Tag Archives: Mathematical

Category Theory for the Sciences

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Category Theory for the Sciences by David I. Spivak
2014 | ISBN: 0262028131 | English | 496 pages | PDF | 7 MB

Category Theory for the Sciences
Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs — categories in disguise. After explaining the "big three" concepts of category theory — categories, functors, and natural transformations — the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with selected solutions. is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
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Stochastic Dynamics by Hans Crauel

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Stochastic Dynamics by Hans Crauel
English | March 26, 1999 | ISBN: 0387985123 | 455 Pages | PDF | 8 MB
Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations.

Stochastic Dynamics by Hans Crauel
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Nonlinear Optical Crystals: A Complete Survey

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Nonlinear Optical Crystals: A Complete Survey
English | Physics, Optics | 9. February 2005 | ISBN-10: 0387220224 | 428 pages | pdf | 3 mb
Nonlinear Optical Crystals contains the most complete and up-to-date reference material on properties of nonlinear optical crystals including:
Traditional and specific applications

Nonlinear Optical Crystals: A Complete Survey
The mathematical formulas necessary for the calculation of the frequency conversion process

A survey of 63 nonlinear optical crystals containing more than 1500 different references with full titles

Recent applications of common and novel nonlinear materials, including quasi-phase matching

Special consideration for periodically-poled and self-frequency-doubling materials

Significant amount of crystallophysical, thermophysical, spectroscopic, electro-optic and magneto-optic information
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Fractal Mechanics of Polymers: Chemistry and Physics of Complex Polymeric Materials

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Fractal Mechanics of Polymers: Chemistry and Physics of Complex Polymeric Materials by G. V. Kozlov, Yu G. Yanovskii
2014 | ISBN: 1771880414 | English | 384 pages | PDF | 11 MB

Fractal Mechanics of Polymers: Chemistry and Physics of Complex Polymeric Materials
This new book explores the consideration of relationships that connect the structural and basic mechanical properties of polymeric mediums within the frameworks of fractal analysis with cluster model representations attraction. Incidentally, the choice of any structural model of medium or their combinations is defined by expediency and further usage convenience only. This book presents leading-edge research in this rapidly changing and evolving field.

The book presents descriptions of the main reactions of high-molecular substances within the frameworks of fractal analysis and irreversible aggregation models. Synergetics and percolation theory were also used. In spite of the enormous number of papers dealing with the influence of the medium on the rate of chemical reactions (including synthesis of polymers), no strict quantitative theory capable of "universal" application has been put forward up until now. It is now possible to describe the relationship between the reaction rate constants and the equilibrium constants with the nature of the medium in which the reactions take place by means of a single equation. This important book for the first time gives structural and physical grounds of polymers synthesis and curing, and the fractal analysis is used for this purpose.

This new book:

* Highlights some important areas of current interest in polymer products and chemical processes

* Focuses on topics with more advanced methods

* Emphasizes precise mathematical development and actual experimental details

* Analyzes theories to formulate and prove the physicochemical principles

* Provides an up-to-date and thorough exposition of the present state of the art of complex polymeric materials
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Fractal Mechanics of Polymers: Chemistry and Physics of Complex Polymeric Materials

FREEDownload : Fractal Mechanics of Polymers: Chemistry and Physics of Complex Polymeric Materials

Fractal Mechanics of Polymers: Chemistry and Physics of Complex Polymeric Materials by G. V. Kozlov, Yu G. Yanovskii
2014 | ISBN: 1771880414 | English | 384 pages | PDF | 11 MB

Fractal Mechanics of Polymers: Chemistry and Physics of Complex Polymeric Materials
This new book explores the consideration of relationships that connect the structural and basic mechanical properties of polymeric mediums within the frameworks of fractal analysis with cluster model representations attraction. Incidentally, the choice of any structural model of medium or their combinations is defined by expediency and further usage convenience only. This book presents leading-edge research in this rapidly changing and evolving field.

The book presents descriptions of the main reactions of high-molecular substances within the frameworks of fractal analysis and irreversible aggregation models. Synergetics and percolation theory were also used. In spite of the enormous number of papers dealing with the influence of the medium on the rate of chemical reactions (including synthesis of polymers), no strict quantitative theory capable of "universal" application has been put forward up until now. It is now possible to describe the relationship between the reaction rate constants and the equilibrium constants with the nature of the medium in which the reactions take place by means of a single equation. This important book for the first time gives structural and physical grounds of polymers synthesis and curing, and the fractal analysis is used for this purpose.

This new book:

* Highlights some important areas of current interest in polymer products and chemical processes

* Focuses on topics with more advanced methods

* Emphasizes precise mathematical development and actual experimental details

* Analyzes theories to formulate and prove the physicochemical principles

* Provides an up-to-date and thorough exposition of the present state of the art of complex polymeric materials
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Distributed Computing: Fundamentals, Simulations, and Advanced Topics

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Hagit Attiya, Jennifer Welch, "Distributed Computing: Fundamentals, Simulations, and Advanced Topics"
2004 | pages: 416 | ISBN: 0471453242 | DJVU | 4 mb

Distributed Computing: Fundamentals, Simulations, and Advanced Topics
* Comprehensive introduction to the fundamental results in the mathematical foundations of distributed computing
* Accompanied by supporting material, such as lecture notes and solutions for selected exercises
* Each chapter ends with bibliographical notes and a set of exercises
* Covers the fundamental models, issues and techniques, and features some of the more advanced topics
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Physical Approaches to Biological Evolution

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Mikhail V. Volkenstein, "Physical Approaches to Biological Evolution"
1994 | pages: 402 | ISBN: 3642787908 | DJVU | 4,5 mb

Physical Approaches to Biological Evolution
"Mr. Wolkenstein's , whether or not it proves to give the ultimate truth on the matters with which it deals, certainly deserves, by its breadth and scope and profundity, to be considered an impor­ tant event in the philosophical world." This is a quotation from an introduction written by Bertrand Russell for Ludwig Wittgenstein's Tractatus Logico-Philosophicus. I exchanged only name and subject. As for the rest, I could continue quoting Russell, but I would rather say something myself. As Wittgenstein did with formal logic, Wolkenstein rectifies our views on how to approach the logic of life from a formal theoretical basis. Many bio­ logists do not believe that their subject lends itself to the scrutiny of physical theory. They certainly admit that one can simulate biological phenomena by models that can be expressed in a mathematical form. However, they do not believe that biology can be given a theoretical foundation that is defined within the general framework of physics. Rather, they insist on a holistic approach, banning any reduction to fundamental principles subject to physical theory.
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Physical Approaches to Biological Evolution

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Mikhail V. Volkenstein, "Physical Approaches to Biological Evolution"
1994 | pages: 402 | ISBN: 3642787908 | DJVU | 4,5 mb

Physical Approaches to Biological Evolution
"Mr. Wolkenstein's , whether or not it proves to give the ultimate truth on the matters with which it deals, certainly deserves, by its breadth and scope and profundity, to be considered an impor­ tant event in the philosophical world." This is a quotation from an introduction written by Bertrand Russell for Ludwig Wittgenstein's Tractatus Logico-Philosophicus. I exchanged only name and subject. As for the rest, I could continue quoting Russell, but I would rather say something myself. As Wittgenstein did with formal logic, Wolkenstein rectifies our views on how to approach the logic of life from a formal theoretical basis. Many bio­ logists do not believe that their subject lends itself to the scrutiny of physical theory. They certainly admit that one can simulate biological phenomena by models that can be expressed in a mathematical form. However, they do not believe that biology can be given a theoretical foundation that is defined within the general framework of physics. Rather, they insist on a holistic approach, banning any reduction to fundamental principles subject to physical theory.
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