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Author: V. Komkov Publisher: Springer Science & Business Media ISBN: 9400945647 Category : Mathematics Languages : en Pages : 394
Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: V. Komkov Publisher: Springer Science & Business Media ISBN: 9400945647 Category : Mathematics Languages : en Pages : 394
Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: Victor Berdichevsky Publisher: Springer ISBN: 9783540884651 Category : Technology & Engineering Languages : en Pages : 0
Book Description
I Fundamentals.- Variational Principles.- Thermodynamics.- Continuum Mechanics.- Principle of least action in continuum mechanics.- Direct methods of calculus of variations.- II Variational features of classical continuum models.- Statics of a geometrically linear elastic body.- Statics of a geometrically nonlinear elastic body.- Dynamics of elastic bodies.- Ideal incompressible fluid.- Ideal compressible fluid.- Steady motion of ideal fluid and elastic body.- Principle of least dissipation.- Motion of rigid bodies in fluids.
Author: Victor Berdichevsky Publisher: Springer ISBN: 9783540884668 Category : Technology & Engineering Languages : en Pages : 586
Book Description
Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.
Author: C. S. Jog Publisher: Cambridge University Press ISBN: 1316528383 Category : Science Languages : en Pages : 878
Book Description
Continuum mechanics studies the foundations of deformable body mechanics from a mathematical perspective. It also acts as a base upon which other applied areas such as solid mechanics and fluid mechanics are developed. This book discusses some important topics, which have come into prominence in the latter half of the twentieth century, such as material symmetry, frame-indifference and thermomechanics. The study begins with the necessary mathematical background in the form of an introduction to tensor analysis followed by a discussion on kinematics, which deals with purely geometrical notions such as strain and rate of deformation. Moving on to derivation of the governing equations, the book also presents applications in the areas of linear and nonlinear elasticity. In addition, the volume also provides a mathematical explanation to the axioms and laws of deformable body mechanics, and its various applications in the field of solid mechanics.
Author: Roberto Lucchetti Publisher: Springer Science & Business Media ISBN: 9401584729 Category : Mathematics Languages : en Pages : 271
Book Description
This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem.
Author: V. Tanaev Publisher: Springer Science & Business Media ISBN: 9401111928 Category : Mathematics Languages : en Pages : 414
Book Description
An increasing interest to scheduling theory can be attributed to the high level of automation of all branches of human activity. The quality of modern production essentially depends on the planning decisions taken at different stages of a production process. Moreover, while the quality of these decisions is improving, the time and flexibility requirements for decision-making are becoming more important. All this stimulates scheduling research. Started as an independent discipline in the early fifties, it now has become an important branch of operations research. In the eighties, the largest Russian publishing house for scientific literature Nauka Publishers, Moscow, issued two books by a group of Byelorussian mathematicians: Scheduling Theory. Single-Stage Systems by V. S. Tanaev, V. S. Gordon and Y. M. Shafransky (1984) and Scheduling Theory. Multi-Stage Systems by V. S. Tanaev, Y. N. Sotskov and V. A. Strusevich (1989). Originally published in Russian, these two books cover two different major problem areas of scheduling theory and can be considered as a two-volume monograph that provides a systematic and comprehensive exposition of the subject. The authors are grateful to Kluwer Academic Publishers for creating the opportunity to publish the English translations of these two books. We are indebted to M. Hazewinkel, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys and W. Szwarc for their supporting the idea of translating the books into English.
Author: V. Tanaev Publisher: Springer Science & Business Media ISBN: 9401111901 Category : Mathematics Languages : en Pages : 382
Book Description
Scheduling theory is an important branch of operations research. Problems studied within the framework of that theory have numerous applications in various fields of human activity. As an independent discipline scheduling theory appeared in the middle of the fifties, and has attracted the attention of researchers in many countries. In the Soviet Union, research in this direction has been mainly related to production scheduling, especially to the development of automated systems for production control. In 1975 Nauka ("Science") Publishers, Moscow, issued two books providing systematic descriptions of scheduling theory. The first one was the Russian translation of the classical book Theory of Scheduling by American mathematicians R. W. Conway, W. L. Maxwell and L. W. Miller. The other one was the book Introduction to Scheduling Theory by Soviet mathematicians V. S. Tanaev and V. V. Shkurba. These books well complement each other. Both. books well represent major results known by that time, contain an exhaustive bibliography on the subject. Thus, the books, as well as the Russian translation of Computer and Job-Shop Scheduling Theory edited by E. G. Coffman, Jr., (Nauka, 1984) have contributed to the development of scheduling theory in the Soviet Union. Many different models, the large number of new results make it difficult for the researchers who work in related fields to follow the fast development of scheduling theory and to master new methods and approaches quickly.
Author: V. Komkov
Author: V. Komkov
Author: V. KOMKOV
Author: Victor Berdichevsky
Author: Vadim Komkov
Author: Victor Berdichevsky
Author: C. S. Jog
Author: Kyūichirō Washizu
Author: Roberto Lucchetti
Author: V. Tanaev
Author: V. Tanaev