Ussr Computational Mathematics And Mathematical Physics
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Stochastic Numerics for Mathematical Physics
| Author | : Grigori N. Milstein |
| Publisher | : Springer Nature |
| Total Pages | : 754 |
| Release | : 2021-12-03 |
| Genre | : Computers |
| ISBN | : 3030820408 |
This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
Matrix Iterative Analysis
| Author | : Richard S Varga |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2009-12-05 |
| Genre | : Mathematics |
| ISBN | : 3642051561 |
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.
Supersonic Flow and Shock Waves
| Author | : Richard Courant |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 488 |
| Release | : 1999-02-11 |
| Genre | : Mathematics |
| ISBN | : 9780387902326 |
Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. However, many aspects make the book just as interesting as a text and a reference today. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it should appeal to engineers, physicists and mathematicians alike.
Mathematical Foundations of Quantum Mechanics
| Author | : George W. Mackey |
| Publisher | : Courier Corporation |
| Total Pages | : 162 |
| Release | : 2013-12-31 |
| Genre | : Mathematics |
| ISBN | : 0486154475 |
This graduate-level text introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.
Optimal Methods for Ill-Posed Problems
| Author | : Vitalii P. Tanana |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 138 |
| Release | : 2018-03-19 |
| Genre | : Mathematics |
| ISBN | : 3110577216 |
The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems
Grid Generation Methods
| Author | : Vladimir D. Liseikin |
| Publisher | : Springer |
| Total Pages | : 541 |
| Release | : 2017-06-12 |
| Genre | : Science |
| ISBN | : 3319578464 |
This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.
Graphs for Pattern Recognition
| Author | : Damir Gainanov |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 182 |
| Release | : 2016-10-10 |
| Genre | : Mathematics |
| ISBN | : 3110480301 |
This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition. Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property – systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology. The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions. Contents: Preface Pattern recognition, infeasible systems of linear inequalities, and graphs Infeasible monotone systems of constraints Complexes, (hyper)graphs, and inequality systems Polytopes, positive bases, and inequality systems Monotone Boolean functions, complexes, graphs, and inequality systems Inequality systems, committees, (hyper)graphs, and alternative covers Bibliography List of notation Index
Trends in the Analysis and Design of Marine Structures
| Author | : Carlos Guedes Soares |
| Publisher | : CRC Press |
| Total Pages | : 666 |
| Release | : 2019-04-15 |
| Genre | : Technology & Engineering |
| ISBN | : 1000024369 |
Trends in the Analysis and Design of Marine Structures is a collection of the papers presented at MARSTRUCT 2019, the 7th International Conference on Marine Structures held in Dubrovnik, Croatia, 6-8 May 2019. The MARSTRUCT series of Conferences started in Glasgow, UK in 2007, the second event of the series having taken place in Lisbon, Portugal in March 2009, the third in Hamburg, Germany in March 2011, the fourth in Espoo, Finland in March 2013, the fifth in Southampton, UK in March 2015, and the sixth in Lisbon, Portugal in May 2017. This Conference series specialises in dealing with Ships and Offshore Structures, addressing topics in the fields of: - Methods and Tools for Loads and Load Effects - Methods and Tools for Strength Assessment - Experimental Analysis of Structures - Materials and Fabrication of Structures - Methods and Tools for Structural Design and Optimisation - Structural Reliability, Safety and Environmental Protection. Trends in the Analysis and Design of Marine Structures is an essential document for academics, engineers and all professionals involved in the area of analysis and design of Ships and Offshore Structures. About the series: The ‘Proceedings in Marine Technology and Ocean Engineering’ series is devoted to the publication of proceedings of peer-reviewed international conferences dealing with various aspects of ‘Marine Technology and Ocean Engineering’. The Series includes the proceedings of the following conferences: the International Maritime Association of the Mediterranean (IMAM) conferences, the Marine Structures (MARSTRUCT) conferences, the Renewable Energies Offshore (RENEW) conferences and the Maritime Technology (MARTECH) conferences. The ‘Marine Technology and Ocean Engineering’ series is also open to new conferences that cover topics on the sustainable exploration and exploitation of marine resources in various fields, such as maritime transport and ports, usage of the ocean including coastal areas, nautical activities, the exploration and exploitation of mineral resources, the protection of the marine environment and its resources, and risk analysis, safety and reliability. The aim of the series is to stimulate advanced education and training through the wide dissemination of the results of scientific research.
