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Books > Academic & Education > Professional & Technical > Mathematics
Quantification and modalities have always been topics of great
interest for logicians. These two themes emerged from philosophy
and
Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications * Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime * Geometric and diffractive optics, including wave interactions Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable
This handbook is the fourth volume in a series of volumes devoted
to self-contained and up-to-date surveys in the theory of ordinary
differential equations, with an additional effort to achieve
readability for mathematicians and scientists from other related
fields so that the chapters have been made accessible to a wider
audience.
This handbook is the sixth and last volume in the series devoted to
stationary partial differential equations. The topics covered by
this volume include in particular domain perturbations for boundary
value problems, singular solutions of semilinear elliptic problems,
positive solutions to elliptic equations on unbounded domains,
symmetry of solutions, stationary compressible Navier-Stokes
equation, Lotka-Volterra systems with cross-diffusion, and fixed
point theory for elliptic boundary value problems.
A collection of self contained state-of-the art surveys. The
authors have made an effort to achieve readability for
mathematicians and scientists from other fields, for this series of
handbooks to be a new reference for research, learning and
teaching.
System administration is about the design, running and maintenance
of human-computer systems. Examples of human-computer systems
include business enterprises, service institutions and any
extensive machinery that is operated by, or interacts with human
beings. System administration is often thought of as the
technological side of a system: the architecture, construction and
optimization of the collaborating parts, but it also occasionally
touches on softer factors such as user assistance (help desks),
ethical considerations in deploying a system, and the larger
implications of its design for others who come into contact with
it.
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features:
The ability of a structural assembly to carry loads and forces
determines how stable it will be over time. Viewing structural
assemblages as comprising columns, beams, arches, rings, and
plates, this book will introduce the student to both a classical
and advanced understanding of the mechanical behavior of such
structural systems under load and how modeling the resulting
strains can predict the overall future performance the stability of
that structure. While covering traditional beam theory, the book is
more focused on elastica theory in keeping with modern approaches.
This text will be an expanded and updated version a similar,
previously published book, but with pedagogical improvements and
updated analytical methods.
This monograph provides the most recent and up-to-date developments
on fractional differential and fractional integro-differential
equations involving many different potentially useful operators of
fractional calculus.
It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics.
This book contains around 80 articles on major writings in
mathematics published between 1640 and 1940. All aspects of
mathematics are covered: pure and applied, probability and
statistics, foundations and philosophy. Sometimes two writings from
the same period and the same subject are taken together. The
biography of the author(s) is recorded, and the circumstances of
the preparation of the writing are given. When the writing is of
some lengths an analytical table of its contents is supplied. The
contents of the writing is reviewed, and its impact described, at
least for the immediate decades. Each article ends with a
bibliography of primary and secondary items.
This book is an attempt to give a systematic presentation of both
logic and type theory from a categorical perspective, using the
unifying concept of fibred category. Its intended audience consists
of logicians, type theorists, category theorists and (theoretical)
computer scientists.
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.
A number of monographs of various aspects of complex analysis in
several variables have appeared since the first version of this
book was published, but none of them uses the analytic techniques
based on the solution of the Neumann Problem as the main tool.
These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.
This is the revised and augmented edition of a now classic book
which is an introduction to sub-Markovian kernels on general
measurable spaces and their associated homogeneous Markov chains.
The first part, an expository text on the foundations of the
subject, is intended for post-graduate students. A study of
potential theory, the basic classification of chains according to
their asymptotic behaviour and the celebrated Chacon-Ornstein
theorem are examined in detail.
History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition-one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on linear differential equations and the Sturm-Liouville problem. The succeeding chapters go on to discuss the ""crypto-integral"" equations, including the Dirichlet principle and the Beer-Neumann method; the equation of vibrating membranes, including the contributions of Poincare and H.A. Schwarz's 1885 paper; and the idea of infinite dimension. Other chapters cover the crucial years and the definition of Hilbert space, including Fredholm's discovery and the contributions of Hilbert; duality and the definition of normed spaces, including the Hahn-Banach theorem and the method of the gliding hump and Baire category; spectral theory after 1900, including the theories and works of F. Riesz, Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and the theory of distributions; and applications of functional analysis to differential and partial differential equations. This book will be of interest to practitioners in the fields of mathematics and statistics.
Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Gadel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic, at least a turning point after which oenothing was ever the same. Kleene was an important figure in logic, and lived a long full life of scholarship and teaching. The 1930s was a time of creativity and ferment in the subject, when the notion of aEUROoecomputableaEURO moved from the realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gade1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of aEUROoecomputableaEURO . When they all turned out to be equivalent, there was a collective realization that this was indeed the oeright notion. Kleene played a key role in this process. One could say that he was oethere at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Gadel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.
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.
Plasma engineering applies the unique properties of plasmas (ionized gases) to improve processes and performance over many fields, such as materials processing, spacecraft propulsion, and nanofabrication. "Plasma Engineering" considers this rapidly expanding discipline from a unified standpoint, addressing fundamentals of physics and modeling as well as new real-word applications in aerospace, nanotechnology, and bioengineering. The book starts by reviewing plasma particle collisions, waves, and instabilities, and proceeds to diagnostic tools, such as planar, spherical, and emissive probes, and the electrostatic analyzer, interferometric technique, and plasma spectroscopy. The physics of different types of electrical discharges are considered, including the classical Townsend mechanism of gas electrical breakdown and the Paschen law. Basic approaches and theoretical methodologies for plasma modeling are described, based on the fluid description of plasma solving numerically magnetohydrodynamic (MHD) equations and the kinetic model particle techniques that take into account kinetic interactions among particles and electromagnetic fields. Readers are then introduced to the widest variety of
applications in any text on the market. Space propulsion
applications such as the Hall thruster, pulsed plasma thrusters,
and microthruster are explained. Application of low-temperature
plasmas in nanoscience and nanotechnology, another frontier in
plasma physics, is covered, including plasma-based techniques for
carbon-based nanoparticle synthesis (e.g., fundamental building
blocks like single-walled carbon nanotubes and graphene). Plasma
medicine, an emerging field studying plasmas for therapeutic
applications, is examined as well. The latest original results on
cold atmospheric plasma (CAP) applications in medicine are
presented, with a focus on the therapeutic potential of CAP with a
in selective tumor cell eradication and signaling pathway
deregulation.
This is one book of a four-part series, which aims to integrate discussion of modern engineering design principles, advanced design tools, and industrial design practices throughout the design process.Through this series, the reader will: Understand basic design principles and modern engineering design
paradigms.Understand CAD/CAE/CAM tools available for various design
related tasks.Understand how to put an integrated system together
to conduct product design using the paradigms and tools.Understand
industrial practices in employing virtual engineering design and
tools for product development. Covers CAD/CAE in Structural Analysis using FEM, Motion Analysis of Mechanical Systems, Fatigue and Fracture Analysis. Each chapter includes both analytical methods and computer-aided design methods, reflecting the use of modern computational tools in engineering design and practice A case study and tutorial example at the end of each chapter provide hands-on practice in implementing off-the-shelf computer design tools Provides two projects at the end of the book showing the use of Pro/ENGINEER(r) and SolidWorks (r) to implement concepts discussed in the book |
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