Mathematics

Applied Delay Differential Equations

Author: Thomas Erneux

Publisher: Springer Science & Business Media

ISBN: 0387743723

Category: Mathematics

Page: 204

View: 1843

Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.
Science

Stability of Linear Delay Differential Equations

A Numerical Approach with MATLAB

Author: Dimitri Breda,Stefano Maset,Rossana Vermiglio

Publisher: Springer

ISBN: 149392107X

Category: Science

Page: 158

View: 2555

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.
Technology & Engineering

Mathematical Modeling and Applications in Nonlinear Dynamics

Author: Albert Luo,Hüseyin Merdan

Publisher: Springer

ISBN: 3319266306

Category: Technology & Engineering

Page: 205

View: 2277

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.
Mathematics

Advances in Interdisciplinary Mathematical Research

Applications to Engineering, Physical and Life Sciences

Author: Bourama Toni

Publisher: Springer Science & Business Media

ISBN: 1461463459

Category: Mathematics

Page: 284

View: 8941

This volume contains the invited contributions to the Spring 2012 seminar series at Virginia State University on Mathematical Sciences and Applications. It is a thematic continuation of work presented in Volume 24 of the Springer Proceedings in Mathematics & Statistics series. Contributors present their own work as leading researchers to advance their specific fields and induce a genuine interdisciplinary interaction. Thus all articles therein are selective, self-contained, and are pedagogically exposed to foster student interest in science, technology, engineering and mathematics, stimulate graduate and undergraduate research, as well as collaboration between researchers from different areas. The volume features new advances in mathematical research and its applications: anti-periodicity; almost stochastic difference equations; absolute and conditional stability in delayed equations; gamma-convergence and applications to block copolymer morphology; the dynamics of collision and near-collision in celestial mechanics; almost and pseudo-almost limit cycles; rainbows in spheres and connections to ray, wave and potential scattering theory; null-controllability of the heat equation with constraints; optimal control for systems subjected to null-controllability; the Galerkin method for heat transfer in closed channels; wavelet transforms for real-time noise cancellation; signal, image processing and machine learning in medicine and biology; methodology for research on durability, reliability, damage tolerance of aerospace materials and structures at NASA Langley Research Center. The volume is suitable and valuable for mathematicians, scientists and research students in a variety of interdisciplinary fields, namely physical and life sciences, engineering and technology including structures and materials sciences, computer science for signal, image processing and machine learning in medicine.
Computers

Computer Aided Verification

30th International Conference, CAV 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July 14-17, 2018, Proceedings

Author: Hana Chockler,Georg Weissenbacher

Publisher: Springer

ISBN: 331996142X

Category: Computers

Page: 545

View: 6442

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications.
Mathematics

Stochastic Tools in Mathematics and Science

Author: Alexandre J Chorin,Ole H Hald

Publisher: Springer Science & Business Media

ISBN: 1441910026

Category: Mathematics

Page: 162

View: 7497

This introduction to probability-based modeling covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Topics covered include conditional expectations, stochastic processes, Langevin equations, and Markov chain Monte Carlo algorithms. The applications include data assimilation, prediction from partial data, spectral analysis and turbulence. A special feature is the systematic analysis of memory effects.
English literature

The British National Bibliography

Author: Arthur James Wells

Publisher: N.A

ISBN: N.A

Category: English literature

Page: N.A

View: 9637

Science

Laser Dynamics

Author: Thomas Erneux,Pierre Glorieux

Publisher: Cambridge University Press

ISBN: 1139486977

Category: Science

Page: N.A

View: 1022

Bridging the gap between laser physics and applied mathematics, this book offers a new perspective on laser dynamics. Combining fresh treatments of classic problems with up-to-date research, asymptotic techniques appropriate for nonlinear dynamical systems are shown to offer a powerful alternative to numerical simulations. The combined analytical and experimental description of dynamical instabilities provides a clear derivation of physical formulae and an evaluation of their significance. Starting with the observation of different time scales of an operating laser, the book develops approximation techniques to systematically explore their effects. Laser dynamical regimes are introduced at different levels of complexity, from standard turn-on experiments to stiff, chaotic, spontaneous or driven pulsations. Particular attention is given to quantitative comparisons between experiments and theory. The book broadens the range of analytical tools available to laser physicists and provides applied mathematicians with problems of practical interest, making it invaluable for graduate students and researchers.
Mathematics

Topological Crystallography

With a View Towards Discrete Geometric Analysis

Author: Toshikazu Sunada

Publisher: Springer Science & Business Media

ISBN: 4431541772

Category: Mathematics

Page: 229

View: 6719

Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
Mathematics

Partial Differential Equations I

Basic Theory

Author: Michael Taylor

Publisher: Springer Science & Business Media

ISBN: 144197055X

Category: Mathematics

Page: 654

View: 7820

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
Mathematics

An Introduction to Scientific Computing

Twelve Computational Projects Solved with MATLAB

Author: Ionut Danaila,Pascal Joly,Sidi Mahmoud Kaber,Marie Postel

Publisher: Springer Science & Business Media

ISBN: 0387491597

Category: Mathematics

Page: 294

View: 3640

This book demonstrates scientific computing by presenting twelve computational projects in several disciplines including Fluid Mechanics, Thermal Science, Computer Aided Design, Signal Processing and more. Each follows typical steps of scientific computing, from physical and mathematical description, to numerical formulation and programming and critical discussion of results. The text teaches practical methods not usually available in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. The final section of each project contains the solutions to proposed exercises and guides the reader in using the MATLAB scripts available online.
Mathematics

Symplectic Invariants and Hamiltonian Dynamics

Author: Helmut Hofer,Eduard Zehnder

Publisher: Springer Science & Business Media

ISBN: 9783034801041

Category: Mathematics

Page: 341

View: 2570

The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology. The exposition is self-contained and addressed to researchers and students from the graduate level onwards.
Mathematics

Multiple Time Scale Dynamics

Author: Christian Kuehn

Publisher: Springer

ISBN: 3319123165

Category: Mathematics

Page: 814

View: 4498

This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Education

Education for Life and Work

Developing Transferable Knowledge and Skills in the 21st Century

Author: Committee on Defining Deeper Learning and 21st Century Skills,Center for Education,Board on Testing and Assessment,Division of Behavioral and Social Sciences and Education,National Research Council

Publisher: National Academies Press

ISBN: 030925650X

Category: Education

Page: 229

View: 9299

Americans have long recognized that investments in public education contribute to the common good, enhancing national prosperity and supporting stable families, neighborhoods, and communities. Education is even more critical today, in the face of economic, environmental, and social challenges. Today's children can meet future challenges if their schooling and informal learning activities prepare them for adult roles as citizens, employees, managers, parents, volunteers, and entrepreneurs. To achieve their full potential as adults, young people need to develop a range of skills and knowledge that facilitate mastery and application of English, mathematics, and other school subjects. At the same time, business and political leaders are increasingly asking schools to develop skills such as problem solving, critical thinking, communication, collaboration, and self-management - often referred to as "21st century skills." Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century describes this important set of key skills that increase deeper learning, college and career readiness, student-centered learning, and higher order thinking. These labels include both cognitive and non-cognitive skills- such as critical thinking, problem solving, collaboration, effective communication, motivation, persistence, and learning to learn. 21st century skills also include creativity, innovation, and ethics that are important to later success and may be developed in formal or informal learning environments. This report also describes how these skills relate to each other and to more traditional academic skills and content in the key disciplines of reading, mathematics, and science. Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century summarizes the findings of the research that investigates the importance of such skills to success in education, work, and other areas of adult responsibility and that demonstrates the importance of developing these skills in K-16 education. In this report, features related to learning these skills are identified, which include teacher professional development, curriculum, assessment, after-school and out-of-school programs, and informal learning centers such as exhibits and museums.
Mathematics

Mathematical Biology

Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 3662085429

Category: Mathematics

Page: 770

View: 9027

Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.
Mathematics

Partial Differential Equations III

Nonlinear Equations

Author: Michael Taylor

Publisher: Springer Science & Business Media

ISBN: 9781441970497

Category: Mathematics

Page: 715

View: 5623

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis

Mathematics for Computer Science

Author: Eric Lehman,F. Thomson Leighton,Albert R. Meyer

Publisher: N.A

ISBN: 9789888407064

Category:

Page: 979

View: 9472

This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Mathematics

Parabolic Equations in Biology

Growth, reaction, movement and diffusion

Author: Benoît Perthame

Publisher: Springer

ISBN: 331919500X

Category: Mathematics

Page: 199

View: 1779

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Time-Delay Systems

Author: N.A

Publisher: N.A

ISBN: 9814464880

Category:

Page: N.A

View: 9748

Mathematics

The Survival of a Mathematician

From Tenure-track to Emeritus

Author: Steven George Krantz

Publisher: American Mathematical Soc.

ISBN: 0821846299

Category: Mathematics

Page: 310

View: 9534

"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.