Topics in Integration Research


Mark Burgin (Editor)
UCLA, California, USA

Series: Mathematics Research Developments
BISAC: MAT027000

In calculus, we integrate functions using two types of integration – definite integration and indefinite integration. In functional analysis, we integrate operators. To find a solution of a differential equation, we integrate this equation. Going beyond mathematics, we see that in databases, we integrate data, as well as database schemas. In electronics, integrated circuits have become central components of computers, calculators, cellular phones, and other digital appliances, which are now inextricable parts of the structure of modern societies. In economics, we have integration of the economy of one country into the economy of a union of other countries, e.g., integration of economy of Hungary into the European Union economy. There is political integration and there is social integration. Thus, we can see many types and kinds of integration. Design of complex database schemas is based on a gradual integration of external schemas. Research presented in this book studies integration in mathematics and its applications. However, it is not only classical integration of functions but also fuzzy integration, integration of structures, probability as integration of random characteristics and integral operators in bundles with a hyperspace base. (Imprint: Nova)



Table of Contents

Preface pp i-xv


Chapter 1. Modified Numerical Integral Formula for Unequal Sub-Intervals using Cubic Spline Interpolation Formula

(B.S. Bhadauria, and A.K. Singh)pp. 3-10

Chapter 2. Fuzzy Integral-Based T- and S-Evaluators: Sugeno Integral

(Slavka Bodjanova, and Martin Kalina)pp. 11-30

Chapter 3. Fuzzy Integral-Based T- and S-Evaluators: Shilkret and Choquet Integrals

(Slavka Bodjanova, and Martin Kalina)pp. 31-54

Chapter 4. Named Sets and Integration of Structures

(Mark Burgin)pp. 55-98

Chapter 5. Integration in Bundles with a Hyperspace Base: Indefinite Integration

(Mark Burgin)pp. 99-138

Chapter 6. On New Integral Operator in Complex Domain

(Maslina Darius, Rabha W. Ibrahim)pp. 139-148

Chapter 7. An Abstract Gauge Integral

(Isidore Fleischer)pp. 149-152

Chapter 8. A Criterion for the Saks-Heinstok Lemma in a Topological Vector Space

(Toshiharu Kawasaki)pp. 153-164


Chapter 9. Nonlinear Cauchy-Kowalewski Theorem in Extrafunctions

(Mark Burgin)pp. 167-202

Chapter 10. Existence of Solutions for Fractional Integral Inclusions with Time Delay

(Rabha W. Ibrahim)pp. 203-214

Chapter 11. Length of Ray Images under Analytic Maps

(V. Karunakaran and K. Bhuvaneswari)pp. 215-222

Chapter 12. Generalized Quotients and Laplace Transform

(V. Karunakaran and R. Angeline Chella Rajathi)pp. 223-230

Chapter 13. Nonsquare Constants of Orlicz Sequence Spaces

(Z.D. Ren)pp. 231-248

Chapter 14. An Extension of Stiltjes Transform

(R. Roopkumar)pp. 249-262


Chapter 15. Properties of Conditional Hyperprobabilities

(M. Burgin and A. Krinik)pp. 265-288

Chapter 16. Mathematical Models in Finance and Negative Probability

(Mark Burgin and Gunter Meissner)pp. 289-312

Chapter 17. Some Models for Standard and Assisted Cell Mutations

(J. Gani and R.J. Swift)pp. 313-322

Chapter 18. The Irreducible Three and Four-State Markov Process

(Lilinoe Harbottle , Blake Hunter  and Alan Krinik)pp. 323-342

Chapter 19. Sequential Hypothesis Testing with Spatially Correlated Count Data

(Judy X. Li, Daniel R. Jeske, Jesús R. Lara and Mark Hoddle)pp. 343-358


Chapter 20. Topological Structure of Information Channels and Channel Operators

(Yuichiro Kakihara)pp. 361-374

Chapter 21. The Entropy Functional’s and the Information Path Functional’s Basics with the Thermodynamics and Cooperative Information Dynamics Applications

(Vladimir S. Lerner)pp. 375-416

Chapter 22. An Integral Equation Approach to the Static Analysis of Stiffened Plates – Application to Concrete or to Composite Steel-Concrete Structures

(E.J. Sapountzakis)pp. 417-458

Index pp. 459-465


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