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   -> Volume 11, Issue 1


Book: Defects of Properties in Mathematics. Quantitative Characterizations
 
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Sorin Gal (galso@uoradea.ro)
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PostPosted: Sun Apr 28, 2002 5:56 pm    
Subject: Book: Defects of Properties in Mathematics. Quantitative Characterizations
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Summary: New Book Announcement : "Defects of Properties in Mathematics. Quantitative Characterizations", by Adrian I. Ban & Sorin G. Gal (University of Oradea, Romania).

New Book Announcement :

"Defects of Properties in Mathematics. Quantitative Characterizations",
by Adrian I. Ban & Sorin G. Gal (University of Oradea, Romania),
World Scientific, New Jersey, London,Singapore, Hong Kong, 2002,
346 pages, ISBN 981-02-4924-1, Price : 48 USD or 33 Pounds.

If you are interested for your library, department, your own use or your students, for ordering details please contact Ms Serena Lau, at the e-mail address slau@wspc.com.sg

Brief Description:
This book introduces a method of research which can be used in various fields of mathematics. It examines in a systematic way, the quantitative characterization of the "deviation from a (given) property", called the "defect of property", in : set theory, topology, measure theory, real, complex and functional analysis, algebra, geometry, number theory, fuzzy mathematics.

Readership :
Upper level undergraduates, graduate students, researchers interested in measure theory, real and functional analysis, topology and algebra, geometry, number theory, fuzzy mathematics.

Contents :

1. Introduction

2. Defect of Property in Set Theory
2.1 Measures of Fuzziness
2.2 Intuitionistic Entropies
2.3 Applications
2.4 Bibliographical Remarks

3. Defect of Property in Topology
3.1. Measures of Noncompactness for Classical sets
3.2 Random Measures of Noncompactness
3.3 Measures of Noncompactness for Fuzzy Subsets in Metric Spaces
3.4 Measures of Noncompactness for Fuzzy Subsets in Topological Spaces
3.5 Defects of Opening and of Closure for Subsets in Metric Spaces
3.6 Bibliographical Remarks and Open Problems

4. Defect of Property in Measure Theory
4.1 Defect of Additivity
4.2 Defect of Complementarity
4.3 Defect of Monotonicity
4.4 Defect of Subadditivity and of Superadditivity
4.5 Defect of Measurability
4.6 Bibliogarphical Remarks

5. Defect of Property in Real Function Theory
5.1 Defect of Continuity, of Differentiability and of Integrability
5.2 Defect of Monotonicity, of Convexity and of Linearity
5.3 Defect of Equality for Inequalities
5.4 Bibliographical Remarks and Open Problems

6. Defect of Property in Functional Analysis
6.1. Defect of Orthogonality in Real Normed Spaces
6.2. Defect of Property for Sets in Normed Spaces
6.3 Defect of Property for Functionals
6.4 Defect of Property for Linear Operators on Normed Spaces
6.5 Defect of Fixed Point
6.6 Bibliographical Remarks and Open Problems

7. Defect of Property in Algebra
7.1 Defects of Property for Binary Operations
7.2 Calculation of the Defect of Property
7.3 Defect of Idempotency and Distributivity of Triangular Norms
7.4 Applications
7.5 Bibliographical Remarks

8. Miscellaneous
8.1 Defect of Property in Complex Analysis
8.2 Defect of Property in Geometry
8.3 Defect of Property in Number Theory
8.4 Defect of Property in Fuzzy Logic
8.5 Bibliographical Remarks and Open Problems

BIBLIOGRAPHY
INDEX

Thank you very much for your attention.

Prof.dr. Sorin G. Gal
Department of Mathematics
University of Oradea
3700 Oradea
ROMANIA
All times are GMT + 1 Hour
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