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Differential and Difference Equations through Computer Experiments
Phaser is a sophisticated program for IBM personal com- puters, developed atBrown University by the author and some of his students, which enables usersto experiment with differential and difference equations and dynamical systems in an interactive environment using graphics. This book begins with a brief discussion of the geometric inter- pretation of differential equations and numerical methods, and proceeds to guide the student through the use of the program. To run Phaser, you need an IBM PC, XT, AT, or PS/2 with an IBM Color GRaphics Board (CGB), Enhanced Graphics Adapter (VGA). A math coprocessor is supported; however, one is not required for Phaser to run on the above hardware.
Remote Viewing
Remote viewing is the mental ability to perceive and describe places, persons, or events at distant locations in the past, present, and future. This book describes the science and theory of the remote-viewing phenomenon. The reality of the remote-viewing phenomenon is not in dispute among a large body of respected researchers ¿ both inside and outside of academia ¿ who have published an extensive collection of high-quality investigations over the past few decades. But profound mysteries remain. This volume breaks new ground by resolving some of remote-viewing¿s greatest enigmas. In these pages, new research and new theories explain why remote viewing works, and why it is scientifically po...
Dynamics and Bifurcations
In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.
Shadowing in Dynamical Systems
In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.
Difference Equations
Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced to
Theoretical Approaches to Biological Control
Biological control is the suppression of pest populations using predators, parasitoids and pathogens. Historically, biological control has largely been on a trial-and-error basis, and has failed more often than it has succeeded. However by developing theories based upon fundamental population principles and the biological characteristics of the pest and agent, we can gain a much better understanding of when and how to use biological control. This book gathers together recent theoretical developments and provides a balanced guide to the important issues that need to be considered in applying ecological theory to biological control. It will be a source of productive and stimulating thought for all those interested in pest management, theoretical ecology and population biology.
2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach
This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the Hénon map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters.Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are ori...
Mind, Brain, Quantum AI, and the Multiverse
There is a long-lasting controversy concerning our mind and consciousness. Mind, Brain, Quantum AI, and the Multiverse proposes a connection between the mind, the brain, and the multiverse. The author introduces the main philosophical ideas concerning mind and freedom, and explains the basic principles of computer science, artificial intelligence of brain research, quantum physics, and quantum artificial intelligence. He indicates how we can provide an answer to the problem of the mind and consciousness by describing the nature of the physical world. His proposed explanation includes the Everett Many-Worlds theory. This book tries to avoid any non-essential metaphysical speculations. The text is an essential compilation of knowledge in philosophy, computer science, biology, and quantum physics. It is written for readers without any requirements in mathematics, physics, or computer science.
Insights from Book Translations on the International Diffusion of Knowledge
Increases in the stock of ideas possessed by societies are central to modern economic growth. The implications of idea flows are striking: Klenow and Rodriguez-Clare (2005) estimate world production would be just 6% of its current level if countries did not share ideas. Yet, although theoretical economists have studied ideas and their diffusion extensively, empirical studies are scarce because ideas are inherently difficult to measure. Previous empirical studies of idea flows have tended to use proxies such as trade flows, foreign direct investment, migration, and patent citations. However, with the exception of the latter, these measures are not pure idea flows, and do not capture the key p...
Principles of Differential Equations
An accessible, practical introduction to the principles of differential equations The field of differential equations is a keystone of scientific knowledge today, with broad applications in mathematics, engineering, physics, and other scientific fields. Encompassing both basic concepts and advanced results, Principles of Differential Equations is the definitive, hands-on introduction professionals and students need in order to gain a strong knowledge base applicable to the many different subfields of differential equations and dynamical systems. Nelson Markley includes essential background from analysis and linear algebra, in a unified approach to ordinary differential equations that undersc...
