Think Before You Compute: A Prelude to Computational Fluid Dynamics, E. J. Hinch

Автор: Strang Gilbert
Название: Linear Algebra and Learning from Data
ISBN: 0692196382 ISBN-13(EAN): 9780692196380
Издательство: Cambridge Academ
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Цена: 66520.00 T
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Описание: Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.

Автор: Nederpelt
Название: Type Theory and Formal Proof
ISBN: 110703650X ISBN-13(EAN): 9781107036505
Издательство: Cambridge Academ
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Цена: 70740.00 T
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Описание: Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This book provides a gentle step-by-step introduction in the art of formalizing mathematics on the basis of type theory. It is suitable for a broad audience, ranging from undergraduate students to researchers.

Автор: E. J. Hinch
Название: Think Before You Compute: A Prelude to Computational Fluid Dynamics
ISBN: 1108789994 ISBN-13(EAN): 9781108789998
Издательство: Cambridge Academ
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Цена: 40130.00 T
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Описание: This guide to computational fluid mechanics is for any beginning graduate student who is thinking of computing a flow. The text starts with a quick introduction to enable students to solve numerically a simple problem by a simple method, before detailing all the key essentials and discussing optional advanced topics.

Автор: Chi Tat Chong, Liang Yu
Название: Recursion Theory: Computational Aspects of Definability
ISBN: 3110275554 ISBN-13(EAN): 9783110275551
Издательство: Walter de Gruyter
Цена: 138080.00 T
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Описание: This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory.The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

Автор: von zur Gathen
Название: Modern Computer Algebra
ISBN: 1107039037 ISBN-13(EAN): 9781107039032
Издательство: Cambridge Academ
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Цена: 117210.00 T
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Описание: Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students, this textbook is widely regarded as the `bible of computer algebra`. Its comprehensiveness and reliability also makes it an essential reference for professionals. This updated edition includes an overview of recent improvements in areas like primality testing.

Автор: J.-J. Ch. Meyer, W. van der Hoek
Название: Epistemic Logic for AI and Computer Science
ISBN: 0521602807 ISBN-13(EAN): 9780521602808
Издательство: Cambridge Academ
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Цена: 61240.00 T
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Описание: This book, based on courses taught at universities and summer schools, provides a broad introduction to the subject; many exercises are included with their solutions.

Название: Theoretical and Computational Research in the 21st Century
ISBN: 1771880333 ISBN-13(EAN): 9781771880336
Издательство: Taylor&Francis
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Цена: 122490.00 T
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Описание: This book focuses mainly on the recent developments of all types of theoretical, mathematical, and computational conceptions, as well as modelling and simulation of specific research themes covering all scientific and technical disciplines from chemistry, physics, and engineering to biology and medicine. The book contains timely reviews and research covering fundamental and applied research aspects in all disciplines of natural sciences, including their historical representations and philosophical perspectives. The book discusses the fact that the largest and smallest values of the fukui function and local softness do not necessarily correspond to the softness and hardness regions of the molecules such as porphyrins. The authors have adopted two popular calculation procedures for this venture. One is the very old Huckel molecular orbital calculation, and the other is one of best semi-empirical AM-1 procedures for such systems. Our finding is that neither the fukui functions nor the local softnesses can predict the preferred donor sites of porphyrins toward metal ions.

Автор: Nadezhda M. Afanasyeva,Victor S. Borisov,Aleksandr
Название: Computational Technologies: A First Course
ISBN: 3110359928 ISBN-13(EAN): 9783110359923
Издательство: Walter de Gruyter
Цена: 49530.00 T
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Описание: In this book wedescribe the basic elements of present computational technologies that use the algorithmic languages C/C++. The emphasis is on GNU compilers and libraries, FOSS for the solution of computational mathematics problems and visualization of the obtained data. At the beginning, a brief introduction to C is given with emphasis on its easy use in scientific and engineering computations.We describe the basic elements of the language, such as variables, data types, executable statements, functions, arrays, pointers, dynamic memory and file management. After that, we present some observations on the C++ programming language.We discuss the issues of program compiling, linking, and debugging. A quick guide to Eclipse is also presented in the book. The main features for editing, compiling, debugging and application assembling are considered.As examples, wesolve the standard problems of computational mathematics: operations with vectors and matrices, linear algebra problems, solution of nonlinear equations, numerical differentiation and integration, interpolation, initial value problems for ODEs and so on. Finally, basic features ofcomputational technologies are illustrated with model problems. All programs are implemented in C/C++ with using the GSL library. Gnuplot is employed to visualize the results of computations.

Автор: Petr N. Vabishchevich
Название: Computational Technologies: Advanced Topics
ISBN: 3110359944 ISBN-13(EAN): 9783110359947
Издательство: Walter de Gruyter
Цена: 61920.00 T
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Описание: This book discusses questions of numerical solutions of applied problems on parallel computing systems. Nowadays, engineering and scientific computations are carried out on parallel computing systems, which provide parallel data processing on a few computing nodes. In the development of up-to-date applied software, this feature of computers must be taken into account for the maximum efficient usage of their resources. In constructing computational algorithms, we should separate relatively independent subproblems in order to solve them on a single computing node.

Автор: Wazwaz Abdul-Majid
Название: A First Course in Integral Equations: Solutions Manual: 2nd Edition
ISBN: 9814675156 ISBN-13(EAN): 9789814675154
Издательство: World Scientific Publishing
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Цена: 33790.00 T
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Описание: The second edition of A First Course in Integral Equations integrates the newly developed methods with classical techniques to give modern and robust approaches for solving integral equations.

Автор: Chua Leon O
Название: Nonlinear Dynamics Perspective Of Wolfram`S New Kind Of Science, A (Volume Vi)
ISBN: 9814460877 ISBN-13(EAN): 9789814460873
Издательство: World Scientific Publishing
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Цена: 195360.00 T
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Описание: This invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination.The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V.This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer ?, a positive, or negative, integer ?, and a sign parameter ? > 0, or ? 0 (resp. ? < 0), and then change the color of each cell if ? < 0.As in the five prior volumes, Vol. VI also contains simple recipes which are, in fact, general and original results from the abstract theory of 1-dimensional cellular automata. Indeed, both children and experts from cellular automata will find this volume to be as deep, refreshing, and entertaining, as the previous volumes.

Автор: Viacheslav Karmalita
Название: Digital Processing of Random Oscillations
ISBN: 3110625008 ISBN-13(EAN): 9783110625004
Издательство: Walter de Gruyter
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Цена: 111510.00 T
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Описание: This book deals with the autoregressive method for digital processing of random oscillations. The method is based on a one-to-one transformation of the numeric factors of the Yule series model to linear elastic system characteristics. This parametric approach allowed to develop a formal processing procedure from the experimental data to obtain estimates of logarithmic decrement and natural frequency of random oscillations. A straightforward mathematical description of the procedure makes it possible to optimize a discretization of oscillation realizations providing efficient estimates. The derived analytical expressions for confidence intervals of estimates enable a priori evaluation of their accuracy. Experimental validation of the method is also provided. Statistical applications for the analysis of mechanical systems arise from the fact that the loads experienced by machineries and various structures often cannot be described by deterministic vibration theory. Therefore, a sufficient description of real oscillatory processes (vibrations) calls for the use of random functions. In engineering practice, the linear vibration theory (modeling phenomena by common linear differential equations) is generally used. This theory’s fundamental concepts such as natural frequency, oscillation decrement, resonance, etc. are credited for its wide use in different technical tasks. In technical applications two types of research tasks exist: direct and inverse. The former allows to determine stochastic characteristics of the system output X(t) resulting from a random process E(t) when the object model is considered known. The direct task enables to evaluate the effect of an operational environment on the designed object and to predict its operation under various loads. The inverse task is aimed at evaluating the object model on known processes E(t) and X(t), i.e. finding model (equations) factors. This task is usually met at the tests of prototypes to identify (or verify) its model experimentally. To characterize random processes a notion of "shaping dynamic system" is commonly used. This concept allows to consider the observing process as the output of a hypothetical system with the input being stationary Gauss-distributed ("white") noise. Therefore, the process may be exhaustively described in terms of parameters of that system. In the case of random oscillations, the "shaping system" is an elastic system described by the common differential equation of the second order: X ?(t)+2hX ?(t)+ ?_0^2 X(t)=E(t), where ?0 = 2?/Т0 is the natural frequency, T0 is the oscillation period, and h is a damping factor. As a result, the process X(t) can be characterized in terms of the system parameters – natural frequency and logarithmic oscillations decrement ? = hT0 as well as the process variance. Evaluation of these parameters is subjected to experimental data processing based on frequency or time-domain representations of oscillations. It must be noted that a concept of these parameters evaluation did not change much during the last century. For instance, in case of the spectral density utilization, evaluation of the decrement values is linked with bandwidth measurements at the points of half-power of the observed oscillations. For a time-domain presentation, evaluation of the decrement requires measuring covariance values delayed by a time interval divisible by T0. Both estimation procedures are derived from a continuous description of research phenomena, so the accuracy of estimates is linked directly to the adequacy of discrete representation of random oscillations. This approach is similar a concept of transforming differential equations to difference ones with derivative approximation by corresponding finite differences. The resulting discrete model, being an approximation, features a methodical error which can be decreased but never eliminated. To render such a presentation more accurate it is imperative to decrease the discretization interval and to increase realization size growing requirements for computing power. The spectral density and covariance function estimates comprise a non-parametric (non-formal) approach. In principle, any non-formal approach is a kind of art i.e. the results depend on the performer’s skills. Due to interference of subjective factors in spectral or covariance estimates of random signals, accuracy of results cannot be properly determined or justified. To avoid the abovementioned difficulties, the application of linear time-series models with well-developed procedures for parameter estimates is more advantageous. A method for the analysis of random oscillations using a parametric model corresponding discretely (no approximation error) with a linear elastic system is developed and presented in this book. As a result, a one-to-one transformation of the model’s numerical factors to logarithmic decrement and natural frequency of random oscillations is established. It allowed to develop a formal processing procedure from experimental data to obtain the estimates of ? and ?0. The proposed approach allows researchers to replace traditional subjective techniques by a formal processing procedure providing efficient estimates with analytically defined statistical uncertainties.