الصفحة 1
الصفحة 1
Number Theory and the Periodicity of Matter
The book launch was held at the University of Pretoria (UP) on 26 March 2008. … It’s a fascinating and original concept and I hope you all get the opportunity to read it. It will challenge your current views of numbers. … If there is a link between numbers and the Periodic Table this will of course have major implications as to the ‘meaning’ on the Periodic Table. It’s great to have original thinkers in our midst
Number Theory ; Vol. II : Analytic and Modern Tools
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Number Theory ; Vol. I : Tools and Diophantine Equations
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Number Theory : An Introduction via the Distribution of Primes
This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes.
Number Fields and Function Fields – Two Parallel Worlds
These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.
Nonsmooth Mechanics and Analysis : Theoretical and Numerical Advances
Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification. Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.
Noncommutative Geometry and Number Theory : Where Arithmetic meets Geometry and Physics
This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local Lfactors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
Modern parallel programming with C++ and assembly language : X86 SIMD development using AVX, AVX2, and AVX-512
Understand the essential details about x86 SIMD architectures and instruction sets including AVX, AVX2, and AVX-512. / Master x86 SIMD data types, arithmetic instructions, and data management operations using both integer and floating-point operands. / Code performance-enhancing functions and algorithms that fully exploit the SIMD capabilities of a modern x86 processor. Employ C++ intrinsic functions and x86-64 assembly language code to carry out arithmetic calculations using common programming constructs including arrays, matrices, and user-defined data structures. Harness the x86 SIMD instruction sets to significantly accelerate the performance of computationally intense algorithms in applications such as machine learning, image processing, computer graphics, statistics, and matrix arithmetic. / Apply leading-edge coding strategies and techniques to optimally exploit the x86 SIMD instruction sets for maximum possible performance.
Mathematics Education in Different Cultural Traditions- A Comparative Study of East Asia and the West : The 13th ICMI Study
The volume covers a very wide field including the contexts of mathematics education, the curriculum, teaching and learning, and teachers’ values and beliefs. Within these broad parameters some of the particular cross-cultural issues that are discussed include intuition and logical reasoning, influences of Confucianism and Ancient Greek traditions, basic skills and process abilities, learners’ perspectives, assessment practices, text books and ICT multimedia.
Introduction to Numerical Methods in Differential Equations
This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets.
Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
Intersections de deux quadriques et pinceaux de courbes de genre 1 = Intersections of two quadrics and pencils of curves of genus 1
This research monograph focuses on the arithmetic, over number fields, of surfaces fibred into curves of genus 1 over the projective line, and of intersections of two quadrics in projective space. The first half contains a complete account of the technique initiated by Swinnerton-Dyer in 1993 for studying rational points on pencils of curves of genus 1, while incorporating and generalising most of its subsequent refinements. The second half, which builds upon the first, is devoted to quartic del Pezzo surfaces and higher-dimensional intersections of two quadrics.
Information security practice and experience ; Vol. 3903 ; 2nd International Conference, ISPEC 2006, Hangzhou, China, April 11-14, 2006, Proceedings
Contains the Research Track proceedings of the Second Information Security Practice and Experience Conference 2006 (ISPEC 2006), which took place in Hangzhou, China, April 11–14, 2006. The inaugural ISPEC 2005 was held exactly one year earlier in Singapore. As applications of information security technologies become pervasive, issues pertaining to their deployment and operations are becoming increasingly imp- tant. ISPEC is an annual conference that brings together researchers and pr- titioners to provide a con?uence of new information security technologies, their applications and their integration with IT systems in various vertical sectors. ISPEC 2006 received 307 submissions.
Information security practice and experience ; 4th International Conference, ISPEC 2008 Sydney, Australia, April 21-23, 2008 Proceedings
The 4 th Information Security Practice and Experience Conference (ISPEC2008) was held at Crowne Plaza, Darling Harbour, Sydney, Australia, during April 21-23, 2008. The previous three conferences were held in Singapore in 2005, Hangzhou, China in 2006 and Hong Kong, China in 2007. As with the previous three conference proceedings, the proceedings of ISPEC 2008 were published in the LNCS series by Springer. The conference received 95 submissions, out of which the Program Committee selected 29 papers for presentation at the conference. These papers are included in the proceedings. The accepted papers cover a range of topics in mathem- ics, computer science and security applications.
High performance embedded architectures and compilers ; 3rd International Conference, HiPEAC 2008, Göteborg, Sweden, January 27-29, 2008. Proceedings
This book constitutes the refereed proceedings of the Third International Conference on High Performance Embedded Architectures and Compilers, HiPEAC 2008, held in Göteborg, Sweden, January 27-29, 2008. The 25 revised full papers presented together with 1 invited keynote paper were carefully reviewed and selected from 77 submissions. The papers are organized in topical sections on Multithreaded and Multicore Processors, Reconfigurable - ASIP, Compiler Optimizations, Industrial Processors and Application Parallelization, Power-Aware Techniques, High-Performance Processors, Profiles: Collection and Analysis as well as Optimizing Memory Performance.
Fuzzy probabilities : New approach and applications
In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.
Fuzzy mathematical programming and fuzzy matrix games
This book presents a systematic and focused study of the application of fuzzy sets to two basic areas of decision theory, namely Mathematical Programming and Matrix Game Theory. Apart from presenting most of the basic results available in the literature on these topics, the emphasis is on understanding their natural relationship in a fuzzy environment
Functional and logic programming ; 9th International Symposium, FLOPS 2008, Ise, Japan, April 14-16, 2008. Proceedings
This volume contains the proceedings of the 9th International Symposium on Functional and Logic Programming (FLOPS 2008), held in Ise, Japan, April 14-16, 2008 at the Ise City Plaza. FLOPS is a forum for research on all issues concerning functional progr- ming and logic programming. In particular it aims to stimulate the cro- fertilization as well as integration of the two paradigms. The Program Committee meeting was conducted electro- cally, for a period of two weeks in December 2007. After careful and thorough discussion, the ProgramCommittee selected20 papers(33%)for presentationat theconference.
Frontiers in Hardware Security and Trust : Theory, design and practice
The footprint and power constraints imposed on internet-of-things end-points, smart sensors, mobile and ad hoc network devices make traditional and software based cryptographic solutions that require a general-purpose processor increasingly unfeasible. The fact that security is not the primary functionality of these devices means that only a small portion of their limited processing power and storage is available for security, driving the need for alternative security solutions. Hardware security - including hardware obfuscation, hardware security primitives, side-channel attacks and so on - is therefore becoming an increasingly active research area in both academia and industry.
Foundation Mathematics for Computer Science : A Visual Approach
In this second edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the original book and written new chapters on combinatorics, probability, modular arithmetic and complex numbers. These subjects complement the existing chapters on number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers.
