hilbert transform via trapezoid

type inequalities, J. Appl. Math. Comput. 13 (2003), no. 1-2, 67–84.

2. W. J. Liu and N. Lu, Approximating the finite Hilbert Transform via Simpson type inequalities and applications, Politehnica

University of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, 77 (2015), no. 3, 107-122.

3. F. Usta, Approximating the finite hilbert transform for absolutely continuous mappings and applications in numerical

integration, Advances in Applied Clifford Algebras, (2018) 28: 78. https://doi.org/10.1007/s00006-018-0898-z

4. F. Usta, On approximating the finite hilbert transform and applications in quadrature, Mathematical Methods in the Applied

Sciences, 2018;1–10. https://doi.org/10.1002/mma.5252.



https://doi.org/10.1007/s00006-018-0898-z


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Complete Lift Problems of Projectable Linear Connection in Semi-tangent Bundle

Furkan Yildirim 1 and Murat Polat 2

1Narman Vocational Training School, Atatürk University, 25530, Erzurum, Turkey

[email protected] 2Department of Mathematics, Faculty of Sci. Atatürk University, 25240, Erzurum, Turkey

[email protected]

Abstract

Using the fiber bundle M over a manifold B, we define a pull-back bundle tB. We study the complete lifts of

projectable linear connection for semi-tangent bundle. In addition, a new example for good square is defined in this work.

Keywords: Complete lift, Projectable linear connection, Projectable vector field, Pull-back bundle, Semi-tangent bundle.

References:

1. Yano K. and Ishihara S. Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York, 1973.

2. Husemoller D. Fibre Bundles. Springer, New York, 1994.

3. Lawson H.B. and Michelsohn M.L. Spin Geometry. Princeton University Press., Princeton, 1989.

4. Salimov A. A. and Kadıoğlu E. Lifts of Derivations to the Semitangent Bundle, Turk J. Math. 24(2000), 259-266.

5. Steenrod N. The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.

6. Yıldırım F., On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics,

(ANAS) 41 (2015), no. 1, 25-38.

7. Yıldırım F. and Salimov A. Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.

8. Pontryagin L.S. Characteristic cycles on differentiable manifolds. Rec. Math. (Mat. Sbornik) N.S., 21(63):2, (1947), 233-284.

9. Poor W.A., Differential Geometric Structures, New York, McGraw-Hill (1981).

10. Ostianu N.M., Step-fibred spaces, Tr. Geom. Sem. 5, Moscow. (VINITI), 259-309 (1974).

11. Vishnevskii V. V., Integrable affinor structures and their plural interpretations. Geometry, 7.J. Math. Sci. (New York) 108

(2002), no. 2, 151-187.





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41

Adapted Frames in the Semi-Tensor Bundle

Furkan Yildirim

Narman Vocational Training School, Ataturk University, 25530, Erzurum, Turkey

[email protected]

Abstract

The main purpose of this paper is to investigate adapted frames for semi-tensor (pull-back) bundle tB of type

(p,q).

Keywords: Vector field, horizontal lift, pull-back bundle, semi-tensor bundle.

References:

1. T.V. Duc, Structure presque-transverse. J. Diff. Geom., 14 (1979), no. 2, 215-219.

2. H. Fattaev, The Lifts of Vector Fields to the Semitensor Bundle of the Type (2, 0), Journal of Qafqaz University, 25 (2009),

no. 1, 136-140.

3. D. Husemoller, Fibre Bundles. Springer, New York, 1994.

4. V. Ivancevic and T. Ivancevic, Applied Differential Geometry, A Modern Introduction, World Scientific, Singapore, 2007.

5. H.B. Lawson and M.L. Michelsohn, Spin Geometry. Princeton University Press., Princeton, 1989.

6. A. Salimov, Tensor Operators and their Applications. Nova Science Publ., New York, 2013.

7. A. A. Salimov and E. KadıoÄŸlu, Lifts of derivations to the semitangent bundle, Turk J. Math. 24 (2000), no. 3, 259-266.




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Investigation of The Suborbital Graphs

Murat Besenk 1 and Gizem Demirbas 2

1Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University, Denizli

[email protected] 2Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University, Denizli

[email protected]

Abstract

Let 𝑃𝑆𝐿(2, ℤ) = {𝑇: ℂ ∪ {∞} → ℂ ∪ {∞} | 𝑇(𝑧) =𝑎𝑧+𝑏

𝑐𝑧+𝑑; 𝑎, 𝑏, 𝑐, 𝑑 ∈ ℤ, 𝑎𝑑 − 𝑏𝑐 = 1} be the Modular group and

Γ0(𝑝) denote the subgroup represented by the matrices Γ0(𝑝) ≔ {(𝑎 𝑏𝑐 𝑑

) ∶ 𝑐 ≡ 0 (𝑚𝑜𝑑𝑝)} where 𝑝 is a prime number.

Let ℍ ≔ {𝑧 ∈ ℂ ∶ 𝐼𝑚𝑧 > 0} denote the upper half plane which the lines of the model are the open rays orthogonal to the

real axis together with the open semicircles orthogonal to the real axis. And also ℍ∗/Γ0(𝑝) is compact Riemann surface

where ℍ∗: = ℍ ∪ ℚ ∪ {∞}. In this paper we investigate some properties of suborbital graphs for a special Möbius

transformation. In addition, we give edge and circuit circumstances for the suborbital graph.

Keywords: Modular group, Suborbital graphs, Congruence subgroup, Orbit, Circuit.

References:

1. Akbaş M., On suborbital graphs for the Modular Group, Bulletin of The London Mathematical Society, Vol. 33 (2001), 647-

652.

2. Beşenk M., The action of 𝑆𝐿(2, ℂ) on hyperbolic 3-space and orbital graphs, Graphs and Combinatorics, Vol. 34

(2018), 545-554.

3. Jones G. A., Singerman D., Wicks K., The Modular group and generalized Farey graphs, Bulletin of The London Mathematical

Society, Vol. 160 (1991), 316-338.

4. Rankin R. A., Modular forms and functions, Cambridge University Press, (2008).

5. Beardon A. F., The geometry of discrete groups, Springer Verlag, Cambridge, (1995).





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43

A Note on Primality Testing: Algorithms and Analyses

Gozde Sarikaya 1 and Enver Ozdemir 2

1Informatics Institute, Istanbul Technical University,

[email protected] 2National HPC Center, Istanbul Technical University,

[email protected]

Abstract

Prime numbers have great impacts in the field of algebraic and computational number theory. Thus, various

primality testing algorithms invented which are probabilistic, deterministic or non-deterministic. However, it is still an

open problem to find a method lead to lower running time complexity.

In this work, various known primality testing algorithms including Atkin’s elliptic curve primality proving, AKS

and Miller-Rabin test will be presented along with a conjectured algorithm developed based on the strong pseudoprime test

by using singular cubic curves and group operation on finite fields. The results show that the algorithm catches all strong

pseudoprimes less than 264. In addition, the compositeness of several million high precision strong pseudoprimes detected

successfully. Finally, theoretical and computational comparison results of given algorithms will be examined along with

their running time analysis.

Keywords: primality testing, elliptic curves, group operation, finite fields, complex multiplication, pseudoprimes

References:

1. M. Agrawal, N. Kayal, N. Saxena, Primes is in P, Annals of Math. 160 (2004), 781793.

2. G. Miller, Riemann’s hypothesis and tests for primality, J. Comput. and System Sci. 13 (1976), 300-317.

3. L. M. Adleman, C. Pomerance, R. S. Rumely, On distinguishing prime numbers from composite numbers, Ann. of Math. 2,

117:1 (1983),173206.

4. H. Cohen, A Course in Computational Algebraic Number Theory, Springer-Verlag, 2000.

5. R. Schoof, Four primality testing algorithms, Algorithmic Number Theory, MSRI Publications, Volume 44, 2008, 101-126.

6. R. Crandall, C. Pomerance, Prime numbers: a computational perspective, Springer, New York, 2001.





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On Lie group analysis of boundary value problem with Caputo fractional derivative

Gulistan Iskenderoglu 1 and Dogan Kaya 2

1,2Department of Mathematics, Istanbul Commerce University, [email protected]

[email protected]

Abstract

Lie symmetry analysis of initial and boundary value problem for partial differential equations with Caputo

fractional derivative is investiged [1,2]. Also given generalized definition and theorem for symmetry method for partial

differential equation with Caputo fractional derivative [3]. The group symmetries and examples on reductıon of fractional

partial differential equations with initial and boundary conditions to nonlinear ordinary differential equations with initial

condition are present.

Keywords: Lie goup method, Caputo type fractional derivative, boundary value problem.

References:

1. Olver, P. Applications of Lie groups to differential equations Springer Science, Germany, 2012.

2. Bluman, G. W. and Anco, S.C. Symmetry and Integration Methods for Differential Equations, 154 Applied Mathematical

Sciences, Springer-Verlag, New York, 2002

3. Gazizov, R.K., Kasatkin, A.A., and Lukashchuk, S.Y. Continuous transformation groups of fractional differential equations,

Vestn. USATU, 9, 125–135, 2007. (in Russian with an abstract in English)





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45

A stochastic approach for the nonlinear Duffing oscillator with damping term

Hande Uslu 1 and Murat Sari 2

1,2Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract

Natural processes have been taken of attention for many years and various methods have been used to find an

appropriate model and a related solution to the processes. Striking physical systems are adequately modelled by the Duffing

equation, which describes an oscillator with various nonlinearities. Since many difficulties are encountered in numerically

solving the problems governed by the Duffing equation with damping effect, a new stochastic approach based on Monte

Carlo technique has been proposed to handle it. To properly realize the simulated behavior of the processes, detailed

discussion has been carried out in the present work.

Keywords: Duffing oscillator, Monte Carlo simulation, Stochastic Method, Nonlinear process, Initial value problem

References:

1. K. Johannessen, The Duffing oscillator with damping, European Journal of Physics. 36 (2015) 065020 (13pp).

2. S. Nourazar and A. Mirzabeigy, Approximate solution for nonlinear Duffing oscillator with damping effect using the modified

differential transform method, Scientica Iranica. Vol.20 (2013) 364- 368.

3. Q. Mao, Design of shaped piezoelectric modal sensors for cantilever beams with intermediate support by using differential

transform method, Applied Acoustics. Vol.73 (2012) 144-149.

4. I. Kovacic and M.J. Brennan, The Duffing equation nonlinear oscillations and their behavior, (2011) New York, Wiley.

5. H.Tunc and M. Sari, A local differential transform approach for the cubic nonlinear Duffing oscillator with damping term,

Scientica Iranica. (2019), (in press).




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46

A Convergence Result for a Three-Step Iterative Algorithm

Harun Polat 1 and Faik Gursoy 2

1Department of Mathematics, Muş Alparslan University,

[email protected] 2Department of Mathematics, Adıyaman University

[email protected]

Abstract

We prove under some mild conditions that iterative algorithm (1.7) of [1] converges strongly to the fixed point of a member

in the class of weak contraction mappings.

Keywords: Fixed Point, Convergence, Iterative algorithm.

References:

1- Karakaya, V., Atalan, Y., Doğan, K. and El Houda Bouzara, N. Some fixed point results for a new three steps iteration

process in Banach spaces, Fixed Point Theory 18, 625-640 (2017).





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47

Involutions in Elliptic Biquaternions

Hasan Es 1 and Murat Bekar 2

1Department of Mathematics, Faculty of Education, Gazi University

[email protected] 2Department of Mathematics, Faculty of Science, Ankara Haci Bayram Veli University

[email protected]

Abstract

An involution (resp., anti-involution) in an algebra 𝐸 over the field of real or complex numbers is a mapping 𝑥 ↦𝑥∗ of 𝐸 onto itself satisfying the following axioms:

(i) 𝑥∗∗ = 𝑥 for all 𝑥 ∈ 𝐸,

(ii) (𝑥 + 𝜆𝑦)∗ = 𝑥∗ + 𝜆̅𝑦∗ for all λ in the corresponding field and for all 𝑥, 𝑦 ∈ 𝐸,

(iii) (𝑥𝑦)∗ = 𝑦∗𝑥∗ (resp., (𝑥𝑦)∗ = 𝑥∗𝑦∗) for all 𝑥, 𝑦 ∈ 𝐸.

The main purpose of this study is to give a brief summary of the concepts real quaternions and elliptic biquaternions.

Afterwards, we define an involution and an anti-involution transformation using elliptic biquaternions.

Keywords: Real quaternion, elliptic biquaternion, involution, anti-involution.

References:

6. K. E. Özen and M. Tosun, Further results for elliptic biquaternions, Conference Proceedings of Science and Technology, 1(1)

2018 20-27.

7. W. R. Hamilton, On a new species of imaginary quantities connected with the theory of quaternions, Proceedings of the Royal

Irish Academy, 2 (1844) 424–434.

8. H. S. M. Coxeter, Quaternions and reflections, The American Mathematical Monthly, 53(3) (1946) 136‐146.

9. T. A. Ell and S. J. Sangwine, Quaternion involutions and anti‐involutions, Computers & Mathematics with Applications, 53(1)

2007 137‐143.

10. J. P. Ward, Quaternions and Cayley Numbers: Algebra and Applications. Kluwer, Dordrecht; 1997.

11. M. Bekar and Y. Yayli, Involutions of complexified quaternions and split quaternions, Advances in Applied Clifford

Algebras, 23(2) 2013 283-299.

12. A. J. Hahn, Quadratic algebras, Clifford algebras, and arithmetic witt groups. New York: Springer‐Verlag; 1994.




https://link.springer.com/journal/6



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48

Involutions in Elliptic Quaternions

Hasan Es 1 and Murat Bekar 2

1Department of Mathematics, Faculty of Education, Gazi University

[email protected] 2Department of Mathematics, Faculty of Science, Ankara Haci Bayram Veli University

[email protected]

Abstract

An involution (resp., anti-involution) in an algebra 𝐸 over the field of real or complex numbers is a transformation

𝑓: 𝐸 → 𝐸 satisfying the following axioms:

(i) 𝑓(𝑓(𝑥)) = 𝑥 for all 𝑥 ∈ 𝐸,

(ii) 𝑓(𝑥 + 𝜆𝑦) = 𝑓(𝑥) + 𝜆̅𝑓(𝑦) for all λ in the corresponding field and for all 𝑥, 𝑦 ∈ 𝐸,

(iii) 𝑓(𝑥𝑦) = 𝑓(𝑦)𝑓(𝑥) (resp., 𝑓(𝑥𝑦) = 𝑓(𝑥)𝑓(𝑦)) for all 𝑥, 𝑦 ∈ 𝐸.

In this study; firstly, we give the basic concepts of real quaternions and elliptic quaternions. Afterwards, we define an

involution and an anti-involution transformation using elliptic quaternions. Finally, we give these transformations

geometric interpretations in Euclidean 3-space.

Keywords: Real quaternion, elliptic quaternion, involution, anti-involution.

References:

13. M. Özdemir, An alternative approach to elliptical motion, Advances in Applied Clifford Algebras, 26(1) 2016 279-304.

14. W. R. Hamilton, On a new species of imaginary quantities connected with the theory of quaternions, Proceedings of the Royal

Irish Academy, 2 (1844) 424–434.

15. H. S. M. Coxeter, Quaternions and reflections, The American Mathematical Monthly, 53(3) (1946) 136‐146.

16. T. A. Ell and S. J. Sangwine, Quaternion involutions and anti‐involutions, Computers & Mathematics with Applications, 53(1)

2007 137‐143.

17. J. P. Ward, Quaternions and Cayley Numbers: Algebra and Applications. Kluwer, Dordrecht; 1997.

18. M. Bekar and Y. Yayli, Involutions of complexified quaternions and split quaternions, Advances in Applied Clifford

Algebras, 23(2) 2013 283-299.

19. A. J. Hahn, Quadratic algebras, Clifford algebras, and arithmetic witt groups. New York: Springer-Verlag; 1994.








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Negative coefficient of Starlike Functions of order 𝟏

𝟐

Hasan Sahin 1, Ismet Yildiz 2 and Umran Menek 3

1,2,3Department of Mathematics, Düzce Technical University,

[email protected]

ismetyildiz@düzce.edu.tr [email protected]

Abstract

Geometric function theory is a branch of complex analysis that seeks to relate analytic properties of conformal

maps to geometric properties of their images. The subject has deep connections with other areas of mathematics such as

potential theory, hyperbolic geometry, and dynamical systems. Theory, mainly concerning univalent functions but, also,

other analytic or harmonic mappings in the unit disk : 1U z z . Significant for the development of the theory has

been the Bieberbach conjecture which states that the coefficients of normalized univalent functions must satisfy na n .

The study of complex function theory is one of the most fascinating aspects of the theory of analytic function of a complex

variable. Complex function theory has profound impact on the entire range of mathematics. Many mathematical concepts

become clear when examined in light of complex function theory. In this field we are mainly concerned with the power

series of the form 2

0 1 2 ...f z a a z a z of the complex variable z that are convergent in a domain D . Such a power

series may be interpreted as a mapping of domain D in the z -plane onto some range of set f D in the w -plane. A

geometric property from the point of view of conformal mapping possessed by an analytic function f z is that of

univalence inU . A function f z defined in a domain D is said to be univalent in D if it is one-to-one in D , that is,

f z takes no value more than once in D , in other words, if 1 2f z f z and 1 2,z z D , then 1 2z z .

In this paper, we present a univalent function

1

2

1, ,03

A

called starlike function and a negative coefficient.

Keywords: Analytic Functions, Negative Coefficient, Starlike Functions, Univalent Functions.

References:

1. S. K. Chatterjea, Onstarlike functions, J. Pure Math. 1(1981), 23-26.

2. V. S. Kiryakova, M. Saigo and S. Owa, Distortion and characterization teorems for starlike and convex functions related

to generalized fractional calculus, Publ. Res. Inst. Math. Sci.1012(1997), 25-46.

3. T. Sekine, On new generalized classes of analytic functions with negative coefficients, Report Res. Inst. Sci. Tec. Nihon

Univ. 35(1987), 1-26.

4. T. Sekine and S. Owa, New problems of coefficients inequalities, Publ. Res. Inst.Math. Sci. 1012(1997), 164-176.

5. H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51(1975), 109-116.

6. H. M. Srivasta, S. Owa and S. K. Chatterjea, A note on certainleclass of starlike functions, Rend. Sem. Mat. Univ.

Padova 77(1987), 115-124.






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On the Conversion of Convex Functions to Certain within the Unit Disk

Hasan Sahin 1, Ismet Yildiz 2 and Umran Menek 3

1,2,3Department of Mathematics, Düzce Technical University,

[email protected]

ismetyildiz@düzce.edu.tr [email protected]

Abstract

A function f(z) is said to be univalent in a domain D if it provides a one-to-one mapping onto its image, f(D).

Geometrically , this means that the representation of the image domain can be visualized as a suitable set of points in the

complex plane. We are mainly interested in univalent functions that are also regular (analytic, holomorphik) in U. Without

lost of generality we assume D to be unit disk : 1U z z . One of the most important events in the history of

complex analysis is Riemann’s mapping theorem, that any simply connected domain in the complex plane which is not

the whole complex plane, can be mapped by any analytic function univalently on the unit diskU . The investigation of

analytic functions which are univalent in a simply connected region with more than one boundary point can be confined to

the investigation of analytic functions which are univalent inU . The theory of univalent functions owes the modern

development the amazing Riemann mapping theorem. In 1916, Bieberbach proved that for every 2

n

n

n

f z z a z

in

class S , 2 2a with equality only for the rotation of Koebe function 2

1k z z z

.

We give an example of this univalent function with negatice cofficients of order 1

4 and we try to explain

1

4

1, , 13

B

with convex functions.

Keywords: Univalent Functions, Convex Functions, Class S.

References:

1. S. K. Chatterjea, Onstarlike functions, J. Pure Math. 1(1981), 23-26.

2. V. S. Kiryakova, M. Saigo and S. Owa, Distortion and characterization teorems for starlike and convex functions related

to generalized fractional calculus, Publ. Res. Inst. Math. Sci.1012(1997), 25-46.

3. T. Sekine, On new generalized classes of analytic functions with negative coefficients, Report Res. Inst. Sci. Tec. Nihon

Univ. 35(1987), 1-26.

4. T. Sekine and S. Owa, New problems of coefficients inequalities, Publ. Res. Inst.Math. Sci. 1012(1997), 164-176.

5. H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51(1975), 109-116.

6. H. M. Srivasta, S. Owa and S. K. Chatterjea, A note on certainleclass of starlike functions, Rend. Sem. Mat. Univ.

Padova 77(1987), 115-124.






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51

Simple Undirected Graphs Topology

Hatice Kubra Sari 1 and Abdullah Kopuzlu 2

1,2Department of Mathematics, Ataturk University,

[email protected]

[email protected]

Abstract

It is given serial preclusive relations corresponding to simple undirected graphs without isolated vertice.

Topologies is generated by using simple undirected graphs without isolated vertice. Relasionship between definable sets

with regard to serial preclusive relation corresponding to a simple undirected graph and both open and closed sets of

topology generated by this graph.

Keywords: Rough set, Graph theory, topological space, definable set.

References:

1. E.A. Abo-Tabl, Rough Sets and Topological Spaces Based on Similarity, International Journal of Machine Learning and

Cybernetics 4 (2013) 451-458.

2. J.A. Bondy, U.S.R. Murty, Graph Theory, Springer, Berlin, 2008.

3. J. Chen, J. Li, An Application of Rough Sets to Graph Theory, Information Sciences, 201 (2012) 114-127.

4. J. Järvinen, Lattice Theory for Rough Sets, Transactions on Rough Sets VI, LNSC, vol. 4374, Springer-Verlag, Berlin,

Heidelberg, 2007. pp. 400-498.

5. S. Lipschutz, Schaum’s Outline of Theory and Problems of General Topology, Mcgraw-Hill Book Company, New York, St.

Louis,San Francisco, Toronto,Sydney, 1965.

6. S. Hatice Kübra, K. Abdullah, A Note on a Binary Relation corresponding to a Bipartite Graph, ITM Web of Conferences 22

(2018) 01039.

7. Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (1982) 341–356.

8. L, Polkowski Rough sets: mathematical foundations. Physica-Verlag, Heidelberg, 2002.

9. Skowron A ,On topology in information system. Bulletin of the Polish Academy of Sciences Mathematics 36 (1988) 477–480.

10. A, Wiweger, On topological rough sets. Bull Pol Acad Sci Math 37 (1988) 51–62.





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52

A Study on the Role of Drama in Learning Mathematics

Ilknur Yilmaz 1 and Adem Cevikel 2

1,2Department of Mathematics Education, Yildiz Technical University,

[email protected]

[email protected]

Abstract

In this study we searched that dramatic practices can help to better learning of mathematical concepts and these

students have better perception of concepts

Keywords: Maths education, Students, Drama, Teaching methods

References:

1. V. Elahe Masoum and A. Meskhi, A Study on the Role of drama in learning mathematics, Mathematics Education and Trends, 2013 (2013) 7-11.

2. Joy Faini Saab, The effects of creative drama methods on mathematics achievement, attitudes and creativity, West Virginia

University, 1987. 3. P. Chaviaris, S. Kafoussi, Learning mathematics with creative drama, Journal of Inquiry Based Activities 5 2 (2010) 91-110.





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53

Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

Faruk Dusunceli 1 1Department of Economics, University of Mardin Artuklu, Mardin, Turkey

[email protected]

Abstract

In this paper, we studied exact solutions of generalized (3+1) shallow water-like (SWL) equation by using the

bernoulli sub-equation function method. Firstly, SWL Equation is transformed into nonlinear ordinary differential equation

by using a wave transformation. Later, nonlinear ordinary differential equation is solved by bernoulli sub-equation function

method.

Keywords: Generalized (3+1) shallow water-like (SWL) equation, bernoulli sub-equation function method, exact solution.

References:

1. R. Sadat, M. Kassem, and Wen-Xiu Ma, “Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1)

Dimensional Model,” Advances in Mathematical Physics, vol. 2018, Article ID 9178480, 8 pages, 2018.

https://doi.org/10.1155/2018/9178480.

2. Düşünceli, F. New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model, Advances

in Mathematical Physics, vol. 2019, Article ID 7801247, 9 pages, 2019. https://doi.org/10.1155/2019/7801247.

3. Düşünceli, F . (2019). New Exact Solutions for the (3 + 1) Dimensional B-type Kadomtsev-Petviashvili Equation. Erzincan

Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12 (1), 463-468. DOI: 10.18185/erzifbed.493777

4. Y. Zhang, H. Dong, X. Zhang, and H. Yang, “Rational solutions and lump solutions to the generalized (3+1)-dimensional

Shallow Water-like equation,” Computers & Mathematics with Applications, vol. 73, no. 2, pp. 246–252, 2017.

5. H.M. Baskonus, H. Bulut, On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation

function method, Waves in Random and Complex Media, 25:4, 720-728, 2015.




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54

A Characterization of Homogeneous Fractional Hardy-Type Integrals on Variable Exponent

Spaces

Lutfi Akin

Department of Bussiness Administration, Mardin Artuklu University

[email protected]

Abstract

In this study, we establish boundedness of homogeneous fractional Hardy-type integral on variable exponent spaces.

Keywords: Variable exponent Lebesgue space, Fractional Hardy-Type integral, Boundedness,

References:

1. Akin, L.: A Characterization of Approximation of Hardy Operators in VLS, Celal Bayar University Journal of Science Volume

14, Issue 3, p 333-336, (2018).

2. Christ, M. and Grafakos, L.: Best constants for two non-convolution inequalities, Proc.Amer. Math. Soc. 123, no. 6, 1687–

1693, (1995).

3. Fu, Z., Liu, Z., Lu, S. and Wang, H.: Characterization for commutators of n-dimensional fractional Hardy operators, Sci. China

Ser. A 50, no. 10, 1418–1426, (2007).

4. Akin, L.: Compactness of Fractional Maximal Operator in Weighted and Variable Exponent Spaces, Erzincan University,

Journal of Science and Technology, Volume12, issue:1, pp:185-190, (2019).

5. Cruz-Uribe, D., SFO, Fiorenza, A., Martell, J. and Prez, C.: The boundedness of classical operators on variable Lp spaces,

Ann. Acad. Sci. Fenn. Math., 31, 239-264, (2006).

6. Mamedov, F., Zeren, Y. and Akın, L.: Compactification of Weighted Hardy Operator in Variable Exponent Lebesgues Spaces,

Asian Journal of Mathematics and Computer Research 17(1): 38-47, (2017).

7. Lu, S., Ding, Y. and Yan, D.: Singular integrals and related topics,World Scientific Press, (2011).

8. Akin, L.: On Two Weight Criterions for The Hardy Littlewood Maximal Operator in BFS, Asian Journal of Science and

Technology Vol. 09, Issue, 05, pp.8085-8089, May, (2018).

9. Akin, L.: A Characterization of Boundedness of Fractional Maximal Operator with Variable Kernel on Herz-Morrey spaces,

Analysis in Theory and Applications, (accepted,2019).




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55

New Exact Solutions for Ablowitz-Kaup-Newell-Segur Wave Equation via Bernoulli Sub-

equation Function Method

Faruk Dusunceli 1 1Department of Economics, University of Mardin Artuklu, Mardin, Turkey

[email protected]

Abstract

In this Paper, we have generated new exact solutions of Ablowitz-Kaup-Newell-Segur Wave Equation with Fourth

Order by using the bernoulli sub-equation function method. Firstly, Ablowitz-Kaup-Newell-Segur Wave Equation which

being nonlinear partial differential equation is transformed into nonlinear ordinary differential equation by using a wave

transformation. Later, nonlinear ordinary differential equation is solved by bernoulli sub-equation method.

Keywords: Ablowitz-Kaup-Newell-Segur Wave Equation, bernoulli sub-equation method, exact solution.

References:

1. Düşünceli, F. and Çelik, E. Numerical Solution for High-Order Linear Complex Differential Equations By Hermite

Polynomials, Iğdır University Journal of the Institute of Science and Technology, 7(4): 189-201, 2017.

2. Düşünceli, F. New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model, Advances

in Mathematical Physics, vol. 2019, Article ID 7801247, 9 pages, 2019. https://doi.org/10.1155/2019/7801247.

3. Düşünceli, F . (2019). New Exact Solutions for the (3 + 1) Dimensional B-type Kadomtsev-Petviashvili Equation. Erzincan

Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12 (1), 463-468. DOI: 10.18185/erzifbed.493777

4. H.M. Baskonus, H. Bulut, On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation

function method, Waves in Random and Complex Media, 25:4, 720-728, 2015.




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56

Strong Convergence Result for The Faster Iterative Scheme

Yunus Atalan 1 and Faik Gursoy 2

1Department of Mathematics, Aksaray University,

[email protected] 2 Department of Mathematics, Adıyaman University

[email protected]

Abstract

In this study, the strong convergence of a fixed point iterative scheme has been examined under appropriate

conditions and it has been proved that the convergence rate of an iterative scheme is not independent of the selection of its

control sequences. Also an example has been given to support this result.

Keywords: Strong convergence, rate of convergence, control sequences, iterative scheme.

References:

1. Y. Atalan, On numerical approach to the rate of convergence and data dependence results for a new iterative scheme, Konuralp

J. Math. 7 (1) (2019) 97-106.

2. K. Doğan, Daha hızlı Mann sabit nokta yinelemesi üzerine bir çalışma, AKU. J. Sci. Eng. 18(3) (2018) 852–860.

3. V. Karakaya, Y. Atalan, K. Dogan, NEH. Bouzara. Some Fixed Point Results for a new three steps iteration process in Banach

spaces. Fixed Point Theory, 18(2) (2017) 625-640.





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57

Some Properties for Higher Order Commutators of Hardy-Type Integral Operator on Herz–

Morrey Spaces with Variable Exponent

Yusuf Zeren 1 and Lutfi Akin 2


[email protected] 2Department of Bussiness Administration, Mardin Artuklu University

[email protected]

Abstract

In this work, the boundedness for higher order commutators of Hardy-Type integrals is obtained on Herz–Morrey spaces

with variable exponent 𝐌�̇�𝐩,𝐪(.)𝛃(.),𝛌

(𝐑𝐧) applying some properties of variable exponent and BMO function, where 𝛃(𝒙) ∈

𝑳∞(𝑹𝒏) are log-Hölder continuous both at the origin and at infinity and 𝐪(𝐱) satisfies the logarithmic continuity condition.

Keywords: Variable exponent, Hardy-Type integral, Herz–Morrey space,

References:

1. Ruzicka, M.: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes

in Mathematics, vol. 1748. Springer, New York (2000).

2. Diening, L., Ruzicka, M.: Calder´on–Zygmund operators on generalized Lebesgue spaces

Lp(·) and problems related to fluid dynamics. Journal f¨ur die reine und angewandte

Mathematik 563, 197–220 (2003).

3. Levine, S., Chen, Y., Stanich, J.: Image restoration via nonstandard diffusion. Technical

Report: 04-01, Department of Mathematics and Computer Science, Duquesne University

(2004).

4. Chen, Y., Levine, S., Rao, M.: Variable exponent, linear growth functionals in image

restoration. SIAM J. Appl. Math. 66(4), 1383–1406 (2006).

5. Li, F., Li, Z., Pi, L.: Variable exponent functionals in image restoration. Appl. Math. Comput.

216(3), 870–882 (2010).





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58

Some Fixed Point Theorems with 𝒘-𝜶-distance Method

Fatma Polat 1 and Gulcan Atici Turan 2

1Muş Alparslan University, Turkey

[email protected] 2Department of Mathematics, Muş Alparslan University, Turkey

[email protected]

Abstract

In this study, we define 𝑤-𝛼-distance and generalized 𝑤-𝛼-rational contraction mapping. We also give related

theorem and example.

Keywords: Binary relation, Fixed Point, 𝛼-complete space, 𝑤-distance.

References:

1. Alam, A., Imdad, M., (2015). Relation-theoretic contractive principle. Journal Fixed Point Theory Applications, 17 (4), 693-

702.

2. Hussain, N., Kutbi, M. A., Salimi, P., (2014). Fixed point theory in 𝛼-complete metric spaces with applications. Abstract and

Applied Analysis, 1-2, 1-11.

3. Kada, O., Suzuki, T., Takahashi, W., (1996). Nonconvex minimization theorems and fixed point theorems in complete metriz

spaces. Mathematica Japonica, 44 (2), 381-391.

4. Kutbi, M. A., Sintunavarat, W., (2013). The existence of fixed point theorems via 𝑤-distance and 𝛼-admissible mappings and

applications. Abstract and Applied Analysis, 141, 1-8.

5. Kutbi, M. A., Sintunavarat, W., (2014). Fixed point theorems for generalized 𝑤𝛼- contraction multivalued mappings in 𝛼-

complete metric spaces. Fixed Point Theory and Applications, 139, 1-9.

6. Samet, B., Vetro, C., Vetro, P., (2012). Fixed point theorems 𝛼-𝜓-conractive type mappings. Nonlinear Analysis: Theory,

Methods and Applications, 75 (4), 2154- 2165.

7. Senapati, T., Dey, K. D., (2017). Relation-theoretic metrical fixed point results via 𝑤- distance with applications. Journal of

Fixed Point Theory and Applications, 19, 2945- 2961.

8. Suzuki, T., Takahashi, W., (1996). Fixed point theorems and characterizations of metric completeness. Topological Methods

Nonlinear Analysis, 8, 371- 382.





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59

Amalgam Spaces with Variable Exponent

Ismail Aydin 1 and Cihan Unal 2

1Department of Mathematics, Sinop University,

[email protected] 2Department of Mathematics, Sinop University

[email protected]

Abstract

Let 1 ≤ 𝑠 < ∞ and 1 ≤ 𝑟(. ) ≤ ∞, where 𝑟(. ) is a variable exponent. In this study, we define variable exponent

amalgam space (𝐿𝑟(.), 𝑙𝑠). Moreover, we give some examples about inclusion properties of this space. Finally, we obtain

that the space is a Banach function space.

Keywords: Amalgam spaces with variable exponent, Banach function spaces, Inclusions.

References:

1. I. Aydın, On vector-valued classical and variable exponent amalgam spaces. Commun.Fac. Sci. Univ. Ank. Series A1, 66(2),

(2017), 100--114.

2. I.Aydın, On variable exponent amalgam spaces. Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica,

20(3), (2012), 5--20.

3. L. Diening, Maximal function on generalized Lebesgue spaces 𝐿𝑝(.). Mathematical Inequalities and Applications, 7, (2004),

245--253.

4. A. T. Gürkanlı, I.Aydın, On the weighted variable exponent amalgam space 𝑊(𝐿𝑝(𝑥), 𝐿𝑚𝑞). Acta Mathematica Scientia, 34B(4),

(2014), 1--13.

5. A. T. Gürkanlı: The amalgam spaces 𝑊(𝐿𝑝(𝑥); 𝐿{𝑝𝑛}) and boundedness of Hardy-Littlewood maximal operators. Current

Trends in Analysis and Its Applications: Proceedings of the 9th ISAAC Congress, Krakow 2013.





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60

The Rate of Convergence of two fixed point iterative schemes for Continuous Functions on

Closed Intervals

Kadri Dogan 1 and Faik Gursoy 2

1Department of Computer Engineering, Artvin Coruh University, Artvin/TURKEY,

[email protected] 2Department of Mathematics, Adiyaman University, 02040 Adiyaman, Turkey

[email protected]

Abstract

In this study, two fixed point iteration methods are taken into consideration and the comparison of the rate

convergence of these iteration methods are examined for continous functions on Closed intervals. Also numerical examples

supporting these results are given and constructed tables and graphs.

References:

1. K. Dogan, V. Karakaya, On the Convergence and Stability Results for a New General Iterative Process. SCIENTIFIC

WORLD JOURNAL (2014).

2. V. Karakaya, K. Dogan, F. Gursoy, and M. Erturk, \Fixed point of a new three-step iteration algorithm under contractive-like

operators over normed spaces," Abstract and Applied Analysis, vol. 2013, Article ID 560258, 9 pages, 2013.

3. F. Gursoy, V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument,

arXiv preprint arXiv:1403.2546 (2014).





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61

Introduction to HOL Theorem Proving

Kubra Aksoy 1, Sofiène Tahar 2 and Yusuf Zeren 3


[email protected] 2Department of Electirical &Computer Engineering, Concordia University


[email protected]

Abstract

The HOL interactive theorem prover is a proof assistant based on Higher-Order Logic. It is an ML based

programming environment in which mathematical functions and predicates can be defined and theorems can be proven.

The core of the HOL theorem prover is composed of a small set of axioms and inference rules, making proofs in HOL

sound and trustable. The HOL prover includes several theories (libraries) that cover most subjects of classical mathematics.

The tool also provides a set of built-in decision procedures that can help automatically prove many simple theorems of

arithmetic and Boolean algebra. In this tutorial we provide an introduction to the HOL theorem prover and show how this

tool can be used in the formal analysis of advanced mathematics problems.

Keywords: Higher-Order Logic, Theorem Proving, Proof Tool, HOL4

References:

[1] hol-theorem-prover.org

[2] M. J. C. Gordon and T. F. Melham, Introduction to HOL: A theorem proving environment for higher order logic,

Cambridge University Press, 1993

[3] J. Harrison, Theorem Proving with the Real Numbers, Springer, 2011





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62

Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable

Exponent Lebesgue spaces

Lutfi Akin

Department of Bussiness Administration, Mardin Artuklu University,

[email protected]

Abstract

We show that when the infimum of the exponent function, Hardy integral operator is a bounded operator from the Morrey

space with variable exponent to the weak Morrey space with variable exponent.

Keywords: Hardy integral operator, Morrey spaces, Weak Morrey spaces, Variable exponent.

References:

1. Ferreira, L., On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations, J. Math. Pures Appl.

(9) 105, 228–247 (2016)

2. Mizuta, Y., Shimomura, T.: Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent. J.

Math. Soc. Jpn. 60, 583–602 (2008)

3. Sawano, Y., Sugano, S., Tanaka, H.: Orlicz-Morrey spaces and fractional operators. Potential Anal. 36,517–556 (2012)

4. Ho, K.-P., Atomic decompositions and Hardy’s inequality on weak Hardy-Morrey spaces. Sci. China Math. 60, 449–468

(2017)

5. Ho, K.-P., Weak Type Estimates of the Fractional Integral Operators on Morrey Spaces with Variable Exponents, Acta Appl

Math (2019) 159:1–10




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63

Necessary Conditions for the Optimal Control of the Plates under Moving Mass

Melih Cinar 1 and Aydin Secer 2

1,2Department of Mathematical Engineering, Yildiz Technical University,

[email protected],

[email protected]

Abstract

In this paper, we study the optimal control of the plates under moving mass. The aim of the paper is to get rid of

vibrations in the plates under moving mass. To achieve this, the actuators are added to the domain of the plate. A

performance index functional which measure the dynamic response of the system is given. The calculus of variation is used

for minimization of the performance index functional and the necessary conditions for the optimality are determined. A

numerical example is given for the applicability of control mechanism.

Keywords: Optimal control, plates, moving mass

References:

1. Iwan WD, Stah KJ. The response of an elastic disk with a moving mass system. Journal of Applied Mechanics 1973;40.

2. Cifuentes A, Lalapet S. A general method to determine the dynamic response of a plate to a moving mass. Computers &

Structures 1992;42(1).

3. Humar JL, Kashif AM. Dynamic response analysis of slab-type bridges. ASCE Journal of Structural Engineering 1995;121(1).

4. Saigal S, Agrawal OP, Stanisic MM. Influence of moving masses on rectangular plate dynamics. Ingenieur — Archiv 1987;57.

5. Rofooei, F. R., and Nikkhoo, A. (2009). Application of active piezoelectric patches in controlling the dynamic response of a

thin rectangular plate under a moving mass. International Journal of Solids and structures, 46(11-12), 2429-2443.

6. Yob, N., Ismail, K. A., Rojan, M. A., Othman, M. Z., and Zaidi, A. M. A. (2016). Quasi Static Axial Compression of Thin

Walled Aluminum Tubes: Analysis of Flow Stress in the Analytical Models. Modern Applied Science, 10(1), 34.





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64

A Numerical Approach to Active Damping of Beam-String System

Melih Cinar 1 and Aydin Secer 2

1,2Department of Mathematical Engineering, Yildiz Technical University,

[email protected],

[email protected]

Abstract

The control of vibrations in beam-string complex system is considered by applying piezoelectric patch actuators.

An optimization problem is to find the control voltage applied to the actuators with least control effort. The objective

functional is given as a weighted quadratic functional of the displacement and velocity and a penalty term which includes

expenditure of the actuators. The equation of the motion is transformed to a number of coupled ordinary differential

equations by using eigenfunction expansion and optimal control law is derived by using the variational theory. The

effectiveness of the method is demonstrated by a numerical example.

Keywords: Optimal control, beam, string

References:

1. F. Cheli and G. Diana, Vibrations in Continuous Systems, in Advanced Dynamics of Mechanical Systems. Springer

International Publishing, 2015, pp. 241–309.

2. Z. Oniszczuk, Transverse vibrations of the elastically connected rectangular double-membrane compound system, Journal of

Sound and Vibration, vol. 221, no. 2, pp. 235–250, 1999.

3. Z. Oniszczuk, Free transverse vibrations of an elastically connected rectangular simply supported double-plate complex

system, Journal of Sound and Vibration, vol. 236, no. 4, pp. 595–608, 2000.

4. Z. Oniszczuk, Free transverse vibrations of an elastically connected complex beam–string system, Journal of Sound and

Vibration, vol. 254, no. 4, pp. 703–715, 2002.

5. I. Kucuk and I. Sadek, Active vibration control of an elastically connected double-string continuous system, Journal of the

Franklin Institute, vol. 344, no. 5, pp. 684–697, 2007.

6. M. Razzaghi and S. Yousefi, Legendre wavelets method for the solution of nonlinear problems in the calculus of variations,

Mathematical and Computer Modelling, vol. 34, no. 1-2, pp. 4554, jul 2001.

7. F. Khellat and S. Yousefi, The linear Legendre mother wavelets operational matrix of integration and its application, Journal

of the Franklin Institute, vol. 343, no. 2, pp. 181190, mar 2006.





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Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis

Melike Keles 1, Serdal Pamuk 2

1,2Department of Mathematics, Kocaeli University,


Abstract

In this work we obtain the perturbation solutions of a mathematical model in tumor angiogenesis which is

originally presented in [1]. Our results show that the solutions we have obtained are in good agreement with the solutions

obtained by other methods.We also present our results in Matlab generated figures.

Keywords: Perturbation solutions, tumor angiogenesis, endothelial cell.

References:

1. H.A. Levine, B. D. Sleeman , M. Nilsen-Hamilton, A mathematical model for the roles of pericytes and macrophages in the

initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis, Mathematical Biosciences, 168 (2000),

77-115.




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Cyclic Codes over a Special Non-Chain Ring with Respect to the Homogeneous Weight

Merve Bulut Yilgor 1, Elif Segah Oztas 2 and Fatih Demirkale 3


[email protected], [email protected] 2 Department of Mathematics, Karamanoğlu Mehmetbey University

[email protected]

Abstract

Recently, several studies have been conducted to identify error-correcting codes over non-chain rings. Edgar et

al. [2] determined the structure of local non-chain rings of order 16. In [1], cyclic codes over local frobenius non-chain

rings of order 16 have been investigated. In this study, we determine generators of cyclic codes in a different way over a

special local frobenius non-chain ring of order 16. In addition, we define a Gray map over this ring with respect to the

homogeneous weight.

Keywords: Cyclic codes, Codes over rings, Homogeneous weight

References:

1. Dougherty, S.T., Kaya, A., Salturk, E. Cyclic codes over local frobenius rings of order 16. Adv. Math. Commun. 11(1), 99-

114 (2017)

2. Martinez-Moro, E., Szabo, S. On codes over local Frobenius non-chain rings of order 16. Contemp. Math. 634, 227-241 (2015)






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67

On Weak Biharmonic Generalized Rotation Surface in E4

Merve Harmanli 1, Kadri Arslan 2 and Betul Bulca 3

1Department of Mathematics, Institute of Natural and Applied Science, Bursa UludağUniversity,

[email protected] 2,3Department of Mathematics, Arts and Science Faculty, Bursa Uludağ University


Abstract

In this paper we investigate Weak biharmonic general rotation surfaces in Euclidean 4-space E⁴. We show that if a generalized

rotational surface of constant mean curvature is weak biharmonic then either it is minimal or a CMC-surface of E⁴. Further, we give the

necessary and sufficent conditions for Vranceanu rotation surface to become weak biharmonic.

Keywords: Generalized rotation surface, CMC surface, biharmonic, weak biharmonic.

References:

1. K. Arslan, B. Kılıç Bayram, B. Bulca, and G. Öztürk, Generalized Rotation Surfaces in E⁴. Results in Math. 61(2012), 315-

327

2. P. Baird and D. Kamissoko, On constructing biharmonic maps and metrics, Ann. Global Anal. Geom. 23(1) (2003), 65-75.

3. A. Balmu¸s, S. Montaldo, C. Oniciuc. Classification results for biharmonic submanifolds in spheres. Israel J. Math. 168

(2008), 201-220.

4. M. Barros and O.J. Garay, Euclidean Submanifolds with Jacobi mean curvature vector field. J. Geom. 58(1997), 15-25.

5. M. Barros, O.J. Garay, On submanifolds with harmonic mean curvature, Proc. Amer. Math. Soc. 129 (1995), 2545-2549.

6. B. Y. Chen, Geometry of Submanifols,. Dekker, New York(1973).

7. I. Dimitric, Submanifolds of Em with harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica 20 (1992), 53-65.

8. B. Kiliç, K. Arslan , Ü. Lumiste and C. Murathan, On weak biharmonic submanifolds and 2-parallelity. Diff. Geo. Dyn. Sys.

5(2003), 39-48.

9. S. T. Yau, Submanifolds with constant mean curvature, I, Amer. J. Math. 96 (1974), 346-366.





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Some geometric properties of Euler Totient sequence space

Merve Ilkhan 1 and Emrah Evren Kara 2


[email protected] 2Department of Mathematics, Düzce University,

[email protected]

Abstract

In this presentation, we examine some geometric properties of a newly introduced Banach sequence space. This space is constructed by means of the domain of Euler Totient matrix. Keywords: Euler Totient function, sequence spaces, Banach-Saks property.

References:

1. E. Savaş, V. Karakaya, N. Şimşek, Some-type new sequence spaces and their geometric properties, Abstract and Applied

Analysis, 2009, Article ID 696971, 12 pages.

2. N. Şimşek, E. Savaş, V. Karakaya, On geometrical properties of some Banach spaces, Applied Mathematics & Information

Sciences, 7(1) (2013), 295-300.

3. M. Karakas, M. Çınar, M Et, Some geometric properties of a new sequence space, Journal of Computational Analysis and

Applications, 15(1) (2013), 23-31.

4. M. İlkhan, E. E. Kara, A new Banach space defined by Euler totient matrix operator, Operators and Matrices (in press).




https://scholar.google.com.tr/citations?user=1Ac0LucAAAAJ&hl=tr&oi=sra

https://scholar.google.com.tr/citations?user=w1lqxXMAAAAJ&hl=tr&oi=sra

https://scholar.google.com.tr/citations?user=eFCn5H8AAAAJ&hl=tr&oi=sra

https://www.hindawi.com/journals/aaa/2009/696971/abs/

https://scholar.google.com.tr/citations?user=eFCn5H8AAAAJ&hl=tr&oi=sra

https://scholar.google.com.tr/citations?user=1Ac0LucAAAAJ&hl=tr&oi=sra

https://scholar.google.com.tr/citations?user=w1lqxXMAAAAJ&hl=tr&oi=sra

https://scholar.google.com.tr/citations?user=0TGMDEcAAAAJ&hl=tr&oi=sra

https://scholar.google.com.tr/citations?user=wiWl1w8AAAAJ&hl=tr&oi=sra

https://scholar.google.com.tr/citations?user=6uSWHVIAAAAJ&hl=tr&oi=sra

https://www.researchgate.net/profile/Javad_Balooee2/publication/268071872_Fixed_Point_Theorems_for_Set-valued_Contractions_in_Ordered_Cone_Metric_Spaces/links/54737fde0cf29afed60f557d.pdf#page=23


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Euler Totient sequence spaces in generalized Orlicz space

Merve Ilkhan 1 and Emrah Evren Kara 2


[email protected] 2Department of Mathematics, Düzce University,

[email protected]

Abstract

In this presentation, we introduce the Euler Totient sequence spaces consisting of certain sequences in generalized

Orlicz space 𝑳𝑴. By using the Luxemburg norm, we examine some topological properties of the spaces.

Keywords:Orlicz space, Euler Totient function, Luxemburg norm, Lebesgue measurable function.

References:

1. J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10(3) (1971), 379- 390.

2. I. Bala, On Cesàro sequence space defined by an Orlicz function, Commun. Math. Appl. 3(2) (2012), 197-204.

3. H. Haryadi, S. Supama, A. Zulijanto, The Cesaro sequence spaces defined on a generalized Orlicz space, Far East J. Math.

Sci. 101(9) (2017), 1897-1911.

4. H. Haryadi, S. Supama, A. Zulijanto, A generalization of Cesaro sequence spaces in the Orlicz space, J. Phys. Conf. Ser. 1008

(2018), 012020.





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70

On Some Subspace of Grand-Lebesgue Space

Yusuf Zeren 1, Migdad Ismailov 2 and Selim Yavuz 3


[email protected] 2 Baku State University,


[email protected] 3Yildiz TechnicalUniversity

[email protected]

Abstract

Based on shift operator, we define the subspace );() pG of the space );() pL , where continuous functions

are dense, and study some properties of the functions belonging to this space. We establish the basicity of exponential

system Zne int

for );() pG and the basicity of trigonometric systems Nnnt sin and 0

cos Nnnt for );0() pG .

Keywords: grand Lebesgue space, exponential system, minimality, density, basis.

Reference:

1- Capone, C., Formica, M. R., & Giova, R. (2013). Grand Lebesgue spaces with respect to measurable functions.

Nonlinear Analysis: Theory, Methods & Applications, 85, 125-131.

2- Fiorenza, A. (2000). Duality and reflexivity in grand Lebesgue spaces. Collectanea Mathematica, 51(2), 131-148.

3- Umarkhadzhiev, S. M. (2014). Generalization of the notion of grand Lebesgue space. Russian Mathematics, 58(4),

35-43.






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71

On Spectral Properties of Second Order Discontinuous Differential Operator in 𝑳𝒑)⊕ℂ

Yusuf Zeren 1, Migdad Ismailov 2 and Fatih Sirin 3


[email protected] 2Baku State University,


[email protected] 3Istanbul Aydin University

[email protected]

Abstract

We consider second order discontinuous differential operator with spectral parameter in the boundary condition

and study basic properties of eigenfucntions of this problem in spaces 𝐿𝑝)⊕ℂ, 1 < 𝑝 < ∞.

Keywords: grand Lebesgue space, spectral properties, grand sobolev spaces, basicity

Reference:

1- Gasymov, Telman B. , and Shakhrizad J. Mammadova. “On convergence of spectral expansions for one

discontinuous problem with spectral parameter in the boundary condition.” Trans. NAS Azerb 26.4 (2006): 103-

116.

2- Kokilashvili, Vakhtang, and Alexander Meskhi. "A note on the boundedness of the Hilbert transform in weighted

grand Lebesgue spaces." Georgian Mathematical Journal 16.3 (2009): 547-551.






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72

Interval Analysis Of Natural Frequency Of Composite Beam Of Which Material Having Local

Curvature

Muhammed Furkan Simsek 1, Zafer Kutug 2 and Ayse Erdolen 3

1Graduate School of Science and Engineering, Yildiz Technical University

[email protected] 2Department of Civil Engineering, Yildiz Technical University


[email protected]

Abstract

Composite materials are increasingly becoming common in important industries such as health, construction,

aviation, and ship building. Composites have high strength obtained by combining two or more different materials with the

result of mechanical or chemical processes as reinforcement and filling material. During the preparation of composite

materials, local defects may occur in the structure of the fibers and plates resulting from a number of incompatibilities due

to the technological processes used. The plates in layered composites, that are constituted of a material having woven fabric

threads, can be given as an example. Although it is very common to investigate the mechanical and technical properties of

such composite materials, it naturally involves challenging mathematical equations resulting from their models. In this

study, natural vibration frequencies are calculated for a strip-plate (beam) having local curves in its layers by using interval

analysis method. Interval analysis is a method that gives the exact range of the values which are obtained to determine if

geometrical and dynamic values are given in a specific range. The results obtained by the interval analysis, applied for the

first time to such a problem, were found close enough to the results obtained in the literature.

Keywords: composite, natural frequency, interval analysis, vibration.

References: 1. S.D. Akbarov, The influence of the forms of the small-sacale local curving in the laminated composites structure on the distribution

of self-equilibrated stresses, Prikl. Mech. 24 (1988) 30-37 (in Russian)

2. R.E. Moore, Methods and Applications of Interval Analysis, (1979) Philadelphi, PA:SIAM.

3. D.J. Gorman, Free vibration analysis of rectangular plates, (1982), Elsevier Publications

4. Z. Kütüğ, Natural vibration of beam-strip fabricated from a composite material with small-scale curvings in structure, Mechanics of

Composite Materials (1996) 32, 502-512.






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Developing a STEM Module with an Engineering Design Process

Murat Akarsu 1

1Department of Pre-School Education, Agrı Ibrahim Cecen University,

[email protected]

Abstract

According to The North Central Regional Educational Laboratory (NCREL), 21st-century education model should

include 21st-century skills such as Digital-age literacy, Inventive thinking, and Effective Communication. Students need

to improve their Digital-age literacy to have effective communications skills, to analyze and interpret the data, to do task

management and task prioritization, and to solve problems. Inventive thinking is important for students to produce

multiple solutions in design activities. During this process, students can manage complexities, and take risks to develop

high-level thinking. Effective Communication provides opportunities for students to increase social responsibilities, have

interactive communication, and build successful teamwork. To develop 21st-century skills for students, STEM (science,

technology, engineering and mathematics) education has a vital role. The purpose of this study is to explain how to

develop A STEM module with an Engineering Design Process (EDP). According to Moore et al., (2013), an effective

STEM module should involve engineering design tasks, student-centered pedagogies, opportunities learn from failure

and redesign, evidence based reasoning, and communication and teamwork skills

Keywords: STEM, engineering design process, STEM integration

References

[1] Moore, T. J., & Glancy, A. W., & Tank, K. M., & Kersten, J. A., & Stohlmann, M. S., & Ntow, F. D., & Smith, K. A.

(2013, June), A Framework for Implementing Quality K-12 Engineering Education Paper presented at 2013 ASEE

Annual Conference & Exposition, Atlanta, Georgia. https://peer.asee.org/19060



https://peer.asee.org/19060


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In-service Teachers’ Understanding of Geometric Reflections: Motion and Mapping view

Murat Akarsu 1, Selim Yavuz 2, Fatih Sirin 3

1Department of Pre-School Education, Agrı Ibrahim Cecen University,


[email protected] 3Department of Computer Programming, Istanbul Aydin University,

[email protected]

Abstract

Among four main transformations (translations, reflections, rotations, and dilations), reflections, most familiar to

students, are an important milestone before learning other transformations. Students are supposed to understand functions

and congruence from reflections and know how to describe the relationship between the pre-image and the final image

and further prove the congruent properties. This study investigates four in-service mathematics teachers’ understanding

of geometric reflection in terms of motion and a mapping view. A motion view is necessary to develop a mapping view

of geometric reflection. To be more specific, in the process of the geometric reflection, in-service teachers need to have a

mapping view of reflection line, domain and plane (Flanagan, 2006). However, it is not clear how in-service teachers’

motion view of geometric reflection evolves to a mapping view of geometric reflection. A clinical methodology was used

to examine in-service teachers’ mental structures of geometric reflections in terms of a motion view and a mapping view,

and how their mental structures of motion view evolve to have mental structures of mapping view. Transcript audio

records, videos, and written work were collected from four case studies. Ongoing and retrospective analysis was used to

analyze data using Dubinsky’s action, process, object and schema (APOS) framework. The results of four case studies

indicated that all four in-service teachers had a motion view of geometric reflections at the end of the first interview and

they reached the mapping view of geometric reflections at the end of the third interview. The results also indicated that

perpendicularity and equidistance properties of geometric reflections, reflection line, domain, plane, and type of figures

(circle, semicircle, interior and exterior points of the figures) are crucial to moving from motion view of geometric

reflections to mapping view of geometric reflections.

Keywords: reflections, in-service teachers, motion view, mapping view.

References

1. Flanagan, K. A. (2001). High school students’ understandings of geometric transformations in the context of a

technological environment. (Doctoral Dissertation, The Pennsylvania State University, 2001). Dissertation

Abstracts International: AAI3020450.






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75

A Bilinear Hirota-Kimura Discretization of the Motion of a Rigid Body in an Ideal Fluid

Zerrin Ozcubukcu 1 , Murat Turhan 2 , Serpil Uslu 3 and Oya Baykal Unal 4

Yildiz Technical University, Faculty of Science and Letters, 1,2,3,4Department of Mathematics, Davutpaşa Campus, Esenler-Istanbul-Turkey

[email protected], [email protected], [email protected] and [email protected]

Abstract

The Clebsch system is one of the few classical examples of rigid bodies in an ideal fluid whose equations of

motion are known to be integrable and given by the following system:

{

�̇� = 𝐱 × 𝜕𝐻

𝜕𝒑

�̇� = 𝐱 × 𝜕𝐻

𝜕𝒙+ 𝒑 ×

𝜕𝐻

𝜕𝒑

where 𝐻 ∈ 𝐶∞(ℝ6, ℝ) is a quadratic polynomial in 𝐱 and 𝒑.

Integrable systems are nonlinear differential equations which ‘in principle’ can be solved analytically. This means

that the solution can be reduced to a finite number of algebraic operations and integrations. Such systems are very rare -

most nonlinear differential equations admit chaotic behaviour and no explicit solutions can be written down. Integrable

systems nevertheless lead to a very interesting mathematics ranging from differential geometry and complex analysis to

quantum field theory and fluid dynamics.

Concerning Clebsch system, the explicit solution of its equations of motion, however, is particularly hard, and it

has defeated many attempts in the past. Discrete systems are a vast undeveloped area of study. Recent progress in integrable

discrete systems includes the discovering of remarkable relationships in otherwise unrelated areas of research such as

numerical algorithms, discrete geometry, cellular automaton, and quantum integrable systems. In this work we present a

different type of discrete solutions. Applying bilinear method and using the gauge invariance and the time reversibility of

the equations, we get gauge-invariant bilinear difference equations. Finally, we derive the explicit discrete system by

considering bilinear transformation method and present sufficient number of the discrete conserved quantities for

integrability. Bilinear discreteziaton leads to the discovery of four independent integrals, namely conserved quantities, of

motion of the discrete-time system, which turn out to be much more complicated than the integrals of the continuous-time

system.

Keywords: Discretization, rigid body, bilinear method, gauge invariance.

References:

1. Abraham, R., Marsden, J.E. and Ratiu, T.S., Manifolds, Tensor Analysis, and Applications, v.75 of Applied Mathematical

Sciences, Springer-Verlag, (1988).

2. http://www.asir.org

3. Kowalevski, S. [1889], Sur le problème de la rotation d’un corps solide autour d’un point fixe, Acta Math. 12, 177–232.

4. Marsden, J.E. and Ratiu, T.S.: Introduction to Mechanics and Symmetry, Texts in Applied Mathematics, Second Edition,

second printing, 2017, Springer-Verlag.

5. Lesser, M., The Analysis of Complex Nonlinear Mechanical Systems: A Computer Algebra Assisted Approach, World

Scientific, Series A, Vol.17, (1995).

6. Hirota, R., Kimura, K. and Yahagi, H., How to find the conserved quantities of nonlinear discrete equations,

J.Phys.A:Math.Gen. 34, 10377–10386, (2001).

7. Zhivkov, A., Christov, O., Effective solutions of Clebsch and C. Neumann systems, Sitzungsberichte der Berliner

Mathematischen Gesellschaft, (2001).

8. Perelomov, A.M., A few remarks about integrability of the equations of motion of a rigid body in ideal fluid, Phys.Lett.A 80,

no:2-3, 156–158, (1980).






http://www.asir.org/


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76

Mathematical Behavior of Solutions of p-Laplacian Equation with Logarithmic Source Term

Erhan Piskin 1 and Nazli Irkil 2 1,2Department of Mathematics, Dicle University


Abstract

In this presentation, we consider nonnlinear evolution equation with nonlinear 𝛁(|𝛁|𝒑−𝟐𝛁𝐮) term and logarithmic

nonlinearity source term. By using Galerkin method, logarithmic Sobolev inequality and potential well method we obtain

the existence and nonexistence of solutions for logarithmic wave equation [1, 2, 3].

Keywords: Local existence, decay estimate, growth of solution

References:

1. C., Yang and C., Liu, Initial boundary value problem for a mixed Pseudo-Parabolic p-Laplacian type equation with logarithmic

nonlinearity, Electronic Journal of Differantial Equation, No. 116, (2018) 1–19.

2. V., Padron, Effect of aggregation on population recovery modeled by a forward-backward pseudo parabolic equation, Trans.

Amer. Math. Soc., 356(7) (2004), 2739-2756.

3. C.N., Le and X.T., Le, Global solution and blow up for a Class of p-Laplacian evolution equations with logarithmic

nonlinearity, Acta. Appl. Math (2017) 149-169.





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Mathematical Behavior of Solutions of Fourth-Order Hyperbolic Equation with Logarithmic

Source Term

Erhan Piskin 1and Nazli Irkil 2 1Department of Mathematics, Dicle University

[email protected], 2Department of Mathematics, Institute of Natural and Applied Sciences, Dicle University

[email protected]

Abstract

In this presantation, we consider hyperbolic type wave equation with logarithmic nonlinearity. We use Galerkin

method and potential depth to obtain the global existence of solutions. The logarithmic nonlinear source term is related with

many branches of physics. Cause of this is interest in it occurs naturally in inflation cosmology and super-symmetric field

theories, quantum mechanics, nuclear physics [1,2,3].

Keywords: Local existence, decay estimate, growth of solution

References:

1. Buljan, H., Siber, A., Soljacic, M., Schwartz, T., Segev, M., Christodoulides, D. N.:

Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media,

Phys. Rev. E (3) 68 (2003).

2. M.M. Al-Gharabli, S.A. Messaoudi, The existence and the asymptotic behavior of a plate equation with

frictional damping and a logarithmic source term. J. Math. Anal. Appl., vol. 454 (2017) 1114-1128.

3. Zhang, H.W., Liu, G.W., Hu, Q.Y.: Asymptotic Behavior for a Class of Logarithmic Wave Equations with

Linear Damping. Appl Math Optim DOI 10.1007/s00245-017-9423-3(2017)





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78

Solutions of Some Generalized Pell Equations with Recurrence Relations

Nazlihan Erten 1and Murat Alan 2


[email protected]

[email protected]

Abstract

Let d>1 be a positive non-square integer and N be any fixed positive integer then the equation 2 2x dy N

is called a Generalized Pell Equation. In this study we consider the recurrence relations between the solutions of this

equation when the parameter N is of the form tp for some fixed prime p.

Keywords: Pell Equations, Generalized Pell Equations

References:

1. K. Rosen , Elementary Number Theory and Its Applications.

2. K. Matthews, The Diophantine equation 2 2x Dy N ,D>0 , Exposition. Math. 18 (2000) 323–331.





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79

Health Efficiency Measurement In Turkey By Using Data Envelopment Analysis

Nedim Ertugay 1, Zulal Tuzuner 2 and Hasan Bal 3

1Department of Statisticss, Gazi University,

[email protected] 2Department of Statisticss, Gazi University,

[email protected] 3Department of Statisticss, Gazi University

[email protected]

Abstract A performance indicator of the relative activity measurements are classified into two groups, parametric and

nonparametric methods. Nonparametric methods measure the distance between the value of the efficiency obtained from

the calculation and the distance from the efficiency limit by using techniques of linear programming. Data Envelopment

Analysis (DEA) which is frequently used in nonparametric measurement methods. Data Envelopment Analysis is a method

used to measure the relative effectiveness of economic or non-profit organizations that convert the input called the decision-

making unit into output.

In this study, health performances of provinces were examined by using statistical yearbook published by Ministry of

Health. CCR and BCC models, which are the basic models of data envelopment analysis, were examined according to the

cases of constant returns to scale and variable returns to scale.

Keywords: Data Envelopment Analysis, health performance, efficiency, Turkey

References: 1. Charnes A., Cooper W.W. and Rhodes E. Measuring the Efficiency of Decision Making Units, European Journal of Operational

Research, vol.2, s.429-444 (1978).

2. Banker, R.D., Charnes A., Cooper, W.W., “Some models for estimating technical and scale inefficiencies in data envelopment

analysis”, Management Science, 30 (9): 1078-1092 (1984).

3. Subhash C.R. . Data Envelopment Analysis Theory and Techniques for Economics and Operation Research. New York:Cambridge

University Press, (2004).

4. 2017 health yearbook, https://www.saglik.gov.tr/TR,11588/istatistik-yilliklari.html






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On the Control of the Seven-Mode Truncation System of the 2-d Navier-Sokes Equations

Nejib Smaoui 1, Alaa El-Khadri 2and Mohamed Zribi 3

1,2Department of Mathematics, Kuwait University, Kuwait

[email protected]

[email protected] 3Department of Electrical Engineering, Kuwait University, Kuwait

[email protected]

Abstract

The adaptive control problem of a nonlinear dynamical system obtained by a truncation of the two dimensional

(2-d) Navier-Stokes (N-S) equations with periodic boundary conditions and a sinusoidal external force along the x-direction

is considered. First, the dynamics of the 2-d Navier-Stokes equations represented by a nonlinear dynamical system of seven

ordinary differential equations (ODEs) of a laminar steady state flow regime and a periodic flow regime are analyzed.

Then, an adaptive control is designed and applied on the system of seven ODEs to control its dynamics either to a steady-

state regime or to a periodic regime. Finally, numerical simulations are undertaken to show the effectiveness of the designed

control.

Keywords: Two-dimensional Navier-Stokes equations; Bifurcations; Dynamical systems; Control.

References:

1. Franceschini, V., and Tebaldi, C., A seven-mode truncation of the plane incompressible Navier-Stokes equations, J. Stat. Phys.,

25 (3), 397-417, 1981.

2. Armbruster, D., Nicolaenko, B., Smaoui, N., and Chossat, P., Symmetries and dynamics for

2-d Navier-Stokes flow, Physica D, 95, 81-93, 1996.

3. Chen, Z. and Price, W. Chaotic behavior of a Galerkin model of a two-dimensional flow, Chaos, 14 (4), 1056-68, 2004.

4. Smaoui, N., and Zribi, M. On the Control of the Chaotic Attractors of the 2-d Navier-Stokes Equations. Chaos, Vol. 27, 033111,

2017.

5. Smaoui, N., Symmetries, Dynamics and Control for the 2-d Kolmogorov Flow. Complexity, Vol. 2018, 1-15, 2018.






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81

On Generalization Sister Celine’s Polynomials

Nejla Ozmen Department of Mathematics, Düzce University,

[email protected]

Abstract

In this research, we esteblish some properties for the generalization Sister Celine’s polynomials. We derive

various families of multilinear and multilateral generating functions for a family of generalization Sister Celine’s

polynomials.

Keywords: Generalization Sister Celine’s polynomials, multilinear and multilateral generating functions, recurrence

relations.

References:

1. Srivastava, H. M. and Manocha, H. L. (1984). A Trease on Generating Functions, Halsted Press, John Wiley and Sons, New

York.

2. Ahmad, K., Kamarujjama, M. and Ghayasuddin, M. (2016). On Generalization of Sister Celine’s Polynomials. Palestine

Journal of Mathematics, 5(1), 105-110.

3. Fasenmyer, Sister, M. Celine, (1947). Some generalized hypergeometric polynomials. Bulletin of the American Society, 53(8),

806-812.




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82

A note on Shively’s Pseudo-Laguerre Polynomials

Nejla Ozmen

Department of Mathematics, Düzce University,

[email protected]

Abstract

In this research, we esteblish some properties for the Shively’s Pseudo-Laguerre polynomials. We derive various

families of multilinear and multilateral generating functions for a family of Shively’s Pseudo-Laguerre polynomials.

Keywords: Shively’s Pseudo-Laguerre polynomials, multilinear and multilateral generating functions, recurrence

relations.

References:

1. Srivastava, H. M. and Manocha, H. L. (1984). A Trease on Generating Functions, Halsted Press, John Wiley and Sons, New

York.

2. Rainville, E. D. (1971). Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing

Company, Bronx, New York.

3. Szegö, G. (1975). Orthogonal Polynomials, Fourth ed., American Mathematical Society, Providence, Rhode Island.

4. Srivastava, H. M., Lin, S.-D., Liu, S.-J., Lu, H.-C. (2012). Integral representations for the Lagrange polynomials, Shivelys

pseudo-Laguerre polynomials, and the generalized bessel polynomials. Russ J Math Phys, 19 (1), 121-130.

5. Jana, R.K., Salehbhai, I.A., Shukla, A.K. (2012). Shivley’s polynomials of two variables. Int. J. Math. Anal., 6 (36), 1757-

1762.

6. Özmen, N. and Erkus-Duman, E. (2018). Some families of generating functions for the generalized Cesaro polynomials. J.

Comput. Anal. Appl., 25(4), 670-683.




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83

Analysis of Some Features of Daily Transportation Movements in Istanbul by Spatial

Statistics1

Nuran Kose Cerci 1 and Ibrahim Demir 2

1Science Institute, Yildiz Technical University,

[email protected] 2 Department of Statistics, Yildiz Technical University

[email protected]

Abstract

Transportation problems all around the world are aimed to be solved with more planned and effective investments.

Within the scope of the study, the data of the Istanbul Metropolitan Area Urban Transportation Master Plan Household

Survey, which was carried out in 2006 for this purpose, was utilized. Pedestrian and vehicle travel rates have been examined

by means of global and local spatial statistics. According to the results of the study, distributions of pedestrian and vehicle

trip rates in Istanbul are not random, but are observed to have spatial autocorrelation (Global Moran I). Adopting Anselin

Local Moran I statistics brought forth clustered values in 5 districts (Esenler, Gaziosmanpaşa, Beşiktaş, Kadıköy and

Üsküdar) and outlier values in Başakşehir.

Keywords: Spatial statistics, Spatial autocorrelation (Moran I), Cluster and outlier Analysis (Anselin Locak Moran I),

Household survey

References:

1. Anselin, L. (1995), Local indicators of spatial association-LISA, Geographical Analysis, 27, 93–115.

2. Çubukçu, K.M. (2014), Planlamada ve Coğrafyada Temel İstatistik ve Mekansal İstatistik, Ankara: Nobel.

3. İstanbul Urban Metropolitan Area Urban Transport Master Plan. (2011). Istanbul Metropolitan Municipality.

4. Sánchez-Díaz, I., Holguín-Veras, J. and Wang, X. (2016), An exploratory analysis of spatial effects on freight trip attraction,

Journal of Transportation. Vol. 43(1), 177-196.

1

This study was produced from the master thesis study "Analysis of Daily Transportation Movements in Istanbul by Spatial Statistical

Method".





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84

Interval Analysis Of Natural Frequency Of Composite Beam Of Which Material Having

Periodical Curvings

Orhan Senyener 1, Zafer Kutug 2 and Ayse Erdolen 3

1Graduate School of Science and Engineering, Yildiz Technical University



[email protected]

Abstract

Composite materials are increasingly becoming common in important industries such as health, construction,

aviation, and ship building. Composites have high strength obtained by combining two or more different materials with the

result of mechanical or chemical processes as reinforcement and filling material. Due to the designing of composite

materials, periodical curvings occur in the structure of the fibers and plates. The plates in layered composites, that are

constituted of a material having woven fabric threads, can be given as an example. Although it is very common to

investigate the mechanical and technical properties of such composite

materials, it naturally involves challenging mathematical equations resulting from their models. In this study, natural

vibration frequencies are calculated for a strip-plate (beam) having periodical curvings in its layers by using interval

analysis method. Interval analysis is a method that gives the exact range of the values which are obtained to determine if

geometrical and dynamic values are given in a specific range. The results obtained by the interval analysis, applied for the

first time to such a problem, were found close enough to the results obtained in the literature.

Keywords: composite, natural frequency, interval analysis, vibration.

References: 1. S.D. Akbarov, On the determination of normalized nonlinear mechanical properties of composite materials with periodically curved layers, Int. J. Solids and Structures (1995) 32(21)-3129-3143. 2. R.E. Moore, Methods and Applications of Interval Analysis, (1979) Philadelphi, PA:SIAM. 3. D.J. Gorman, Free vibration analysis of rectangular plates, (1982), Elsevier Publications 4. Z. Kütüğ, Natural vibration of beam-strip fabricated from a composite material with small-scale curvings in structure, Mechanics of Composite Materials (1996) 32, 502-512.






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85

Lie Point Symmetries of Difference Equation

Ozgur Yildirim 1 and Sumeyra Caglak 2



[email protected]

Abstract

A method for obtaining the Lie point symmetries of difference schemes is presented. The invariant discretization

of difference schemes is investigated. The symmetry transformations that leave the solution set of the difference scheme

invariantis presented.

Keywords: Partial difference equations, Symmetry analysis.

References:

1. Yildirim O., Caglak S., “Lie point symmetries of difference equation for nonlinear sine-Gordon equation”, Phys. Scr. ,

doi.org/10.1088/1402-4896/ab1180, 2019.

2. Baumann G., Symmetry Analysis of Differential Equations with Mathematica (New York:

3. Springer), 2000.

4. Ibragimov N. H., CRC Handbook of Lie Group Analysis of Differential Equations. Vol. 1.

W. F. Ames et al., CRC Press, Boca Raton, FL, 1994.

5. Levi D, Tremblay S and Winternitz P., Lie point symmetries of difference equations and

lattices J. Phys.A: Math. Gen. 33 8507, 2000.

6. Ovsiannikov L V, Group Analysis of Differential Equations, Academic Press, New York,

1982.





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86

Some Pascal Spaces of Difference Sequences Spaces of Order m

Saadettin Aydin 1 and Harun Polat 2

1Kilis 7 Aralık University, Faculty of Education, Department of Mathematics Education, Kilis, Turkey

saadettinaydı[email protected] 2Muş Alparslan Universities, Faculty of Arts and Sciences, Department of Mathematics

[email protected]

Abstract

The main purpose of this article is to introduce the new sequence spaces )( mp , )( m

cp and )(0

mp which are

consist of all sequences whose thm order differences are in the Pascal sequence spaces p , cp and 0p , respectively. Furthermore,

the bases of the new difference sequence spaces )( m

cp and )(0

mp , and the α-, β- and γ-duals of the new difference sequence

spaces )( mp , )( m

cp and )(0

mp have been determined. Finally, the necessary and sufficient conditions on an infinite

matrix belonging to the classes ( )( m

cp : l ) and ( l : c) are obtained.

Keywords: Pascal difference sequence spaces, difference operator of order m, α-, β- and γ-duals; Matrix mappings.

References:

1. G. H. Lawden, Pascal matrices, Mathematical Gazette, 56 (398) (1972), 325-327.

2. W.H. Ruckle Sequence spaces Pitman Publishing, Toronto (1981).

3. H. Kızmaz, On certain sequence space, Canad. Math. Bull. 24(2) (1981), 169-176.

4. R. Brawer, Potenzen der Pascal matrix und eine Identitat der Kombinatorik, Elem. der Math. 45 (1990), 107-110.

5. A. Edelman and G. Strang, Pascal Matrices, The Mathematical Association of America, Monthly 111 (2004), 189-197.


mailto:saadettinaydı[email protected]



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87

Coefficient bounds for a subclass of m-fold symmetric bi-univalent functions involving

Hadamard product and differential operator

F. Muge Sakar 1, S. Melike Aydogan 2 and Sahsene Altinkaya 3

1Department of Business Administration, Batman University, Batman, Turkey,

[email protected] 2Department of Mathematics, Istanbul Technical University, Istanbul, Turkey,

[email protected] 3Department of Mathematics, Bursa Uludag University, Bursa, Turkey,

[email protected]

Abstract In this study, we construct a new subclass of m-fold symmetric bi-univalent functions using by Hadamard product and generalized

Salagean differential operator in the open unit disk {z : 1}.U z

We establish upper bounds for the coefficients 1ma and

2 1ma belonging to this new class. The results presented here generalize some of the earlier studies

Keywords: Coefficient estimates, bi-univalent functions, m-fold symmetric functions.

References: 1. F. M. Al-Oboudi, On univalent functions defined by a generalized Sǎlǎgean operator, Int. J. Math. Math. Sci., 27 (2004) 1429-

1436.

2. D.A. Brannan, T.S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babeş-Bolyai Mathematica, 31

(1986) 70–77.

3. S. Bulut, Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions, Turkish J. Math.,

40 (2016) 1386 – 1397.

4. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 1983.

5. S.G. Hamidi, J.M. Jahangiri, Unpredictability of the coefficients of m-fold symmetric bi-starlike functions, Internat. J. Math.,

25 (2014) 1-8.

6. M. Lewin, On a coefficient problem for bi-univalent functions, Proceedings of the American Mathematical Society, 18 (1967)

63–68.

7. E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function

in 1z , Arch. Rational Mech. Anal., 32 (1969) 100-112.

8. Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Göttingen, 1975.

Acknowledgement: The work presented here is supported by Batman University Scientific Research Project

Coordination Unit. Project Number: BTUBAP2018-IIBF-2.




Istanbul / TURKEY


88

A Study on balance states, step counts for state change and absorptive situations in stochastic

processes

Servet Es Department of Mathematics, Yildiz Technical University

[email protected]

Abstract In the stochastic processes that take an important place in decision making, especially in the market and in the

process of determining the market share, I present a statement examing the balance status, the number of steps for change

of situation and the absorptive stituations. this paper is important and will contribute in similar fields of science, especially

in mathematics, statistics, industry, business and marketing.

Keywords: Absorptive cases, steady state, step counts for status change

References: 1. Samuel Karlin, Howard M. Taylor. A first course in stochastic prosses. Second edition. 1975, New York. ISBN -0-12-398552-8.

2. Ximi Hang- wai-ki chiains-Micheal K. Ng-Tak-kuensiv, Markov Chains, Springer, ISBN 978-1-4614-6311-5, 2013, New York.




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89

A Method for Creating Mortality Tables in the Actuary.

Servet Es Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract My aim in this paper, parallel developments in the life and health insurance to the development of the insurance

to the development of the insurance sector in the Turkey has increased in the recent years in the competition. Need to

maximize profit and minimize cost. The costumer should offer the cheapest premium and minimize cost. The costumer

should offer the cheapest premium and the highest salary and compensation. In the order to solve this problem, it is

necessary to determine the mortality table used in the calculation of the premium and compensation. In this report I will a

propose and illustrate a method to determine the mortality table.

Keywords: Mortality tables, Actuary, Life insurance.

References: 1. Shao and shao , Mathematics for management and finance, Eight Edition, International Thomson Publeshing .1998 , ISBN -0-538-

87099-0 .

2. Nilgün Moralı ,Hayat Sigortaları için Aktüeryal Teknikler . Gesid yayınları 1997 İzmir .

3. Kenan Ural, Yaşam Sigortalarının Aktüeryal Prensipleri. Aktüerler Derneği Yayını, 1994, İstanbul.

4. Marek Capinski and Thomasz Zastavniciak . Mathematics for Finance An Introdiction to Financial Engineering . Springer, 2003,

London .




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90

Motorcycle Accident Model Prediction by Approaching Generalized Linear Model

Sobri Abusini Department of Mathematics, Brawijaya University, Malang, Indonesia

[email protected]

Abstract WHO (World Health Organization) monitors that road traffic accidents in the world is very high, approximately

1.2 million people deaths and over 30 million injured/ disabled per year. Eighty five percent of traffic accidents motorcyclist

died occurring in developing countries means the rate of motorcyclist as dominant victims. Several factors influence road

traffic accidents, such as road geometry, traffic, human, vehicle and environment. Currently, insufficient studies related to

motorcycle accident model considering combination of those factors were conducted. By employing the Generalized Linear

Model (GLM) to set up motorcycle accident model, this research focuses on serious crash involving motorcyclist as a

victim. Motorcycle accident data was collected for several years occurred in Malang City, East Java Province. The results

from the analysis of statistical test are found out that traffic flow, the number of road lanes, shoulder width and speed have

the effects on the number of motorcycle accidents. The combination of traffic factors and road geometry should be

considered in order to minimize the number of motorcycle accidents in Malang City. Therefore, safety program related to

limiting speed in order to decrease motorcycle accidents is required as well as the improvement of the number of road lanes

and shoulder width should be considered by the local government.

Keywords: accident, motorcycle, model, geometric road.

References: 1. Aitkin, M., Anderson, D., Francis. B. and Hindle, J. (1989), Statistical Modelling in GLIM, Clarendon Press, Oxpord,

England.

2. Conover, W.J., 1999, Practical Nonparametric Statistics, Thir Edition, John Wiley & Sons, Inc. Texas Tech University,

New York.

3. Francesco Russo and Antonio Comi, A modelling System to Link end-consumers and Distribution Logistics, European

Transport n.28 (2004) : 6-19, Departement of Computer Science, Mathematics, Elektronics and Transportation,

University Mediterranea of Reggio Calabria.

4. Ghozali,I., 2006, Multivariate Analysis Application with Program SPSS, Publisher Diponegoro University, Semarang.

5. J. D. Ortuzar dan L. G. Wilumsen, (1994), Modelling Transport, John Wiley & Sons, New York – Singapura.




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91

The Existence of Positive Solutions and a Lyapunov type Inequality for Boundary Value

Problems of the Fractional Caputo-Fabrizio Di_erential Equations

Suayip Toprakseven 1 1Faculty of Engineering, Department of Computer Science,

Artvin Çoruh University, Artvin, 08100, Turkey,

[email protected]

Abstract

In this paper, the existence of the positive solutions for boundary value problems of the nonlinear fractional

Caputo-Fabrizio di_erential equation have been has been presented. By using the fixed point theorem on a normal cone

and the properties of the associated Green function, we construct two monotone iterative sequences that converge to the

solutions of the problem. Additionally, we derive a Lyapunov-type inequality for the fractional boundary value problem

of the Caputo-Fabrizio di_erential equation with nonlocal boundary condition. Using this result, we also show

nonexistence of some fractional boundary value problem.

Keywords: Lyapunov's inequality; Fractional Caputo-Fabrizio derivative, Green's function; Positive solution, Fixed

point.

References:

1. KS. Miller, B. Ross, (Eds.), An introduction to the fractional cxalculus and fractional differential equations,

John Wiley, NY 1993.

2. I. Podlubny, Fractional di_erential equations, Academic Press, New York 1999.

3. A.A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations,

North-Holland Mathematical Studies, Amsterdam, 2006.

4. M. Caputo, M. Fabrizio, A New Definition of Fractional Derivative without Singular Kernel, Progr. Fract. Di_er.

Appl., 1:1 (2015), 1-13.

5. J. Losada, J.J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Di_er. Appl.,

1 (2016), 87-92.




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92

A Padé-Legendre Reconstruction for Difference Solutions of Shock Behaviour

Huseyin Tunc 1, Murat Sari 2, Sufii Hamad Mussa 3 1,2,3Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract

This work considers some finite difference solutions of PDEs governing shock behaviour and to vanish unwanted

oscillations a Padé-Legendre reconstruction is introduced. Almost discontinuous behaviours are correctly captured by the

current method. To illustrate the efficiency of the present approach, advection dominated cases of the advection-diffusion

mechanisms are considered both linearly and nonlinearly.

Keywords: Pade-Legendre Reconstruction, Advection-Diffusion Processes, Shoch Problem, Runge Phenomena, Finite

Difference

References:

1. D. Gottlieb and C. W. Shu, On the Gibbs Phenomenon and Its Resolutiont, SIAM REV., vol.39(4), (1997), 644–668.

2. J.S. Hesthaven, S.M. Kaber and L. Lurati, Padé -Legendre Interpolants for gibbs Reconstruction, Journal of Scientific

Computing, vol.28(2-3), (2006,) 337–359.

3. F. Haider, B. Courbet and J.P. Croisille, A high-order interpolation for the finite volume method: The Coupled Least Squares

reconstruction. Computers & Fluids, vol.176, (2018), 20-39.

4. A. Reyes, D. Lee, C. Graziani, P. Tzeferacos, A variable high-order shock-capturing finite difference method with GP-WENO,

Journal of Computational Physics, vol.381, 2019, 189-217.

5. M. Sari, H. Tunc, M. Seydaoglu, Higher order splitting approaches in analysis of the Burgers equation, Kuwait Journal of

Science, 46(1), (2019), 1-14.

6. M. Sari, H. Tunc, Finite element based hybrid techniques for advection-diffusion-reaction processes, An International Journal

of Optimization and Control: Theories Applications, vol.8, (2018), 127-136.




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93

On the Inclusiın Properties of Copson-type Function Spaces

Tugce Unver Yildiz 1

1Department of Mathematics, Kirikkale University,

[email protected]

Abstract

The aim of this talk is to give the necessary and sufficient conditions ensuring the boundedness of the identity

operator between weighted Copson function spaces. The results will be based on the method that reduces this problem to

the characterizations of some new iterated Hardy-type inequalities.

Keywords: Copson operator, Copson function space, iterated inequalities, imbeddings

References:

1. S.V. Astashkin and L. Maligranda, Structure of Cesàro function spaces: a survey, Banach Center Publ. 102 (2014) 13-40.

2. A. Gogatishvili, R.Ch. Mustafayev and T. Ünver, Embeddings between weighted Copson and Cesàro function spaces,

Czechoslovak Math. J. 67 (142) (4), (2017) 1105-1132.

3. K.-G. Grosse-Erdmann, The blocking technique, weighted mean operators and Hardy’s inequality, Lecture Notes in

Mathematics, 1679, Springer-Verlag, Berlin (1998) x+114.

4. M. Křepela, Integral conditions for Hardy-type operators involving suprema, Collect. Math. 68 (1), (2017) 21-50.

5. M. Křepela and L. Pick, Weighted inequalities for iterated Copson integral operators, arXiv:1806.04909, Preprint (2018).




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94

A variable exponent boundedness of the Steklov operator

Yusuf Zeren 1, Farman Mamedov 2 and Fatih Sirin 3


[email protected] 2”Oil Gas science research project” Institute of SOCAR company, Azerbaijan

[email protected], 3Department of Computer Programming, Istanbul Aydin University

[email protected]

Abstract

A sufficiency condition has been proved in this paper for the Steklov operator

𝑆ℎ𝑓(𝑥) =1

ℎ∫ 𝑓(𝑡)𝑑𝑡

𝑥+ℎ

𝑥

, ℎ > 0,

to be bound in variable exponent Lebesgue space 𝐿𝑝(⋅)(0,∞). Here an infinite interval (0, ∞) has been considered with a

new decay condition on infinity. A finite interval [0, 2π] case with a local logregularity condition before was studied, in

order to be applied on approximation problems.

Keywords: Steklov’s operator, variable exponent, uniform boundedness

Reference:

1- D. Cruz-Uribe and A. Florenzia. Variable Lebesgue Spaces. Foundations and Harmonic Analysis, Birkhauser,

2013.

2- D. Cruz-Uribe and F.I. Mamedov, On a general weighted Hardy type inequality in the variable exponent

Lebesgue spaces, Rev. Mat. Compl., 25(2), 2012, 335–367.

3- L. Diening, P. Harjulehto, P. Hasto and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents,

Lecture Not. in Math., 2017, 2011, Springer, Heldelberg, Germany.






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95

POSTER SESSION

Impact of non-linear effects on propagation

Boutheina Boutabia-Chéraitia 1and Houria Triki 2 1Faculty of Medicine, University Badji-Mokhtar of Annaba

[email protected] 2Faculty of Sciences, University Badji-Mokhtar of Annaba

[email protected]

Abstract

We modelize the second-order dispersion effect, as well as the non-linear effects on pulse propagation, by

numerical simulation of the non-linear Shrodinger equation.

Keywords: Kerr effect, non-Kerr effect, optical fiber, optical soliton, induced chirp,

References:

1. Govind P. Agrawal, nonlinear fiber optics. Academic Press, New York, 3rd edition (2001)

2. C. Fortier, Génération de sources optiques fibrées très hautes cadences et caractérisation de fibres optiques microstructurées

en verre de Chalcogénure. Thèse de Doctorat, Université de Bourgogne (2011)

3. J. Fatom, Propagation d’impulsions ultra-courtes dans des lignes de fibres optiques gérées en dispersion. Thèse de Doctorat,

université de Bourgogne (2004)

4. S.L. Placios and J.M. Fernandez-Diaz, Black optical solitons for media with parabolic non-linearity law in the presence of

fourth order dispersion. Optics. Communications 178(2000)457-460





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96

Matricial SDE of the derivative of the solution of SDE in the non linear framework

Hacène Boutabia

LaPS Laboratory, Badji Mokhtar-Annaba University, Po Box 12, Algeria

[email protected]

Abstract

We give, under suitable assumptions, the matricial stochastic differential equation (SDE in short) of the derivative of the

solution for a general SDE driven by G-Brownian motion. An intermediate result, which states that this derivative is

invertible and satisfies a particular matricial SDE.

Keywords: Non linear expectation, G-Brownian motion, quadratic variation, G-Stochastic differential equation,

differentiability.

References:

1. X. Bai, Y. Lin, On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion

with Integral-Lipschitz coefficients, Acta Mathematicae Applicatae Sinica, English Series 3(30) (2014) 589610.

2. M. Hu and S. Peng, On representation theorem of G-expectations and paths of G-Brownian motion, Acta Math. Sin., English

Ser. 25 (2009) 1-8.

3. Q.Lin, Differentialbility of stochastic differential equations driven by G-Brownian motion. Science China Mathematics. 56,

1087-1107 (2013).

4. S. Peng, "G-expectation, G-Brownian motion and related stochastic calculus of It o type", in Proceeeding of the Abel

Symposium, F. E. Benth, G. Di Nunno,T.Lindstrom,B.Ksendal, and T.Zhang, Eds., pp. 541--567, Springer, Berlin, Germany

(2006).

5. S. Peng, "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation", Stochastic Processes

and their Applications, vol. 118, no. 12, pp. 2223--2253, (2008).




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97

Vector Lattices Of Weakly Compact Operators on Banach Lattices

Semra Kiris 1 and Omer Gok 2 1,2Department of Mathematics, Yildiz Technical University,

[email protected]

[email protected]

Abstract

In this presentation ,we investigate that the set of weakly compact operators from Banach lattices to Banach lattices

is a vector lattice in some spacial cases,[3].

Keywords: Banach Lattices, vector lattices, AL-space, KB-space, compact operators.

References:

1. C.D.Aliprantis and O.Burkinshaw , On weakly compact operators on Banach lattices.Proc,Amer.

Math.Soc. 83(1981) 573-578 MR 82j: 47057

2. C.D. Aliprantis and O.Burkinshaw ,Positive Operators ,Academic Press,New York & London , 1985. MR 87h: 47086

3. Z.L.Chen and A.W. Wichstead,Vector Lattices Of Weakly Compact Operators on Banach Lattices,Amer.Math.Soc(1999)

Volume 352, Number 1,pages 397-412





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98

On Spectral Properties and Fundamental Solutions of a Discontinuous One-Point Boundary

Value Problem

Seda Kizilbudak Caliskan 1, Sukru Oynar 2 1,2Department of Mathematics, Yildiz Technical University,

[email protected]

[email protected]

Abstract

In this study, we investigate spectral properties and fundamental solutions of a discontinuous one-point

boundary value problem which is formed by second order differential equation, the boundary conditions which has

spectral parameter and transmision conditions.

Reference:

1. O. Sh. Mukhtarov, M.Kadakal and N. Altinisik, ‘’Eigenvalues And Eigenfunctions Of Discontinuous Sturm-

Liouville Problems With Eigenparameter-Depent Boundary Conditions,’’ Acta Math. Hungar. no.102, pp 159-

175, (2004).

2. S. Caliskan , A. Bayramov , Z. Oer and S. Uslu ,’’ Eigenvalues And Eigenfunctions Of Discontinuous Two-Point

Boundary Value Problems With An Eigenparameter In The Boundary Condition,’’ Rocky Mountain Journal Of

Mathematics vol . 43 no . 6 , 2013.

3. Erdogan Sen , ‘’Asymptotic Properties Of Eigenvalues And Eigenfunctions Of A Sturm-Liouville Problem With

Discontinuous Weight Function,’’ Miskolc Mathematical Notes, vol . 15 , no . 1 , pp. 197-209 , 2014.

4. N. Altinisik , O. Sh. Mukhtarov and M.Kadakal , ‘’Asymptotic Formulas For Eigenfunctions Of The Sturm-

Liouville Problems With Eigenvalue Parameter In The Boundary Conditions,’’ Kuwait J. Sci 39 (1A) pp. 1-

17, 2012.





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99

INDEX

A

Abdullah Kopuzlu · 51 Abuzer Gunduz · 20 Adem Cevikel · 52 Alaa El-Khadri · 80 Amiran Gogatishvili · 12 Arzu Akgul · 21 Aydin Secer · 63, 64 Ayse Erdolen · 72, 84 Ayse Yavuz Tasci · 22 Ayten Ozkan · 37

B

Banu Diri · 26 Bayram Ali Ersoy · 20 Betul Bulca · 33, 67 Bilal Bilalov · 13 Boutheina Boutabia-Chéraitia · 95

C

Cemil Karacam · 5, 23, 24 Cihan Unal · 25, 59 Cihat Erdogan · 26

D

Deniz Demircanli · 27 Diana M. Audi · 28 Dilek Kayacelik · 29 Dogan Kaya · 44

E

E. Aydan Pamuk · 33 Ekrem Savas · 14 Elif Deniz · 5, 31, 32 Elif Ozturk · 30 Elif Segah Oztas · 66 Emrah Evren Kara · 68, 69 Enver Ozdemir · 43 Erhan Piskin · 34, 76, 77

F

F. Muge Sakar · 87 Faik Gursoy · 5, 35, 46, 56, 60 Farman Mamedov · 6, 15, 94 Faruk Dusunceli · 5, 53, 55 Fatih Demirkale · 66 Fatih Sirin · 6, 7, 9, 18, 36, 71, 74, 94 Fatma Polat · 58 Fatmanur Gursoy · 37 Filiz Seckin · 38 Fuat Usta · 39 Furkan Yildirim · 40, 41 Fusun Ozen Zengin · 22

G

Gizem Demirbas · 42 Gozde Sarikaya · 43 Gulcan Atici Turan · 58 Gulistan Iskenderoglu · 44

H

Hacène Boutabia · 96 Hande Uslu · 5, 45 Harun Polat · 46, 86 Hasan Bal · 79 Hasan Es · 47, 48 Hasan Sahin · 49, 50 Hatice Kubra Sari · 51 Houria Triki · 95 Huseyin Tunc · 92

I

Ibrahim Demir · 5, 83 Ilknur Yilmaz · 52 Ismail Aydin · 25, 59 Ismet Yildiz · 49, 50

K

Kadri Arslan · 67 Kadri Dogan · 5, 60 Kubra Aksoy · 5, 31, 61



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100

L

Lutfi Akin · 54, 57, 62 Lyoubomira Softova · 16

M

Mansur I. Ismailov · 27 Melih Cinar · 5, 63, 64 Melike Keles · 65 Merve Bulut Yilgor · 66 Merve Harmanli · 67 Merve Ilkhan · 68, 69 Migdad Ismailov · 18, 70, 71 Mohamed Zribi · 80 Muhammed Furkan Simsek · 72 Murat Akarsu · 73, 74 Murat Alan · 78 Murat Bekar · 47, 48 Murat Besenk · 42 Murat Polat · 40 Murat Sari · 45, 92 Murat Turhan · 5, 75 Mustafa Asci · 29

N

Narmin Amanova · 15 Nazli Irkil · 76, 77 Nazlihan Erten · 78 Nedim Ertugay · 79 Nejib Smaoui · 80 Nejla Ozmen · 81, 82 Nuran Kose Cerci · 83

O

Omer Gok · 97 Orhan Senyener · 84 Oya Baykal Unal · 75 Ozgur Yildirim · 5, 85

S

S. Melike Aydogan · 87

Saadettin Aydin · 86 Sahsene Altinkaya · 87 Seda Kizilbudak Caliskan · 98 Selim Yavuz · 5, 70, 74 Semra Kiris · 97 Serdal Pamuk · 65 Serpil Uslu · 75 Servet Es · 88, 89 Sobri Abusini · 90 Sofiène Tahar · 17, 31, 61 Suayip Toprakseven · 5, 91 Sufii Hamad Mussa · 92 Sukru Oynar · 98 Sumeyra Caglak · 85 Susumu Tanabe · 20

T

Tugce Unver Yildiz · 93

U

Umran Menek · 49, 50

V

Varga K. Kalantarov · 19

Y

Yunus Atalan · 5, 56 Yusuf Zeren · 6, 7, 8, 9, 18, 23, 24, 31, 32, 36, 57, 61, 70, 71,

94

Z

Zafer Kutug · 72, 84 Zerrin Ozcubukcu · 75 Zeyneb Kurt · 26 Zulal Tuzuner · 79



Istanbul / TURKEY


101


nd - icomaa 2019...a note on approximating finite hilbert transform and quadrature formula.....39...

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