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Books > Academic & Education > Professional & Technical > Mathematics
Computational Materials Engineering is an advanced introduction to
the computer-aided modeling of essential material properties and
behavior, including the physical, thermal and chemical parameters,
as well as the mathematical tools used to perform simulations. Its
emphasis will be on crystalline materials, which includes all
metals. The basis of Computational Materials Engineering allows
scientists and engineers to create virtual simulations of material
behavior and properties, to better understand how a particular
material works and performs and then use that knowledge to design
improvements for particular material applications. The text
displays knowledge of software designers, materials scientists and
engineers, and those involved in materials applications like
mechanical engineers, civil engineers, electrical engineers, and
chemical engineers.
Readers from students to practicing engineers to materials research
scientists will find in this book a single source of the major
elements that make up contemporary computer modeling of materials
characteristics and behavior. The reader will gain an understanding
of the underlying statistical and analytical tools that are the
basis for modeling complex material interactions, including an
understanding of computational thermodynamics and molecular
kinetics; as well as various modeling systems. Finally, the book
will offer the reader a variety of algorithms to use in solving
typical modeling problems so that the theory presented herein can
be put to real-world use.
Balanced coverage of fundamentals of materials modeling, as well
as more advanced aspects of modeling, such as modeling at all
scales from the atomic to the molecular to the macro-material
Concise, yet rigorous mathematical coverage of such analytical
tools as the Potts type Monte Carlo method, cellular automata,
phase field, dislocation dynamics and Finite Element Analysis in
statistical and analytical modeling
Companion web site will offer ample workable programs, along with
suggested projects, resources for further reading, and useful
classroom exercises"
The book is designed for researchers, students and practitioners
interested in using fast and efficient iterative methods to
approximate solutions of nonlinear equations. The following four
major problems are addressed. Problem 1: Show that the iterates are
well defined. Problem 2: concerns the convergence of the sequences
generated by a process and the question of whether the limit points
are, in fact solutions of the equation. Problem 3: concerns the
economy of the entire operations. Problem 4: concerns with how to
best choose a method, algorithm or software program to solve a
specific type of problem and its description of when a given
algorithm succeeds or fails. The book contains applications in
several areas of applied sciences including mathematical
programming and mathematical economics. There is also a huge number
of exercises complementing the theory.
- Latest convergence results for the iterative methods
- Iterative methods with the least computational cost
- Iterative methods with the weakest convergence conditions
- Open problems on iterative methods
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
This book (along with volume 2 covers most of the traditional
methods for polynomial root-finding such as Newton s, as well as
numerous variations on them invented in the last few decades.
Perhaps more importantly it covers recent developments such as
Vincent s method, simultaneous iterations, and matrix methods.
There is an extensive chapter on evaluation of polynomials,
including parallel methods and errors. There are pointers to robust
and efficient programs. In short, it could be entitled A Handbook
of Methods for Polynomial Root-finding . This book will be
invaluable to anyone doing research in polynomial roots, or
teaching a graduate course on that topic.
- First comprehensive treatment of Root-Finding in several
decades.
- Gives description of high-grade software and where it can be
down-loaded.
- Very up-to-date in mid-2006; long chapter on matrix
methods.
- Includes Parallel methods, errors where appropriate.
- Invaluable for research or graduate course.
"
The book is an almost self-contained presentation of the most
important concepts and results in viability and invariance. The
viability of a set K with respect to a given function (or
multi-function) F, defined on it, describes the property that, for
each initial data in K, the differential equation (or inclusion)
driven by that function or multi-function) to have at least one
solution. The invariance of a set K with respect to a function (or
multi-function) F, defined on a larger set D, is that property
which says that each solution of the differential equation (or
inclusion) driven by F and issuing in K remains in K, at least for
a short time.
The book includes the most important necessary and sufficient
conditions for viability starting with Nagumo's Viability Theorem
for ordinary differential equations with continuous right-hand
sides and continuing with the corresponding extensions either to
differential inclusions or to semilinear or even fully nonlinear
evolution equations, systems and inclusions. In the latter (i.e.
multi-valued) cases, the results (based on two completely new
tangency concepts), all due to the authors, are original and extend
significantly, in several directions, their well-known classical
counterparts.
- New concepts for multi-functions as the classical tangent vectors
for functions
- Provides the very general and necessary conditions for viability
in the case of differential inclusions, semilinear and fully
nonlinear evolution inclusions
- Clarifying examples, illustrations and numerous problems,
completely and carefully solved
- Illustrates the applications from theory into practice
- Very clear and elegant style
The book is meant to serve two purposes. The first and more obvious
one is to present state of the art results in algebraic research
into residuated structures related to substructural logics. The
second, less obvious but equally important, is to provide a
reasonably gentle introduction to algebraic logic. At the
beginning, the second objective is predominant. Thus, in the first
few chapters the reader will find a primer of universal algebra for
logicians, a crash course in nonclassical logics for algebraists,
an introduction to residuated structures, an outline of
Gentzen-style calculi as well as some titbits of proof theory - the
celebrated Hauptsatz, or cut elimination theorem, among them. These
lead naturally to a discussion of interconnections between logic
and algebra, where we try to demonstrate how they form two sides of
the same coin. We envisage that the initial chapters could be used
as a textbook for a graduate course, perhaps entitled Algebra and
Substructural Logics.
As the book progresses the first objective gains predominance over
the second. Although the precise point of equilibrium would be
difficult to specify, it is safe to say that we enter the technical
part with the discussion of various completions of residuated
structures. These include Dedekind-McNeille completions and
canonical extensions. Completions are used later in investigating
several finiteness properties such as the finite model property,
generation of varieties by their finite members, and finite
embeddability. The algebraic analysis of cut elimination that
follows, also takes recourse to completions. Decidability of
logics, equational and quasi-equational theories comes next, where
we show how proof theoretical methods like cut elimination are
preferable for small logics/theories, but semantic tools like
Rabin's theorem work better for big ones. Then we turn to
Glivenko's theorem, which says that a formula is an intuitionistic
tautology if and only if its double negation is a classical one. We
generalise it to the substructural setting, identifying for each
substructural logic its Glivenko equivalence class with smallest
and largest element. This is also where we begin investigating
lattices of logics and varieties, rather than particular examples.
We continue in this vein by presenting a number of results
concerning minimal varieties/maximal logics. A typical theorem
there says that for some given well-known variety its subvariety
lattice has precisely such-and-such number of minimal members
(where values for such-and-such include, but are not limited to,
continuum, countably many and two). In the last two chapters we
focus on the lattice of varieties corresponding to logics without
contraction. In one we prove a negative result: that there are no
nontrivial splittings in that variety. In the other, we prove a
positive one: that semisimple varieties coincide with discriminator
ones.
Within the second, more technical part of the book another
transition process may be traced. Namely, we begin with logically
inclined technicalities and end with algebraically inclined ones.
Here, perhaps, algebraic rendering of Glivenko theorems marks the
equilibrium point, at least in the sense that finiteness
properties, decidability and Glivenko theorems are of clear
interest to logicians, whereas semisimplicity and discriminator
varieties are universal algebra par exellence. It is for the reader
to judge whether we succeeded in weaving these threads into a
seamless fabric.
- Considers both the algebraic and logical perspective within a
common framework.
- Written by experts in the area.
- Easily accessible to graduate students and researchers from other
fields.
- Results summarized in tables and diagrams to provide an overview
of the area.
- Useful as a textbook for a course in algebraic logic, with
exercises and suggested research directions.
- Provides a concise introduction to the subject and leads directly
to research topics.
- The ideas from algebra and logic are developed hand-in-hand and
the connections are shown in every level.
This volume is a collection of surveys of research problems in
topology and its applications. The topics covered include general
topology, set-theoretic topology, continuum theory, topological
algebra, dynamical systems, computational topology and functional
analysis.
* New surveys of research problems in topology
* New perspectives on classic problems
* Representative surveys of research groups from all around the
world
This Handbook covers latent variable models, which are a flexible
class of models for modeling multivariate data to explore
relationships among observed and latent variables.
- Covers a wide class of important models
- Models and statistical methods described provide tools for
analyzing a wide spectrum of complicated data
- Includes illustrative examples with real data sets from business,
education, medicine, public health and sociology.
- Demonstrates the use of a wide variety of statistical,
computational, and mathematical techniques.
The year 2007 marks the 300th anniversary of the birth of one of
the Enlightenment's most important mathematicians and scientists,
Leonhard Euler. This volume is a collection of 24 essays by some of
the world's best Eulerian scholars from seven different countries
about Euler, his life and his work.
Some of the essays are historical, including much previously
unknown information about Euler's life, his activities in the St.
Petersburg Academy, the influence of the Russian Princess Dashkova,
and Euler's philosophy. Others describe his influence on the
subsequent growth of European mathematics and physics in the 19th
century. Still others give technical details of Euler's innovations
in probability, number theory, geometry, analysis, astronomy,
mechanics and other fields of mathematics and science.
- Over 20 essays by some of the best historians of mathematics and
science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson,
Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin
Wilson, Ivor Grattan-Guinness and Karin Reich
- New details of Euler's life in two essays, one by Ronald Calinger
and one he co-authored with Elena Polyakhova
- New information on Euler's work in differential geometry, series,
mechanics, and other important topics including his influence in
the early 19th century
Many problems for partial difference and integro-difference
equations can be written as difference equations in a normed space.
This book is devoted to linear and nonlinear difference equations
in a normed space. Our aim in this monograph is to initiate
systematic investigations of the global behavior of solutions of
difference equations in a normed space. Our primary concern is to
study the asymptotic stability of the equilibrium solution. We are
also interested in the existence of periodic and positive
solutions. There are many books dealing with the theory of ordinary
difference equations. However there are no books dealing
systematically with difference equations in a normed space. It is
our hope that this book will stimulate interest among
mathematicians to develop the stability theory of abstract
difference equations.
Note that even for ordinary difference equations, the problem of
stability analysis continues to attract the attention of many
specialists despite its long history. It is still one of the most
burning problems, because of the absence of its complete solution,
but many general results available for ordinary difference
equations
(for example, stability by linear approximation) may be easily
proved for abstract difference equations.
The main methodology presented in this publication is based on a
combined use of recent norm estimates for operator-valued functions
with the following
methods and results:
a) the freezing method;
b) the Liapunov type equation;
c) the method of majorants;
d) the multiplicative representation of solutions.
In addition, we present stability results for abstract Volterra
discrete equations.
The bookconsists of 22 chapters and an appendix. In Chapter 1,
some definitions and preliminary results are collected. They are
systematically used in the next chapters.
In, particular, we recall very briefly some basic notions and
results of the theory of operators in Banach and ordered spaces. In
addition, stability concepts are presented and Liapunov's functions
are introduced. In Chapter 2 we review various classes of linear
operators and their spectral properties. As examples, infinite
matrices are considered. In Chapters 3 and 4, estimates for the
norms of operator-valued and matrix-valued functions are suggested.
In particular, we consider Hilbert-Schmidt, Neumann-Schatten,
quasi-Hermitian and quasiunitary operators. These classes contain
numerous infinite matrices arising in applications. In Chapter 5,
some perturbation results for linear operators in a Hilbert space
are presented. These results are then used in the next chapters to
derive bounds for the spectral radiuses. Chapters 6-14 are devoted
to asymptotic and exponential stabilities, as well as boundedness
of solutions of linear and nonlinear difference equations. In
Chapter 6 we investigate the linear equation with a bounded
constant operator acting in a Banach space. Chapter 7 is concerned
with the Liapunov type operator equation. Chapter 8 deals with
estimates for the spectral radiuses of concrete operators, in
particular, for infinite matrices. These bounds enable the
formulation of explicit stability conditions. In Chapters 9 and 10
we consider nonautonomous (time-variant) linear equations. An
essential role in this chapter is played by the evolution operator.
In addition, we use the "freezing" method and
multiplicativerepresentations of solutions to construct the
majorants for linear equations. Chapters 11 and 12 are devoted to
semilinear autonomous and nonautonomous equations. Chapters 13 and
14 are concerned with linear and nonlinear higher order difference
equations. Chapter 15 is devoted to the input-to-state stability.
In Chapter 16 we study periodic solutions of linear and nonlinear
difference equations in a Banach space, as well as the global
orbital stability of solutions of vector difference equations.
Chapters 17 and 18 deal with linear and nonlinear Volterra discrete
equations in a Banach space. An important role in these chapter is
played by operator pencils. Chapter 19 deals with a class of the
Stieltjes differential equations.
These equations generalize difference and differential equations.
We apply estimates for norms of operator valued functions and
properties of the multiplicative integral to certain classes of
linear and nonlinear Stieltjes differential equations to obtain
solution estimates that allow us to study the stability and
boundedness of solutions. We also show the existence and uniqueness
of solutions as well as the continuous dependence of the solutions
on the time integrator. Chapter 20 provides some results regarding
the Volterra--Stieltjes equations. The Volterra--Stieltjes
equations include Volterra difference and Volterra integral
equations. We obtain estimates for the norms of solutions of the
Volterra--Stieltjes equation. Chapter 21 is devoted to difference
equations with continuous time. In Chapter 22, we suggest some
conditions for the existence of nontrivial and positive steady
states of difference equations, as well as bounds for the
stationary solutions.
- Deals systematically with difference equations in normed spaces
- Considers new classes of equations that could not be studied in
the frameworks of ordinary and partial difference equations
- Develops the freezing method and presents recent results on
Volterra discrete equations
- Contains an approach based on the estimates for norms of operator
functions
This handbook is the third volume in a series of volumes devoted to
self contained and up-to-date surveys in the tehory of ordinary
differential equations, written by leading researchers in the area.
All contributors have made an additional effort to achieve
readability for mathematicians and scientists from other related
fields so that the chapters have been made accessible to a wide
audience.
These ideas faithfully reflect the spirit of this multi-volume and
hopefully it becomes a very useful tool for reseach, learing and
teaching. This volumes consists of seven chapters covering a
variety of problems in ordinary differential equations. Both pure
mathematical research and real word applications are reflected by
the contributions to this volume.
- Covers a variety of problems in ordinary differential
equations
- Pure mathematical and real world applications
- Written for mathematicians and scientists of many related fields
The monograph is written with a view to provide basic tools for
researchers working in Mathematical Analysis and Applications,
concentrating on differential, integral and finite difference
equations. It contains many inequalities which have only recently
appeared in the literature and which can be used as powerful tools
and will be a valuable source for a long time to come. It is
self-contained and thus should be useful for those who are
interested in learning or applying the inequalities with explicit
estimates in their studies.
- Contains a variety of inequalities discovered which find numerous
applications in various branches of differential, integral and
finite difference equations.
- Many inequalities which have only recently discovered in the
literature and can not yet be found in bother book.
- A valuable reference for someone requiring results about
inequalities for use in some applications in various other branches
of mathematics.
- Will be of interest to researchers working both in pure and
applied mathematics and other areas of science and technology, and
it could also be used as a text for an advanced graduate course.
- Contains a variety of inequalities discovered which find numerous
applications in various branches of differential, integral and
finite difference equations
- Valuable reference for someone requiring results about
inequalities for use in some applications in various other branches
of mathematics
- Highlights pure and applied mathematics and other areas of
science and technology
The modern theory of algebras of binary relations, reformulated by
Tarski as an abstract, algebraic, equational theory of relation
algebras, has considerable mathematical significance, with
applications in various fields: e.g., in computer
science---databases, specification theory, AI---and in
anthropology, economics, physics, and philosophical logic.
This comprehensive treatment of the theory of relation algebras and
the calculus of relations is the first devoted to a systematic
development of the subject.
Key Features:
- Presents historical milestones from a modern perspective
- Careful, thorough, detailed guide to understanding relation
algebras
- Provides a framework and unified perspective of the subject
This book is a collection of eleven articles, written by leading
experts and dealing with special topics in Multivariate
Approximation and Interpolation. The material discussed here has
far-reaching applications in many areas of Applied Mathematics,
such as in Computer Aided Geometric Design, in Mathematical
Modelling, in Signal and Image Processing and in Machine Learning,
to mention a few. The book aims at giving a comprehensive
information leading the reader from the fundamental notions and
results of each field to the forefront of research. It is an ideal
and up-to-date introduction for graduate students specializing in
these topics, and for researchers in universities and in industry.
- A collection of articles of highest scientific standard.
- An excellent introduction and overview of recent topics from
multivariate approximation.
- A valuable source of references for specialists in the
field.
- A representation of the state-of-the-art in selected areas of
multivariate approximation.
- A rigorous mathematical introduction to special topics of
interdisciplinary research.
"Materials Science in Manufacturing" focuses on materials science
and materials processing primarily for engineering and technology
students preparing for careers in manufacturing. The text also
serves as a useful reference on materials science for the
practitioner engaged in manufacturing as well as the beginning
graduate student.
Integrates theoretical understanding and current practices to
provide a resource for students preparing for advanced study or
career in industry. Also serves as a useful resource to the
practitioner who works with diverse materials and processes, but is
not a specialist in materials science. This book covers a wider
range of materials and processes than is customary in the
elementary materials science books.
This book covers a wider range of materials and processes than is
customary in the elementary materials science books.
* Detailed explanations of theories, concepts, principles and
practices of materials and processes of manufacturing through
richly illustrated text
* Includes new topics such as nanomaterials and nanomanufacturing,
not covered in most similar works
* Focuses on the interrelationship between Materials Science,
Processing Science, and Manufacturing Technology
The book contains a systematic treatment of the qualitative theory
of elliptic boundary value problems for linear and quasilinear
second order equations in non-smooth domains. The authors
concentrate on the following fundamental results: sharp estimates
for strong and weak solutions, solvability of the boundary value
problems, regularity assertions for solutions near singular points.
Key features:
* New the Hardy - Friedrichs - Wirtinger type inequalities as well
as new integral inequalities related to the Cauchy problem for a
differential equation.
* Precise exponents of the solution decreasing rate near boundary
singular points and best possible conditions for this.
* The question about the influence of the coefficients smoothness
on the regularity of solutions.
* New existence theorems for the Dirichlet problem for linear and
quasilinear equations in domains with conical points.
* The precise power modulus of continuity at singular boundary
point for solutions of the Dirichlet, mixed and the Robin
problems.
* The behaviour of weak solutions near conical point for the
Dirichlet problem for m - Laplacian.
* The behaviour of weak solutions near a boundary edge for the
Dirichlet and mixed problem for elliptic quasilinear equations with
triple degeneration.
* Precise exponents of the solution decreasing rate near boundary
singular points and best possible conditions for this.
* The question about the influence of the coefficients smoothness
on the regularity of solutions.
* New existence theorems for the Dirichlet problem for linear and
quasilinear equations in domains with conical points.
* The precise power modulus of continuity atsingular boundary point
for solutions of the Dirichlet, mixed and the Robin problems.
* The behaviour of weak solutions near conical point for the
Dirichlet problem for m - Laplacian.
* The behaviour of weak solutions near a boundary edge for the
Dirichlet and mixed problem for elliptic quasilinear equations with
triple degeneration.
This volume introduces a unified, self-contained study of linear
discrete parabolic problems through reducing the starting discrete
problem to the Cauchy problem for an evolution equation in discrete
time. Accessible to beginning graduate students, the book contains
a general stability theory of discrete evolution equations in
Banach space and gives applications of this theory to the analysis
of various classes of modern discretization methods, among others,
Runge-Kutta and linear multistep methods as well as operator
splitting methods.
Key features:
* Presents a unified approach to examining discretization methods
for parabolic equations.
* Highlights a stability theory of discrete evolution equations
(discrete semigroups) in Banach space.
* Deals with both autonomous and non-autonomous equations as well
as with equations with memory.
* Offers a series of numerous well-posedness and convergence
results for various discretization methods as applied to abstract
parabolic equations; among others, Runge-Kutta and linear multistep
methods as well as certain operator splitting methods.
* Provides comments of results and historical remarks after each
chapter.
. Presents a unified approach to examining discretization methods
for parabolic equations.
. Highlights a stability theory of discrete evolution equations
(discrete semigroups) in Banach space.
. Deals with both autonomous and non-autonomous equations as well
as with equations with memory.
. Offers a series of numerous well-posedness and convergence
results for various discretization methods as applied to abstract
parabolic equations; among others, Runge-Kutta and linear multistep
methods as well as certain operator splitting methods as well as
certain operator splitting methods are studied in detail.
.Provides comments of results and historical remarks after each
chapter."
The aim of this Handbook is to acquaint the reader with the current
status of the theory of evolutionary partial differential
equations, and with some of its applications. Evolutionary partial
differential equations made their first appearance in the 18th
century, in the endeavor to understand the motion of fluids and
other continuous media. The active research effort over the span of
two centuries, combined with the wide variety of physical phenomena
that had to be explained, has resulted in an enormous body of
literature. Any attempt to produce a comprehensive survey would be
futile. The aim here is to collect review articles, written by
leading experts, which will highlight the present and expected
future directions of development of the field. The emphasis will be
on nonlinear equations, which pose the most challenging problems
today.
. Volume I of this Handbook does focus on the abstract theory of
evolutionary equations.
. Volume 2 considers more concrete problems relating to specific
applications.
. Together they provide a panorama of this amazingly complex and
rapidly developing branch of mathematics.
This handbook is the second volume in a series devoted to self
contained and up-to-date surveys in the theory of ordinary
differential equations, written
by leading researchers in the area. All contributors have made an
additional effort to achieve readability for mathematicians and
scientists from other related fields, in order to make the chapters
of the volume accessible to a wide audience.
. Six chapters covering a variety of problems in ordinary
differential equations.
. Both, pure mathematical research and real word applications are
reflected
. Written by leading researchers in the area.
This book familiarizes both popular and fundamental notions and
techniques from the theory of non-normed topological algebras with
involution, demonstrating with examples and basic results the
necessity of this perspective. The main body of the book is
focussed on the Hilbert-space (bounded) representation theory of
topological *-algebras and their topological tensor products, since
in our physical world, apart from the majority of the existing
unbounded operators, we often meet operators that are forced to be
bounded, like in the case of symmetric *-algebras. So, one gets an
account of how things behave, when the mathematical structures are
far from being algebras endowed with a complete or non-complete
algebra norm. In problems related with mathematical physics, such
instances are, indeed, quite common.
Key features:
- Lucid presentation
- Smooth in reading
- Informative
- Illustrated by examples
- Familiarizes the reader with the non-normed *-world
- Encourages the hesitant
- Welcomes new comers.
- Well written and lucid presentation.
- Informative and illustrated by examples.
- Familiarizes the reader with the non-normed *-world.
For more than forty years, the equation y (t) = Ay(t) + u(t) in
Banach spaces has been used as model for optimal control processes
described by partial differential equations, in particular heat and
diffusion processes. Many of the outstanding open problems,
however, have remained open until recently, and some have never
been solved. This book is a survey of all results know to the
author, with emphasis on very recent results (1999 to date).
The book is restricted to linear equations and two particular
problems (the time optimal problem, the norm optimal problem) which
results in a more focused and concrete treatment. As experience
shows, results on linear equations are the basis for the treatment
of their semilinear counterparts, and techniques for the time and
norm optimal problems can often be generalized to more general cost
functionals.
The main object of this book is to be a state-of-the-art monograph
on the theory of the time and norm optimal controls for y (t) =
Ay(t) + u(t) that ends at the very latest frontier of research,
with open problems and indications for future research.
Key features:
. Applications to optimal diffusion processes.
. Applications to optimal heat propagation processes.
. Modelling of optimal processes governed by partial
differential equations.
. Complete bibliography.
. Includes the latest research on the subject.
. Does not assume anything from the reader except
basic functional analysis.
. Accessible to researchers and advanced graduate
students alike
. Applications to optimal diffusion processes.
. Applications to optimal heat propagation processes.
. Modelling of optimal processes governed by partial
differential equations.
. Complete bibliography.
. Includes the latest research on the subject.
. Does not assume anything from the reader except
basic functional analysis.
. Accessible to researchers and advanced graduate
students alike"
The book presents a systematic and compact treatment of the
qualitative theory of half-linear
differential equations. It contains the most updated and
comprehensive material and represents the first attempt to present
the results of the rapidly developing theory of half-linear
differential equations in a unified form. The main topics covered
by the book are oscillation and asymptotic theory and the theory of
boundary value problems associated with half-linear equations, but
the book also contains a treatment of related topics like PDE s
with p-Laplacian, half-linear difference equations and various more
general nonlinear differential equations.
- The first complete treatment of the qualitative theory of
half-linear differential equations.
- Comparison of linear and half-linear theory.
- Systematic approach to half-linear oscillation and asymptotic
theory.
- Comprehensive bibliography and index.
- Useful as a reference book in the topic.
The present work is a continuation of the authors' acclaimed
multi-volume A
Practical Logic of Cognitive Systems. After having investigated the
notion of
relevance in their previous volume, Gabbay and Woods now turn to
abduction. In
this highly original approach, abduction is construed as
ignorance-preserving
inference, in which conjecture plays a pivotal role. Abduction is a
response to a
cognitive target that cannot be hit on the basis of what the agent
currently knows.
The abducer selects a hypothesis which were it true would enable
the reasoner to attain his target. He concludes from this fact that
the hypothesis may be conjectured. In allowing conjecture to stand
in for the knowledge he fails to have, the abducer reveals himself
to be a satisficer, since an abductive solution is not a solution
from knowledge. Key to the authors' analysis is the requirement
that a conjectured proposition is not just what a reasoner might
allow himself to assume, but a proposition he must defeasibly
release as a premiss for further inferences in the domain of
enquiry in which the original abduction problem has arisen.
The coverage of the book is extensive, from the philosophy of
science to
computer science and AI, from diagnostics to the law, from
historical explanation to linguistic interpretation. One of the
volume's strongest contributions is its exploration of the
abductive character of criminal trials, with special attention
given to the standard of proof beyond a reasonable doubt.
Underlying their analysis of abductive reasoning is the authors'
conception of
practical agency. In this approach, practical agency is dominantly
a matter of the
comparativemodesty of an agent's cognitive agendas, together with
comparatively scant resources available for their advancement. Seen
in these ways, abduction has a significantly practical character,
precisely because it is a form of inference that satisfices rather
than maximizes its response to the agent's cognitive target.
The Reach of Abduction will be necessary reading for researchers,
graduate
students and senior undergraduates in logic, computer science, AI,
belief dynamics, argumentation theory, cognitive psychology and
neuroscience, linguistics, forensic science, legal reasoning and
related areas.
Key features:
- Reach of Abduction is fully integrated with a background logic of
cognitive systems.
- The most extensive coverage compared to competitive works.
- Demonstrates not only that abduction is a form of ignorance
preserving
inference but that it is a mode of inference that is wholly
rational.
- Demonstrates the satisficing rather than maximizing character
of
abduction.
- The development of formal models of abduction is considerably
more extensive than one finds in existing literature. It is an
especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.
- Reach of Abduction is fully integrated with a background logic of
cognitive systems.
- The most extensive coverage compared to competitive works
- Demonstrates not only that abduction is a form of ignorance
preserving
inference but that it is a mode of inference that is wholly
rational.
- Demonstrates the satisficing rather than maximizing character
of
abduction.
- The development of formal models of abduction isconsiderably more
extensive than one finds in existing literature. It is an
especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.
The book addresses many important new developments in the field.
All the topics covered are of great interest to the readers because
such inequalities have become a major tool in the analysis of
various branches of mathematics.
* It contains a variety of inequalities which find numerous
applications in various branches of mathematics.
* It contains many inequalities which have only recently appeared
in the literature and cannot yet be found in other books.
* It will be a valuable reference for someone requiring a result
about inequalities for use in some applications in various other
branches of mathematics.
* Each chapter ends with some miscellaneous inequalities for futher
study.
* The work will be of interest to researchers working both in pure
and applied mathematics, and it could also be used as the text for
an advanced graduate course.
This book collects 10 mathematical essays on approximation in
Analysis and Topology by some of the most influent mathematicians
of the last third of the 20th Century. Besides the papers contain
the very ultimate results in each of their respective fields, many
of them also include a series of historical remarks about the state
of mathematics at the time they found their most celebrated
results, as well as some of their personal circumstances
originating them, which makes particularly attractive the book for
all scientist interested in these fields, from beginners to
experts. These gem pieces of mathematical intra-history should
delight to many forthcoming generations of mathematicians, who will
enjoy some of the most fruitful mathematics of the last third of
20th century presented by their own authors.
This book covers a wide range of new mathematical results. Among
them, the most advanced characterisations of very weak versions of
the classical maximum principle, the very last results on global
bifurcation theory, algebraic multiplicities, general dependencies
of solutions of boundary value problems with respect to variations
of the underlying domains, the deepest available results in rapid
monotone schemes applied to the resolution of non-linear boundary
value problems, the intra-history of the the genesis of the first
general global continuation results in the context of periodic
solutions of nonlinear periodic systems, as well as the genesis of
the coincidence degree, some novel applications of the topological
degree for ascertaining the stability of the periodic solutions of
some classical families of periodic second order equations,
the resolution of a number of conjectures related to some very
celebrated approximation problems in topology and inverse problems,
as well as a number of applications to engineering, an extremely
sharp discussion of the problem of approximating topological spaces
by polyhedra using various techniques based on inverse systems, as
well as homotopy expansions, and the Bishop-Phelps theorem.
Key features:
- It contains a number of seminal contributions by some of the most
world leading mathematicians of the second half of the 20th
Century.
- The papers cover a complete range of topics, from the
intra-history of the involved mathematics to the very last
developments in Differential Equations, Inverse Problems, Analysis,
Nonlinear Analysis and Topology.
- All contributed papers are self-contained works containing rather
complete list of references on each of the subjects covered.
- The book contains some of the very last findings concerning the
maximum principle, the theory of monotone schemes in nonlinear
problems, the theory of algebraic multiplicities, global
bifurcation theory, dynamics of periodic equations and systems,
inverse problems and approximation in topology.
- The papers are extremely well written and directed to a wide
audience, from beginners to experts. An excellent occasion to
become engaged with some of the most fruitful mathematics developed
during the last decades.
. It contains a number of seminal contributions by some of the most
world leading mathematicians of the second half of the 20th
Century.
. The papers cover a complete range of topics, from the
intra-history of the involved mathematics to the very last
developments in Differential Equations, Inverse Problems, Analysis,
Nonlinear Analysis and Topology.
. All contributed papers are self-contained works containing rather
complete list of references on each of the subjects covered.
. The book contains some of the very last findings concerning the
maximum principle, the theory of monotone schemes in nonlinear
problems, the theory of algebraic multiplicities, global
bifurcation theory, dynamics of periodic equations and systems,
inverse problems and approximation in topology.
. The papers are extremely well written and directed to a wide
audience, from beginners to experts. An excellent occasion to
become engaged with some of the most fruitful mathematics developed
during the last decades."
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