A Concise Introduction To Hypercomplex Fractals
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A Concise Introduction To Hypercomplex Fractals
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Author : Andrzej Katunin
language : en
Publisher: CRC Press
Release Date : 2017-10-05
A Concise Introduction To Hypercomplex Fractals written by Andrzej Katunin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Computers categories.
This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry – a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.
Hypercomplex Iterations Distance Estimation And Higher Dimensional Fractals With Cd Rom
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Author : Yumei Dang
language : en
Publisher: World Scientific
Release Date : 2002-08-06
Hypercomplex Iterations Distance Estimation And Higher Dimensional Fractals With Cd Rom written by Yumei Dang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-06 with Computers categories.
This book is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. It is self-contained, giving a careful treatment of both the known techniques and the authors' new methods. The distance estimation technique was originally applied to Julia sets and the Mandelbrot set in the complex plane. It was justified, through the work of Douady and Hubbard, by deep results in complex analysis. In this book the authors generalise the distance estimation to quaternionic and other higher dimensional fractals, including fractals derived from iteration in the Cayley numbers (octonionic fractals). The generalization is justified by new geometric arguments that circumvent the need for complex analysis. This puts on a firm footing the authors' present work and the second author's earlier work with John Hart and Dan Sandin. The results of this book will be of great interest to mathematicians and computer scientists interested in fractals and computer graphics.
Dynamical Systems With Applications Using Mathematica
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Author : Stephen Lynch
language : en
Publisher: Birkhäuser
Release Date : 2017-10-12
Dynamical Systems With Applications Using Mathematica written by Stephen Lynch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-12 with Mathematics categories.
This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.
Dynamical Systems With Applications Using Python
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Author : Stephen Lynch
language : en
Publisher: Springer
Release Date : 2018-10-09
Dynamical Systems With Applications Using Python written by Stephen Lynch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-09 with Mathematics categories.
This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams. After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.
A Concise Introduction To Robot Programming With Ros2
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Author : Francisco Martín Rico
language : en
Publisher: CRC Press
Release Date : 2022-09-30
A Concise Introduction To Robot Programming With Ros2 written by Francisco Martín Rico and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-30 with Computers categories.
A Concise Introduction to Robot Programming with ROS2 provides the reader with the concepts and tools necessary to bring a robot to life through programming. It will equip the reader with the skills necessary to undertake projects with ROS2, the new version of ROS. It is not necessary to have previous experience with ROS2 as it will describe its concepts, tools, and methodologies from the beginning. Key Features Uses the two programming languages officially supported in ROS2 (C++, mainly, and Python) Approaches ROS2 from three different but complementary dimensions: the Community, Computation Graph, and the Workspace Includes a complete simulated robot, development and testing strategies, Behavior Trees, and Nav2 description, setup, and use A GitHub repository with code to assist readers It will appeal to motivated engineering students, engineers, and professionals working with robot programming.
Case Based Reasoning
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Author : Beatriz López
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2013
Case Based Reasoning written by Beatriz López and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
Case-based reasoning is a methodology with a long tradition in artificial intelligence that brings together reasoning and machine learning techniques to solve problems based on past experiences or cases. Given a problem to be solved, reasoning involves the use of methods to retrieve similar past cases in order to reuse their solution for the problem at hand. Once the problem has been solved, learning methods can be applied to improve the knowledge based on past experiences. In spite of being a broad methodology applied in industry and services, case-based reasoning has often been forgotten in both artificial intelligence and machine learning books. The aim of this book is to present a concise introduction to case-based reasoning providing the essential building blocks for the designing of case-based reasoning systems, as well as to bring together the main research lines in this field to encourage students to solve current CBR challenges.
Topological Geometrodynamics
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Author : Matti Pitkanen
language : en
Publisher: Luniver Press
Release Date : 2006
Topological Geometrodynamics written by Matti Pitkanen and has been published by Luniver Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Topological GeometroDynamics is a modification of general relativity inspired by the conceptual problems related to the definitions of inertial and gravitational energy in general relativity. Topological geometrodynamics can be also seen as a generalization of super string models. Physical space-times are seen as four-dimensional surfaces in certain eight-dimensional space. The choice of this space is fixed by symmetries of the standard model so that geometrization of known classical fields and elementary particle quantum numbers results. The notion of many-sheeted space-time allows re-interpretation of the structures of perceived world in terms of macroscopic space-time topology. The generalization of the number concept based on fusion of real numbers and p-adic number fields implies a further generalization of the space-time concept allowing to identify space-time correlates of cognition and intentionality. Quantum measurement theory extended to a quantum theory of consciousness becomes an organic part of theory. A highly non-trivial prediction is the existence of a fractal hierarchy of copies of standard model physics with dark matter identified in terms of macroscopic quantum phases characterized by dynamical and quantized Planck constant. The book is a comprehensive overview and analysis of topological geometrodynamics as a mathematical and physical theory.
Rhythms Of The Brain
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Author : Gyorgy Buzsaki
language : en
Publisher: Oxford University Press
Release Date : 2006-08-03
Rhythms Of The Brain written by Gyorgy Buzsaki and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-03 with Medical categories.
This book provides eloquent support for the idea that spontaneous neuron activity, far from being mere noise, is actually the source of our cognitive abilities. In a sequence of "cycles," György Buzsáki guides the reader from the physics of oscillations through neuronal assembly organization to complex cognitive processing and memory storage. His clear, fluid writing-accessible to any reader with some scientific knowledge-is supplemented by extensive footnotes and references that make it just as gratifying and instructive a read for the specialist. The coherent view of a single author who has been at the forefront of research in this exciting field, this volume is essential reading for anyone interested in our rapidly evolving understanding of the brain.
Nature Inspired Algorithms And Applied Optimization
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Author : Xin-She Yang
language : en
Publisher: Springer
Release Date : 2017-10-18
Nature Inspired Algorithms And Applied Optimization written by Xin-She Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-18 with Technology & Engineering categories.
This book reviews the state-of-the-art developments in nature-inspired algorithms and their applications in various disciplines, ranging from feature selection and engineering design optimization to scheduling and vehicle routing. It introduces each algorithm and its implementation with case studies as well as extensive literature reviews, and also includes self-contained chapters featuring theoretical analyses, such as convergence analysis and no-free-lunch theorems so as to provide insights into the current nature-inspired optimization algorithms. Topics include ant colony optimization, the bat algorithm, B-spline curve fitting, cuckoo search, feature selection, economic load dispatch, the firefly algorithm, the flower pollination algorithm, knapsack problem, octonian and quaternion representations, particle swarm optimization, scheduling, wireless networks, vehicle routing with time windows, and maximally different alternatives. This timely book serves as a practical guide and reference resource for students, researchers and professionals.
Exploring Physics With Geometric Algebra
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Author : Peeter Joot
language : en
Publisher: Peeter Joot
Release Date :
Exploring Physics With Geometric Algebra written by Peeter Joot and has been published by Peeter Joot this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
This is an exploratory collection of notes containing worked examples of a number of applications of Geometric Algebra (GA), also known as Clifford Algebra. This writing is focused on undergraduate level physics concepts, with a target audience of somebody with an undergraduate engineering background (i.e. me at the time of writing.) These notes are more journal than book. You'll find lots of duplication, since I reworked some topics from scratch a number of times. In many places I was attempting to learn both the basic physics concepts as well as playing with how to express many of those concepts using GA formalisms. The page count proves that I did a very poor job of weeding out all the duplication. These notes are (dis)organized into the following chapters * Basics and Geometry. This chapter covers a hodge-podge collection of topics, including GA forms for traditional vector identities, Quaterions, Cauchy equations, Legendre polynomials, wedge product representation of a plane, bivector and trivector geometry, torque and more. A couple attempts at producing an introduction to GA concepts are included (none of which I was ever happy with.) * Projection. Here the concept of reciprocal frame vectors, using GA and traditional matrix formalisms is developed. Projection, rejection and Moore-Penrose (generalized inverse) operations are discussed. * Rotation. GA Rotors, Euler angles, spherical coordinates, blade exponentials, rotation generators, and infinitesimal rotations are all examined from a GA point of view. * Calculus. Here GA equivalents for a number of vector calculus relations are developed, spherical and hyperspherical volume parameterizations are derived, some questions about the structure of divergence and curl are examined, and tangent planes and normals in 3 and 4 dimensions are examined. Wrapping up this chapter is a complete GA formulation of the general Stokes theorem for curvilinear coordinates in Euclidean or non-Euclidean spaces is developed. * General Physics. This chapter introduces a bivector form of angular momentum (instead of a cross product), examines the components of radial velocity and acceleration, kinetic energy, symplectic structure, Newton's method, and a center of mass problem for a toroidal segment. * Relativity. This is a fairly incoherent chapter, including an attempt to develop the Lorentz transformation by requiring wave equation invariance, Lorentz transformation of the four-vector (STA) gradient, and a look at the relativistic doppler equation. * Electrodynamics. The GA formulation of Maxwell's equation (singular in GA) is developed here. Various basic topics of electrodynamics are examined using the GA toolbox, including the Biot-Savart law, the covariant form for Maxwell's equation (Space Time Algebra, or STA), four vectors and potentials, gauge invariance, TEM waves, and some Lienard-Wiechert problems. * Lorentz Force. Here the GA form of the Lorentz force equation and its relation to the usual vectorial representation is explored. This includes some application of boosts to the force equation to examine how it transforms under observe dependent conditions. * Electrodynamic stress energy. This chapter explores concepts of electrodynamic energy and momentum density and the GA representation of the Poynting vector and the stress-energy tensors. * Quantum Mechanics. This chapter includes a look at the Dirac Lagrangian, and how this can be cast into GA form. Properties of the Pauli and Dirac bases are explored, and how various matrix operations map onto their GA equivalents. A bivector form for the angular momentum operator is examined. A multivector form for the first few spherical harmonic eigenfunctions is developed. A multivector factorization of the three and four dimensional Laplacian and the angular momentum operators are derived. * Fourier treatments. Solutions to various PDE equations are attempted using Fourier series and transforms. Much of this chapter was exploring Fourier solutions to the GA form of Maxwell's equation, but a few other non-geometric algebra Fourier problems were also tackled.