The Dynamical System Generated by the 3n+1 Function

Author: Günther J. Wirsching

Publisher: Springer

ISBN: 3540696776

Category: Mathematics

Page: 164

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The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.
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The Mathematics of Oz

Mental Gymnastics from Beyond the Edge

Author: Clifford A. Pickover

Publisher: Cambridge University Press

ISBN: 9780521016780

Category: Games & Activities

Page: 351

View: 4891

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Filled with an abundance of complex mysteries, sequences, series, puzzles, mazes, and problems, a perplexing journey through the realm of math, mind, and meaning with the author, Dorothy, and Dr. Oz introduces readers to numbers and their role in creativity, computers, games, and practical research. (Science & Mathematics)
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Infobiotics

Information in Biotic Systems

Author: Vincenzo Manca

Publisher: Springer Science & Business Media

ISBN: 3642362230

Category: Computers

Page: 384

View: 6264

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The book presents topics in discrete biomathematics. Mathematics has been widely used in modeling biological phenomena. However, the molecular and discrete nature of basic life processes suggests that their logic follow principles that are intrinsically based on discrete and informational mechanisms. The ultimate reason of polymers, as key element of life, is directly based on the computational power of strings, and the intrinsic necessity of metabolism is related to the mathematical notion of multiset. The switch of the two roots of bioinformatics suggests a change of perspective. In bioinformatics, the biologists ask computer scientists to assist them in processing biological data. Conversely, in infobiotics mathematicians and computer scientists investigate principles and theories yielding new interpretation keys of biological phenomena. Life is too important to be investigated by biologists alone, and though computers are essential to process data from biological laboratories, many fundamental questions about life can be appropriately answered by a perspicacious intervention of mathematicians, computer scientists, and physicists, who will complement the work of chemists, biochemists, biologists, and medical investigators. The volume is organized in seven chapters. The first part is devoted to research topics (Discrete information and life, Strings and genomes, Algorithms and Biorhythms, Life Strategies), the second one to mathematical backgrounds (Numbers and Measures, Languages and Grammars, Combinations and Chances).
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Tutorials in Mathematical Biosciences II

Mathematical Modeling of Calcium Dynamics and Signal Transduction

Author: James Sneyd

Publisher: Springer Science & Business Media

ISBN: 9783540254393

Category: Mathematics

Page: 202

View: 7841

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This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions. It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.
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Tutorials in Mathematical Biosciences III

Cell Cycle, Proliferation, and Cancer

Author: Avner Friedman

Publisher: Springer

ISBN: 3540324151

Category: Mathematics

Page: 246

View: 4515

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This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.
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The Art of Random Walks

Author: Andras Telcs

Publisher: Springer Science & Business Media

ISBN: 3540330275

Category: Mathematics

Page: 195

View: 9623

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Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality.
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Introduction to Symplectic Dirac Operators

Author: Katharina Habermann,Lutz Habermann

Publisher: Springer

ISBN: 3540334211

Category: Mathematics

Page: 125

View: 9588

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This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
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