The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.
The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.
The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.

This is the first book that can be considered a textbook on thin film science, complete with exercises at the end of each chapter. Ohring has contributed many highly regarded reference books to the AP list, including Reliability and Failure of Electronic Materials and the Engineering Science of Thin Films. The knowledge base is intended for science and engineering students in advanced undergraduate or first-year graduate level courses on thin films and scientists and engineers who are entering or require an overview of the field.
Since 1992, when the book was first published, the field of thin films has expanded tremendously, especially with regard to technological applications. The second edition will bring the book up-to-date with regard to these advances. Most chapters have been greatly updated, and several new chapters have been added.

This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.

The book is devoted to universality problems.
A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as:
universal mappings, dimension theory, action of groups, inverse spectra, isometrical embeddings, and so on.
.Universal spaces
.Universal mappings
.Dimension theory
.Actions of groups
.Isometric Universal Spaces

Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, "A MatLab Companion for Multivariable Calculus" introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http: //www.harcourt-ap.com/matlab.html.
* Computer-oriented material that complements the essential topics in multivariable calculus
* Main ideas presented with examples of computations and graphics displays using MATLAB
* Numerous examples of short code in the text, which can be modified for use with the exercises
* MATLAB files are used to implement graphics displays and contain a collection of mfiles which can serve as demos

"Difference Equations, Second Edition," presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.

* Phase plane analysis for systems of two linear equations
* Use of equations of variation to approximate solutions
* Fundamental matrices and Floquet theory for periodic systems
* LaSalle invariance theorem
* Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
* Appendix on the use of "Mathematica" for analyzing difference equaitons
* Exponential generating functions
* Many new examples and exercises

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-like methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book.

The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.

Agenda Relevance is the first volume in the authors' omnibus investigation of
the logic of practical reasoning, under the collective title, A Practical Logic
of Cognitive Systems. In this highly original approach, practical reasoning is
identified as reasoning performed with comparatively few cognitive assets,
including resources such as information, time and computational capacity. Unlike
what is proposed in optimization models of human cognition, a practical reasoner
lacks perfect information, boundless time and unconstrained access to
computational complexity. The practical reasoner is therefore obliged to be a
cognitive economizer and to achieve his cognitive ends with considerable
efficiency. Accordingly, the practical reasoner avails himself of various
scarce-resource compensation strategies. He also possesses neurocognitive
traits that abet him in his reasoning tasks. Prominent among these is the
practical agent's striking (though not perfect) adeptness at evading irrelevant
information and staying on task. On the approach taken here, irrelevancies are
impediments to the attainment of cognitive ends. Thus, in its most basic sense,
relevant information is cognitively helpful information. Information can then be
said to be relevant for a practical reasoner to the extent that it advances or
closes some cognitive agenda of his. The book explores this idea with a
conceptual detail and nuance not seen the standard semantic, probabilistic and
pragmatic approaches to relevance; but wherever possible, the authors seek to
integrate alternative conceptions rather than reject them outright. A further
attraction of the agenda-relevance approach is the extent to which its principal
conceptual findings lend themselves to technically sophisticated re-expression
in formal models that marshal the resources of time and action logics and
label led deductive systems.

Agenda Relevance is necessary reading for researchers in logic, belief
dynamics, computer science, AI, psychology and neuroscience, linguistics,
argumentation theory, and legal reasoning and forensic science, and will repay
study by graduate students and senior undergraduates in these same fields.

Key features:

relevance
action and agendas
practical reasoning
belief dynamics
non-classical logics
labelled deductive systems

"

In this revolutionary work, the author sets the stage for the science of
the 21st Century, pursuing an unprecedented synthesis of fields previously
considered unrelated. Beginning with simple classical concepts, he ends
with a complex multidisciplinary theory requiring a high level of
abstraction. The work progresses across the sciences in several
multidisciplinary directions: Mathematical logic, fundamental physics,
computer science and the theory of intelligence. Extraordinarily enough,
the author breaks new ground in all these fields.

In the field of
fundamental physics the author reaches the revolutionary conclusion that
physics can be viewed and studied as logic in a fundamental sense, as
compared with Einstein's view of physics as space-time geometry. This opens
new, exciting prospects for the study of fundamental interactions. A
formulation of logic in terms of matrix operators and logic vector spaces
allows the author to tackle for the first time the intractable problem of
cognition in a scientific manner. In the same way as the findings of
Heisenberg and Dirac in the 1930s provided a conceptual and mathematical
foundation for quantum physics, matrix operator logic supports an important
breakthrough in the study of the physics of the mind, which is interpreted
as a fractal of quantum mechanics. Introducing a concept of logic quantum
numbers, the author concludes that the problem of logic and the
intelligence code in general can be effectively formulated as eigenvalue
problems similar to those of theoretical physics. With this important leap
forward in the study of the mechanism of mind, the author concludes that
the latter cannot be fully understood either within classical or quantum
notions. A higher-order covariant theory is required to accommodate the
fundamental effect of high-level intelligence. The landmark results
obtained by the author will have implications and repercussions for the
very foundations of science as a whole. Moreover, Stern's Matrix Logic is
suitable for a broad spectrum of practical applications in contemporary
technologies.

Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

This encyclopedia contains more than 5000 integer sequences, over half of which have never before been catalogued. Because the sequences are presented in the most natural form, and arranged for easy reference, this book is easier to use than the authors earlier classic "A Handbook of Integer Sequences. The Encyclopedia gives the name, mathematical description, and citations to literature for each sequence. Following sequences of particular interest, thereare essays on their origins, uses, and connections to related sequences (all cross-referenced). A valuable new feature to this text is the inclusion of a number of interesting diagrams and illustrations related to selected sequences.
The initial chapters are both amusing and enlightening. They serve as a delightful introduction to the subject and a short course on how to identify and work with integer sequences. This encyclopedia brings Sloanes ground-breaking "Handbook up to date, more than doubling its size, and linking both the old and the new material to an extensive bibliography (over 25 pages long), of current and classic references. An index to all the sequences in the book is also available separately on disk in Macintosh and IBM formats.
Key Features
* Contains more than 5000 integer sequences
* Gives the name and mathematical description of each sequence
* Provides citations to literature for each sequence
* Extensively cross-referenced
* Lists a bibliography of more than 25 pages

The book presents surveys describing recent developments in most of the primary subfields of
General Topology and its applications to Algebra and Analysis during the last decade. It follows freely
the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and
Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in
connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus
in General Topology changed and therefore the selection of topics differs slightly from those
chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including
Infinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic
could be included in this book.

Except surveys, the book contains several historical essays written by such eminent topologists as:
R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added.

List of all authors of surveys:
A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled "The logic of quantum mechanics" quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.
Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate.
The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject.
The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.
- Written by eminent scholars in the field of logic
- A comprehensive presentation of the theory, approaches and results in the field of quantum logic
- Volume focuses on quantum structures

Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker.
In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems.
The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time.
- computable bounds of approximation errors
- checking algorithms
- iteration processes
- finite element methods
- elliptic type problems
- nonlinear variational problems
- variational inequalities

In 1974 the editors of the present volume published a well-received book entitled Latin Squares and their Applications''. It included a list of 73 unsolved problems of which about 20 have been completely solved in the intervening period and about 10 more have been partially solved.
The present work comprises six contributed chapters and also six further chapters written by the editors themselves. As well as discussing the advances which have been made in the subject matter of most of the chapters of the earlier book, this new book contains one chapter which deals with a subject (r-orthogonal latin squares) which did not exist when the earlier book was written.
The success of the former book is shown by the two or three hundred published papers which deal with questions raised by it.

The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.

This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.

The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.

The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.
Key Features
* This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis
* This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis
* Suitable as a textbook for a beginning course on wavelet analysis

The conference took place in Lviv, Ukraine and was dedicated to a famous Polish mathematician Stefan Banach { the most outstanding representative of the Lviv mathematical school. Banach spaces, introduced by Stefan Banach at the beginning of twentieth century, are familiar now to every mathematician. The book contains a short historical article and scientific contributions of the conference participants, mostly in the areas of functional analysis, general topology, operator theory and related topics.

Threshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract much attention.

The book contains many open problems and research ideas which will appeal to graduate students and researchers interested in graph theory. But above all "Threshold Graphs and Related Topics" provides a valuable source of information for all those working in this field.

General concepts and methods that occur throughout mathematics and now also in theoretical computer science are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further.
The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi.
A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.
"

This is the first comprehensive treatment of the theoretical aspects of the discrete cosine transform (DCT), which is being recommended by various standards organizations, such as the CCITT, ISO etc., as the primary compression tool in digital image coding. The main purpose of the book is to provide a complete source for the user of this signal processing tool, where both the basics and the applications are detailed. An extensive bibliography covers both the theory and applications of the DCT. The novice will find the book useful in its self-contained treatment of the theory of the DCT, the detailed description of various algorithms supported by computer programs and the range of possible applications, including codecs used for teleconferencing, videophone, progressive image transmission, and broadcast TV. The more advanced user will appreciate the extensive references. Tables describing ASIC VLSI chips for implementing DCT, and motion estimation and details on image compression boards are also provided.