Differential Equations with Discontinuous Righthand Sides: Control SystemsSpringer Science & Business Media, 30 սեպ, 1988 թ. - 304 էջ 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. |
Բովանդակություն
IV | 3 |
V | 17 |
VI | 29 |
VII | 48 |
VIII | 59 |
IX | 67 |
X | 75 |
XI | 87 |
XVII | 142 |
XVIII | 152 |
XIX | 175 |
XX | 190 |
XXI | 205 |
XXII | 217 |
XXIII | 250 |
XXIV | 259 |
Այլ խմբագրություններ - View all
Differential Equations with Discontinuous Righthand Sides: Control Systems A.F. Filippov Դիտել հնարավոր չէ - 2010 |
Differential Equations with Discontinuous Righthand Sides: Control Systems A.F. Filippov Դիտել հնարավոր չէ - 2014 |
Common terms and phrases
absolutely continuous arcs of trajectories asymptotically stable belong boundary bounded variation Carathéodory equation closed domain closed set closed trajectory common points compactum considered contained convergent convex convex set COROLLARY defined definition degree of structural derivative diffeomorphism differential equations differential inclusion discontinuous right-hand sides domain G endpoints equations with discontinuous exists finite number follows function f graph half trajectory Hence inequality initial data intersection Lemma linear singularities matrix motion neighbourhood nonempty obtain passes plane pointwise singularities polytrajectory PROOF Q+(x right uniqueness S₁ satisfy the conditions sectors of classes segment separatrices set F(t set-valued function singular point singularity of class smooth solution of equation solution x(t stationary points structural instability sufficiently small surfaces of discontinuity system à t₁ tangent Theorem topological classes topological mapping uniformly convergent upper semicontinuous vector field vector-valued function virtue of Lemma x-axis x(to
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Էջ vi - As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection.
Էջ v - 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. This programme, Mathematics and Its Applications, is devoted to new emerging (sub)disciplines and to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathematical and/or scientific specialized areas; - new applications of the...
Էջ v - 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:...
Էջ v - 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...
Էջ v - Applications, is devoted to new emerging (sub)disciplines and to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathematical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific endeavour into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another. The Mathematics and Its Applications programme...
Էջ v - The point of a Pin'. 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...
Էջ 291 - Generalized ordinary differential equations and continuous dependence on a parameter.