![Page 1: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/1.jpg)
Sub-Interval Analysis.
First Results
Alexander [email protected]
As the main source, see the E-Book"Introduction to Sub-Interval Analysis
and its Applications" in Open Access at
http://ideas.repec.org/b/zbw/esmono/62286.html
27 September, 19.30. Auditorium 515.
SeminarSub-Interval Analysis. Detailed
introduction
![Page 2: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/2.jpg)
What is It? What is a Sub-Interval?
A sub-interval is simply
a part of an interval.
?
You may see an example
of an interval X1..2 and its sub-intervals X1 and X2
in the above Figure.
![Page 3: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/3.jpg)
What is It?
What is
a Sub-Interval Analysis?
The sub-interval analysis is based on a very simple and clear idea:
The sub-interval analysis is a tool to calculate
the characteristics of a whole interval
by means of characteristics of its sub-intervals.
![Page 4: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/4.jpg)
The sub-interval analysis
A tool to calculate
the characteristics
of a whole interval
by means of characteristics
of its sub-intervals.
You may see an example
of an interval X1..2 and its sub-intervals X1 and X2
in the above Figure.
![Page 5: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/5.jpg)
What for is It?
What for is the Sub-Interval Analysis?
1) To treat Inexact Data
2) To treat Incomplete Data
3) To treat Numerous Data
![Page 6: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/6.jpg)
Where is the weight?Box with two Sub-Boxes 1.
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Where is the weight?Box with two Sub-Boxes 2.
![Page 8: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/8.jpg)
Where is the weight?
Sub-Boxes treat Inexact Data Sub-Boxes improve the Precision
![Page 9: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/9.jpg)
First Results
of Sub-Interval Analysis
as a New Branch of Interval Analysis
1) New Tools
2) New Theorems and Hypotheses. New realms for Interval Analysis
3) New Prerequisites of Applications
4) New Fields of Applications
![Page 10: Sub-Interval Analysis. First Results Alexander Harin aaharin@yandex.ru As the main source, see the E-Book "Introduction to Sub-Interval Analysis and its](https://reader030.vdocuments.site/reader030/viewer/2022032721/56649cd85503460f949a0e34/html5/thumbnails/10.jpg)
Tools, Theorems and Hypotheses of It
1) Sub-Interval Arithmetic
Incomplete Data Analysis
Sub-Interval Images
2) Theorems of Precision Improvement Theorems of Restrictions Theorems of Interval Character
of Incomplete Knowledge
3) Hypothesis of incompleteness
for measurement interpretation
Hypotheses of Degrees of Cognition
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"Ring of formulas"
S
S
s smSmmsS
S
s smSmmsS
S
sss
S
Mwid
wXwidXwid
XwidwXwid
Xwidw
Mwid
..1
1 |,..,1..1
1 |,..,1..1
1
..1
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What is It?
General tasks of It
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4
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5
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Prerequisites of Applications for It
1.Simplicity and exactness
2.Advantages of mean versus total
3.Low volume, high speed, high capacity
4.Advantages of incomplete data analysis
5.Time sub-intervals
6.Space sub-intervals
7.Enumeration sub-intervals
8.Statistical sub-intervals
9.Fourier sub-intervals
10.Large databases
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Particular Fields for It
1) Economics
2) Internet
3) Military
4) Sociology
5) Technics
6) Statistics
7) Fourier Analysis
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Sub-Interval Analysis.
Alexander [email protected]
As the main source, see the E-Book"Introduction to Sub-Interval Analysis
and its Applications" in Open Access at
http://ideas.repec.org/b/zbw/esmono/62286.html
27 September, 19.30. Auditorium 515.
SeminarSub-Interval Analysis. Detailed introduction. General Picture