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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his …
- Edition
- 1
- ISBN/ISSN
- 978-3-030-95088-0
- Collation
- -
- Series Title
- Developments in Mathematics
- Call Number
- XVIII, 323
Topics in Algebra and Analysis Preparing for the Mathematical Olympiad
The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world. In the first four chapters the authors cover material for competitions at high school level. The level advances with the chapters. The topics explored include po…
- Edition
- -
- ISBN/ISSN
- 978-3-319-11946-5
- Collation
- -
- Series Title
- -
- Call Number
- -
On Meaningful Scientific Laws
The authors describe systematic methods for uncovering scientific laws a priori, on the basis of intuition, or “Gedanken Experiments”. Mathematical expressions of scientific laws are, by convention, constrained by the rule that their form must be invariant with changes of the units of their variables. This constraint makes it possible to narrow down the possible forms of the laws. It is clo…
- Edition
- 1
- ISBN/ISSN
- 978-3-662-46097-9
- Collation
- XIII, 170
- Series Title
- -
- Call Number
- -
Asymptotic Integration of Differential and Difference Equations
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also…
- Edition
- -
- ISBN/ISSN
- 978-3-319-18248-3
- Collation
- -
- Series Title
- -
- Call Number
- -
Stability of Functional Equations in Banach Algebras
Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach …
- Edition
- -
- ISBN/ISSN
- 978-3319187075
- Collation
- -
- Series Title
- -
- Call Number
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Entropy Methods for Diffusive Partial Differential Equations
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of …
- Edition
- -
- ISBN/ISSN
- 978-3-319-34219-1
- Collation
- 1 illustrations in colour
- Series Title
- -
- Call Number
- -
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