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Books > Academic & Education > Professional & Technical > Mathematics
This unique book is a guide for students and graduates of
mathematics, statistics, economics, finance, and other number-based
disciplines contemplating a career in actuarial science. Given the
comprehensive range of the cases that are analyzed in the book, the
Actuaries' Survival Guide can serve as a companion to existing
study material for all courses designed to prepare students for
actuarial examinations.
* Based on the curricula and examinations of the Society of
Actuaries (SOA) and the Casualty Actuarial Society (CAS)
* Presents an overview of career options and details on employment
in different industries
* Provides a link between theory and practice; helps readers gain
the qualitative and quantitative skills and knowledge required to
succeed in actuarial exams
* Includes insights from over 50 actuaries and actuarial
students
* Written by Fred Szabo, who has directed the actuarial co-op
program at Concordia University for over ten years
This book is the first attempt to develop systematically a general
theory of the initial-boundary value problems for nonlinear
evolution equations with pseudodifferential operators Ku on a
half-line or on a segment. We study traditionally important
problems, such as local and global existence of solutions and their
properties, in particular much attention is drawn to the asymptotic
behavior of solutions for large time. Up to now the theory of
nonlinear initial-boundary value problems with a general
pseudodifferential operator has not been well developed due to its
difficulty. There are many open natural questions. Firstly how many
boundary data should we pose on the initial-boundary value problems
for its correct solvability? As far as we know there are few
results in the case of nonlinear nonlocal equations. The methods
developed in this book are applicable to a wide class of dispersive
and dissipative nonlinear equations, both local and nonlocal.
-For the first time the definition of pseudodifferential operator
on a half-line and a segment is done
-A wide class of nonlinear nonlocal and local equations is
considered
-Developed theory is general and applicable to different
equations
-The book is written clearly, many examples are considered
-Asymptotic formulas can be used for numerical computations by
engineers and physicists
-The authors are recognized experts in the nonlinear wave phenomena
All the existing books in Infinite Dimensional Complex Analysis
focus on the problems of locally convex spaces. However, the theory
without convexity condition is covered for the first time in this
book. This shows that we are really working with a new, important
and interesting field.
Theory of functions and nonlinear analysis problems are widespread
in the mathematical modeling of real world systems in a very broad
range of applications. During the past three decades many new
results from the author have helped to solve multiextreme problems
arising from important situations, non-convex and non linear cases,
in function theory.
Foundations of Complex Analysis in Non Locally Convex Spaces is a
comprehensive book that covers the fundamental theorems in Complex
and Functional Analysis and presents much new material.
The book includes generalized new forms of: Hahn-Banach Theorem,
Multilinear maps, theory of polynomials, Fixed Point Theorems,
p-extreme points and applications in Operations Research,
Krein-Milman Theorem, Quasi-differential Calculus, Lagrange
Mean-Value Theorems, Taylor series, Quasi-holomorphic and
Quasi-analytic maps, Quasi-Analytic continuations, Fundamental
Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for
Definite Integral, Bounding and weakly-bounding (limited) sets,
Holomorphic Completions, and Levi problem.
Each chapter contains illustrative examples to help the student and
researcher to enhance his knowledge of theory of functions.
The new concept of Quasi-differentiability introduced by the author
represents the backbone of the theory of Holomorphy for non-locally
convex spaces. In fact it is different but much stronger than the
Frechet one.
The book is intended not only for Post-Graduate (M.Sc.& Ph.D.)
students and researchers in Complex and Functional Analysis, but
for all Scientists in various disciplines whom need nonlinear or
non-convex analysis and holomorphy methods without convexity
conditions to model and solve problems.
bull; The book contains new generalized versions of:
i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in
real and complex cases, Hahn-Banach Theorems, Bolzano Theorem,
Krein-Milman Theorem, Mean value Theorem for Definite Integral, and
many others.
ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's.
bull; The book contains some applications in Operations research
and non convex analysis as a consequence of the new concept
p-Extreme points given by the author.
bull; The book contains a complete theory for Taylor Series
representations of the different types of holomorphic maps in
F-spaces without convexity conditions.
bull; The book contains a general new concept of differentiability
stronger than the Frechet one. This implies a new Differentiable
Calculus called Quasi-differential (or Bayoumi differential)
Calculus. It is due to the author's discovery in 1995.
bull; The book contains the theory of polynomials and Banach
Stienhaus theorem in non convex spaces.
Modal logics, originally conceived in philosophy, have recently
found many applications in computer science, artificial
intelligence, the foundations of mathematics, linguistics and other
disciplines. Celebrated for their good computational behaviour,
modal logics are used as effective formalisms for talking about
time, space, knowledge, beliefs, actions, obligations, provability,
etc. However, the nice computational properties can drastically
change if we combine some of these formalisms into a
many-dimensional system, say, to reason about knowledge bases
developing in time or moving objects.
To study the computational behaviour of many-dimensional modal
logics is the main aim of this book. On the one hand, it is
concerned with providing a solid mathematical foundation for this
discipline, while on the other hand, it shows that many seemingly
different applied many-dimensional systems (e.g., multi-agent
systems, description logics with epistemic, temporal and dynamic
operators, spatio-temporal logics, etc.) fit in perfectly with this
theoretical framework, and so their computational behaviour can be
analyzed using the developed machinery.
We start with concrete examples of applied one- and
many-dimensional modal logics such as temporal, epistemic, dynamic,
description, spatial logics, and various combinations of these.
Then we develop a mathematical theory for handling a spectrum of
'abstract' combinations of modal logics - fusions and products of
modal logics, fragments of first-order modal and temporal logics -
focusing on three major problems: decidability, axiomatizability,
and computational complexity. Besides the standard methods of modal
logic, the technical toolkit includes the method of quasimodels,
mosaics, tilings, reductions to monadic second-order logic,
algebraic logic techniques. Finally, we apply the developed
machinery and obtained results to three case studies from the field
of knowledge representation and reasoning: temporal epistemic
logics for reasoning about multi-agent systems, modalized
description logics for dynamic ontologies, and spatio-temporal
logics.
The genre of the book can be defined as a research monograph. It
brings the reader to the front line of current research in the
field by showing both recent achievements and directions of future
investigations (in particular, multiple open problems). On the
other hand, well-known results from modal and first-order logic are
formulated without proofs and supplied with references to
accessible sources.
The intended audience of this book is logicians as well as those
researchers who use logic in computer science and artificial
intelligence. More specific application areas are, e.g., knowledge
representation and reasoning, in particular, terminological,
temporal and spatial reasoning, or reasoning about agents. And we
also believe that researchers from certain other disciplines, say,
temporal and spatial databases or geographical information systems,
will benefit from this book as well.
Key Features:
Integrated approach to modern modal and temporal logics and their
applications in artificial intelligence and computer science
Written by internationally leading researchers in the field of
pure and applied logic
Combines mathematical theory of modal logic and applications in
artificial intelligence and computer science
Numerous open problems for further research
Well illustrated with pictures and tables
"
This monograph provides a comprehensive treatment of expansion
theorems for regular systems of first order differential equations
and "n"-th order ordinary differential equations.
In 10 chapters and one appendix, it provides a comprehensive
treatment from abstract foundations to applications in physics and
engineering. The focus is on non-self-adjoint problems. Bounded
operators are associated to these problems, and Chapter 1 provides
an in depth investigation of eigenfunctions and associated
functions for bounded Fredholm valued operators in Banach spaces.
Since every "n"-th order differential equation is equivalent
to a first order system, the main techniques are developed for
systems. Asymptotic fundamental
systems are derived for a large class of systems of differential
equations. Together with boundary
conditions, which may depend polynomially on the eigenvalue
parameter, this leads to the definition of Birkhoff and Stone
regular eigenvalue problems. An effort is made to make the
conditions relatively easy verifiable; this is illustrated with
several applications in chapter 10.
The contour integral method and estimates of the resolvent are used
to prove expansion theorems.
For Stone regular problems, not all functions are expandable, and
again relatively easy verifiable
conditions are given, in terms of auxiliary boundary conditions,
for functions to be expandable.
Chapter 10 deals exclusively with applications; in nine sections,
various concrete problems such as
the Orr-Sommerfeld equation, control of multiple beams, and an
example from meteorology are investigated.
Key features:
Expansion Theorems for Ordinary Differential Equations
Discusses Applications to Problems from Physics and
Engineering
Thorough Investigation of Asymptotic Fundamental Matrices and
Systems
Provides a Comprehensive Treatment
Uses the Contour Integral Method
Represents the Problems as Bounded Operators
Investigates Canonical Systems of Eigen- and Associated Vectors
for Operator Functions
"
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
"
Since their introduction in the 1980's, wavelets have become a
powerful tool in mathematical analysis, with applications such as
image compression, statistical estimation and numerical simulation
of partial differential equations. One of their main attractive
features is the ability to accurately represent fairly general
functions with a small number of adaptively chosen wavelet
coefficients, as well as to characterize the smoothness of such
functions from the numerical behaviour of these coefficients. The
theoretical pillar that underlies such properties involves
approximation theory and function spaces, and plays a pivotal role
in the analysis of wavelet-based numerical methods.
This book offers a self-contained treatment of wavelets, which
includes this theoretical pillar and it applications to the
numerical treatment of partial differential equations. Its key
features are:
1. Self-contained introduction to wavelet bases and related
numerical algorithms, from the simplest examples to the most
numerically useful general constructions.
2. Full treatment of the theoretical foundations that are crucial
for the analysis
of wavelets and other related multiscale methods: function spaces,
linear and nonlinear approximation, interpolation theory.
3. Applications of these concepts to the numerical treatment of
partial differential equations: multilevel preconditioning, sparse
approximations of differential and integral operators, adaptive
discretization strategies.
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.
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.
Relation algebras are algebras arising from the study of binary
relations.
They form a part of the field of algebraic logic, and have
applications in proof theory, modal logic, and computer science.
This research text uses combinatorial games to study the
fundamental notion of representations of relation algebras. Games
allow an intuitive and appealing approach to the subject, and
permit substantial advances to be made. The book contains many new
results and proofs not published elsewhere. It should be invaluable
to graduate students and researchers interested in relation
algebras and games.
After an introduction describing the authors' perspective on the
material, the text proper has six parts. The lengthy first part is
devoted to background material, including the formal definitions of
relation algebras, cylindric algebras, their basic properties, and
some connections between them. Examples are given. Part 1 ends with
a short survey of other work beyond the scope of the book. In part
2, games are introduced, and used to axiomatise various classes of
algebras. Part 3 discusses approximations to representability,
using bases, relation algebra reducts, and relativised
representations. Part 4 presents some constructions of relation
algebras, including Monk algebras and the 'rainbow construction',
and uses them to show that various classes of representable
algebras are non-finitely axiomatisable or even non-elementary.
Part 5 shows that the representability problem for finite relation
algebras is undecidable, and then in contrast proves some finite
base property results. Part 6 contains a condensed summary of the
book, and a list of problems. There are more than 400
exercises.
The book is generally self-contained on relation algebras and on
games, and introductory text is scattered throughout. Some
familiarity with elementary aspects of first-order logic and set
theory is assumed, though many of the definitions are given.
Chapter 2 introduces the necessary universal algebra and model
theory, and more specific model-theoretic ideas are explained as
they arise.
This series of volumes covers all the major aspects of numerical
analysis, serving as the basic reference work on the subject. Each
volume concentrates on one to three particular topics. Each
article, written by an expert, is an in-depth survey, reflecting
up-to-date trends in the field, and is essentially self-contained.
The handbook will cover the basic methods of numerical analysis,
under the following general headings: solution of equations in Rn;
finite difference methods; finite element methods; techniques of
scientific computing; optimization theory; and systems science. It
will also cover the numerical solution of actual problems of
contemporary interest in applied mathematics, under the following
headings: numerical methods for fluids; numerical methods for
solids; and specific applications - including meteorology,
seismology, petroleum mechanics and celestial mechanics.
This is a student solutions manual for Elementary Number Theory
with Applications 1st edition by Thomas Koshy (2002). Note that the
textbook itself is not included in this purchase. From the back
cover of the textbook: Modern technology has brought a new
dimension to the power of number theory: constant practical use.
Once considered the purest of pure mathematics, number theory has
become an essential tool in the rapid development of technology in
a number of areas, including art, coding theory, cryptology, and
computer science. The range of fascinating applications confirms
the boundlessness of human ingenuity and creativity. Elementary
Number Theory captures the author's fascination for the subject:
its beauty, elegance, and historical development, and the
opportunities number theory provides for experimentation,
exploration, and, of course, its marvelous applications.
Computable Calculus treats the fundamental topic of calculus in a
novel way that is more in tune with today's computer age.
Comprising 11 chapters and an accompanying CD-ROM, the book
presents mathematical analysis that has been created to deal with
constructively defined concepts. The book's "show your work"
approach makes it easier to understand the pitfalls of various
computations and, more importantly, how to avoid these pitfalls.
The accompanying CD-ROM has self-contained programs that interact
with the text, providing for easy grasp of the new concepts and
enabling readers to write their own demonstration programs.
Contains software on CD ROM:
The accompanying software demonstrates, through simulation and
exercises, how each concept of calculus can be associated with a
program for the 'ideal computer'
Using this software readers will be able to write their own
demonstration programs
Codes on Euclidean spheres are often referred to as spherical
codes. They are of interest from mathematical, physical and
engineering points of view. Mathematically the topic belongs to the
realm of algebraic combinatorics, with close connections to number
theory, geometry, combinatorial theory, and - of course - to
algebraic coding theory. The connections to physics occur within
areas like crystallography and nuclear physics. In engineering
spherical codes are of central importance in connection with
error-control in communication systems. In that context the use of
spherical codes is often referred to as "coded modulation."
The book offers a first complete treatment of the mathematical
theory of codes on Euclidean spheres. Many new results are
published here for the first time. Engineering applications are
emphasized throughout the text. The theory is illustrated by many
examples. The book also contains an extensive table of best known
spherical codes in dimensions 3-24, including exact
constructions.
/homepage/sac/cam/na2000/index.html7-Volume Set now available at
special set price
This volume is dedicated to two closely related subjects:
interpolation and extrapolation. The papers can be divided into
three categories: historical papers, survey papers and papers
presenting new developments.
Interpolation is an old subject since, as noticed in the paper by
M. Gasca and T. Sauer, the term was coined by John Wallis in 1655.
Interpolation was the first technique for obtaining an
approximation of a function. Polynomial interpolation was then used
in quadrature methods and methods for the numerical solution of
ordinary differential equations.
Extrapolation is based on interpolation. In fact, extrapolation
consists of interpolation at a point outside the interval
containing the interpolation points. Usually, this point is either
zero or infinity. Extrapolation is used in numerical analysis to
improve the accuracy of a process depending of a parameter or to
accelerate the convergence of a sequence. The most well-known
extrapolation processes are certainly Romberg's method for
improving the convergence of the trapezoidal rule for the
computation of a definite integral and Aiken's &Dgr;2 process
which can be found in any textbook of numerical analysis.
Obviously, all aspects of interpolation and extrapolation have not
been treated in this volume. However, many important topics have
been covered.
This book introduces interested readers, practitioners, and
researchers to "Mathematica methods for solving practical problems
in linear algebra. It contains step-by-step solutions of problems
in computer science, economics, engineering, mathematics,
statistics, and other areas of application. Each chapter contains
both elementary and more challenging problems, grouped by fields of
application, and ends with a set of exercises. Selected answers are
provided in an appendix. The book contains a glossary of
definitions and theorem, as well as a summary of relevant
"Mathematica tools. Applications of Linear Algebra can be used both
in laboratory sessions and as a source of take-home problems and
projects.
* Concentrates on problem solving and aims to increase the
readers' analytical skills
* Provides ample opportunities for applying theoretical results and
transferring knowledge between different areas of application;
Mathematica plays a key role in this process
* Makes learning fun and builds confidence
* Allows readers to tackle computationally challenging problems by
minimizing the frustration caused by the arithmetic intricacies of
numerical linear algebra
The increased computational power and software tools available to
engineers have increased the use and dependence on modeling and
computer simulation throughout the design process. These tools have
given engineers the capability of designing highly complex systems
and computer architectures that were previously unthinkable. Every
complex design project, from integrated circuits, to aerospace
vehicles, to industrial manufacturing processes requires these new
methods. This book fulfills the essential need of system and
control engineers at all levels in understanding modeling and
simulation. This book, written as a true text/reference has become
a standard sr./graduate level course in all EE departments
worldwide and all professionals in this area are required to update
their skills.
The book provides a rigorous mathematical foundation for modeling
and computer simulation. It provides a comprehensive framework for
modeling and simulation integrating the various simulation
approaches. It covers model formulation, simulation model
execution, and the model building process with its key activities
model abstraction and model simplification, as well as the
organization of model libraries. Emphasis of the book is in
particular in integrating discrete event and continuous modeling
approaches as well as a new approach for discrete event simulation
of continuous processes. The book also discusses simulation
execution on parallel and distributed machines and concepts for
simulation model realization based on the High Level Architecture
(HLA) standard of the Department of Defense.
* Presents a working foundation necessary for compliance with
High Level Architecture (HLA) standards
* Provides a comprehensive framework for continuous and discrete
event modeling and simulation
* Explores the mathematical foundation of simulation modeling
* Discusses system morphisms for model abstraction and
simplification
* Presents a new approach to discrete event simulation of
continuous processes
* Includes parallel and distributed simulation of discrete event
models
* Presentation of a concept to achieve simulator interoperability
in the form of the DEVS-Bus
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.
The aim of the present work is two-fold. Firstly it aims at a
giving an account of many existing algorithms for calculating with
finite-dimensional Lie algebras. Secondly, the book provides an
introduction into the theory of finite-dimensional Lie algebras.
These two subject areas are intimately related. First of all, the
algorithmic perspective often invites a different approach to the
theoretical material than the one taken in various other monographs
(e.g., 42], 48], 77], 86]). Indeed, on various occasions the
knowledge of certain algorithms allows us to obtain a
straightforward proof of theoretical results (we mention the proof
of the Poincare-Birkhoff-Witt theorem and the proof of Iwasawa's
theorem as examples). Also proofs that contain algorithmic
constructions are explicitly formulated as algorithms (an example
is the isomorphism theorem for semisimple Lie algebras that
constructs an isomorphism in case it exists). Secondly, the
algorithms can be used to arrive at a better understanding of the
theory. Performing the algorithms in concrete examples, calculating
with the concepts involved, really brings the theory of life.
In this book, fifteen authors from a wide spectrum of disciplines
(ranging from the natural sciences to the arts) offer assessments
of the way time enters their work, the definition and uses of time
that have proved most productive or problematic, and the lessons
their subjects can offer for our understanding of time beyond the
classroom and laboratory walls. The authors have tried, without
sacrificing analytical rigour, to make their contribution
accessible to a cross-disciplinary readership.
Each chapter reviews time's past and present application in its
respective field, considers the practical and logical problems that
remain, and assesses the methods researchers are using to escape or
resolve them. Particular attention is paid to ways in which the
technical treatment of time, for problem-solving and model-building
around specific phenomena, call on - or clash with - our intuitive
perceptions of what time is and does. The spans of time considered
range from the fractions of seconds it takes unstable particles to
disintegrate to the millions of years required for one species to
give way to another. Like all central conceptual words, time is
understood on several levels. By inviting input from a broad range
of disciplines, the book aims to provide a fuller understanding of
those levels, and of the common ground that lurks at their base.
Much agreement emerges - not only on the nature of the problems
time presents to modern intellectual thought, but also on the clues
that recent discoveries may offer towards possible solutions.
This book treats modal logic as a theory, with several subtheories,
such as completeness theory, correspondence theory, duality theory
and transfer theory and is intended as a course in modal logic for
students who have had prior contact with modal logic and who wish
to study it more deeply. It presupposes training in mathematical or
logic. Very little specific knowledge is presupposed, most results
which are needed are proved in this book.
The objective of Volume II is to show how asymptotic methods, with
the thickness as the small parameter, indeed provide a powerful
means of justifying two-dimensional plate theories. More
specifically, without any recourse to any "a priori" assumptions of
a geometrical or mechanical nature, it is shown that in the linear
case, the three-dimensional displacements, once properly scaled,
converge in "H"1 towards a limit that satisfies the well-known
two-dimensional equations of the linear Kirchhoff-Love theory; the
convergence of stress is also established.
In the nonlinear case, again after "ad hoc" scalings have been
performed, it is shown that the leading term of a formal asymptotic
expansion of the three-dimensional solution satisfies well-known
two-dimensional equations, such as those of the nonlinear
Kirchhoff-Love theory, or the von Karman equations. Special
attention is also given to the first convergence result obtained in
this case, which leads to two-dimensional large deformation,
frame-indifferent, nonlinear membrane theories. It is also
demonstrated that asymptotic methods can likewise be used for
justifying other lower-dimensional equations of elastic shallow
shells, and the coupled pluri-dimensional equations of elastic
multi-structures, i.e., structures with junctions. In each case,
the existence, uniqueness or multiplicity, and regularity of
solutions to the limit equations obtained in this fashion are also
studied.
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.
The problems of constructing covering codes and of estimating their
parameters are the main concern of this book. It provides a unified
account of the most recent theory of covering codes and shows how a
number of mathematical and engineering issues are related to
covering problems.
Scientists involved in discrete mathematics, combinatorics,
computer science, information theory, geometry, algebra or number
theory will find the book of particular significance. It is
designed both as an introductory textbook for the beginner and as a
reference book for the expert mathematician and engineer.
A number of unsolved problems suitable for research projects are
also discussed.
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