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10-07-2014, 00:27
Vector and Tensor Analysis with Applications

A. I. Borisenko, I. E. Tarapov, Mathematics, Richard A. Silverman, "Vector and Tensor Analysis with Applications"
English | 1979 | ISBN: 0486638332 | PDF | pages: 265 | 8,6 mb


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8-07-2014, 19:17
Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum

Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum by Maresuke Shiraishi
English | ISBN: 4431541799 | 2013 | 165 pages | PDF | 3,7 MB

The non-Gaussianity in the primordial density fluctuations is a key feature to clarify the early Universe and it has been probed with the Cosmic Microwave Background (CMB) bispectrum. In recent years, we have treated the novel-type CMB bispectra, which originate from the vector- and tensor-mode perturbations and include the violation of the rotational or parity invariance.

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1-07-2014, 09:29
Tensor Product Model Transformation in Polytopic Model-Based Control

Tensor Product Model Transformation in Polytopic Model-Based Control (Automation and Control Engineering) by Peter Baranyi, Yeung Yam and Peter Varlaki
English | ISBN: 1439818169 | 2013 | 262 pages | PDF | 4,1 MB

Tensor Product Model Transformation in Polytopic Model-Based Control offers a new perspective of control system design. Instead of relying solely on the formulation of more effective LMIs, which is the widely adopted approach in existing LMI-related studies, this cutting-edge book calls for a systematic modification and reshaping of the polytopic convex hull to achieve enhanced performance.

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15-06-2014, 16:56
Categories and Modules with K-Theory in View
A. J. Berrick, M. E. Keating, "Categories and Modules with K-Theory in View"
2000 | pages: 391 | ISBN: 0521632765 | PDF | 28,9 mb


This book develops aspects of category theory fundamental to the study of algebraic K-theory. Starting with categories in general, the text then examines categories of K-theory and moves on to tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits. The authors consider local-global techniques that supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry. Many useful exercises, concrete illustrations of abstract concepts, and an extensive list of references are included.

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13-05-2014, 20:16

A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathem...

A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity by Peter Collier
2013 | ISBN: 0957389442 | English | 364 pages | PDF | 13 MB


Based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence - Einstein's theories of special and general relativity together form a cornerstone of modern physics. Special relativity has some strangely counter-intuitive consequences, including time dilation, length contraction, the relativity of simultaneity and mass-energy equivalence, whilst general relativity is at the heart of our understanding of black holes and the evolution of the universe.

Using straightforward, accessible language, with numerous fully solved problems and clear derivations and explanations, this book is aimed at the enthusiastic general reader who wants to move beyond maths-lite popularisations and tackle the essential mathematics of this fascinating theory. (To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics.) For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution; the four classical tests of general relativity; simple black holes; the mysteries of dark energy and the cosmological constant; and the Friedmann equations and Friedmann-Robertson-Walker cosmological models.

Understand even the basics of Einstein's amazing theory and the world will never seem the same again.

Contents
Preface
Introduction
1 Foundation mathematics
2 Newtonian mechanics
3 Special relativity
4 Introducing the manifold
5 Scalars, vectors, one-forms and tensors
6 More on curvature
7 General relativity
8 The Newtonian limit
9 The Schwarzschild metric
10 Schwarzschild black holes
11 Cosmology
Bibliography
Appendix - Planetary motion data
Acknowledgements

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