Stability of Motion by A.M. Liapunov (Eds.)

By A.M. Liapunov (Eds.)

During this publication, we learn theoretical and functional facets of computing equipment for mathematical modelling of nonlinear structures. a few computing innovations are thought of, akin to tools of operator approximation with any given accuracy; operator interpolation recommendations together with a non-Lagrange interpolation; tools of method illustration topic to constraints linked to thoughts of causality, reminiscence and stationarity; tools of method illustration with an accuracy that's the most sensible inside of a given type of types; equipment of covariance matrix estimation;methods for low-rank matrix approximations; hybrid tools according to a mix of iterative techniques and most sensible operator approximation; andmethods for info compression and filtering lower than clear out version should still fulfill regulations linked to causality and varieties of memory.As a end result, the booklet represents a mix of recent equipment often computational analysis,and particular, but in addition popular, options for learn of platforms idea ant its particularbranches, akin to optimum filtering and data compression. - most sensible operator approximation,- Non-Lagrange interpolation,- primary Karhunen-Loeve remodel- Generalised low-rank matrix approximation- optimum facts compression- optimum nonlinear filtering

Show description

By A.M. Liapunov (Eds.)

During this publication, we learn theoretical and functional facets of computing equipment for mathematical modelling of nonlinear structures. a few computing innovations are thought of, akin to tools of operator approximation with any given accuracy; operator interpolation recommendations together with a non-Lagrange interpolation; tools of method illustration topic to constraints linked to thoughts of causality, reminiscence and stationarity; tools of method illustration with an accuracy that's the most sensible inside of a given type of types; equipment of covariance matrix estimation;methods for low-rank matrix approximations; hybrid tools according to a mix of iterative techniques and most sensible operator approximation; andmethods for info compression and filtering lower than clear out version should still fulfill regulations linked to causality and varieties of memory.As a end result, the booklet represents a mix of recent equipment often computational analysis,and particular, but in addition popular, options for learn of platforms idea ant its particularbranches, akin to optimum filtering and data compression. - most sensible operator approximation,- Non-Lagrange interpolation,- primary Karhunen-Loeve remodel- Generalised low-rank matrix approximation- optimum facts compression- optimum nonlinear filtering

Show description

Read or Download Stability of Motion PDF

Similar mathematics books

Multiparameter Eigenvalue Problems and Expansion Theorems

This e-book presents a self-contained remedy of 2 of the most difficulties of multiparameter spectral concept: the lifestyles of eigenvalues and the growth in sequence of eigenfunctions. the implications are first got in summary Hilbert areas after which utilized to essential operators and differential operators.

Séminaire Bourbaki, Vol. 1, 1948-1951, Exp. 1-49

Desk of Contents

* 1 Henri Cartan Les travaux de Koszul, I (Lie algebra cohomology)
* 2 Claude Chabauty Le théorème de Minkowski-Hlawka (Minkowski-Hlawka theorem)
* three Claude Chevalley L'hypothèse de Riemann pour les corps de fonctions algébriques de caractéristique p, I, d'après Weil (local zeta-function)
* four Roger Godement Groupe complexe unimodulaire, I : Les représentations unitaires irréductibles du groupe complexe unimodulaire, d'après Gelfand et Neumark (representation thought of the complicated specified linear group)
* five Léo Kaloujnine Sur l. a. constitution de p-groupes de Sylow des groupes symétriques finis et de quelques généralisations infinies de ces groupes (Sylow theorems, symmetric teams, countless crew theory)
* 6. Pierre Samuel l. a. théorie des correspondances birationnelles selon Zariski (birational geometry)
* 7 Jean Braconnier Sur les suites de composition d'un groupe et los angeles travel des groupes d'automorphismes d'un groupe fini, d'après H. Wielandt (finite groups)
* eight Henri Cartan, Les travaux de Koszul, II (see 1)
* nine Claude Chevalley, L'hypothèse de Riemann pour les groupes de fonctions algébriques de caractéristique p, II,, d'après Weil (see 3)
* 10 Luc Gauthier, Théorie des correspondances birationnelles selon Zariski (see 6)
* eleven Laurent Schwartz, Sur un mémoire de Petrowsky : "Über das Cauchysche challenge für ein process linearer partieller Differentialgleichungen im gebiete nichtanalytischen Funktionen" (partial differential equations)
* 12 Henri Cartan, Les travaux de Koszul, III (see 1)
* thirteen Roger Godement, Groupe complexe unimodulaire, II : los angeles transformation de Fourier dans le groupe complexe unimodulaire à deux variables, d'après Gelfand et Neumark (see 4)
* 14 Marc Krasner, Les travaux récents de R. Brauer en théorie des groupes (finite groups)
* 15 Laurent Schwartz, Sur un deuxième mémoire de Petrowsky : "Über das Cauchysche challenge für method von partiellen Differentialgleichungen" (see 11)
* sixteen André Weil Théorèmes fondamentaux de los angeles théorie des fonctions thêta, d'après des mémoires de Poincaré et Frobenius (theta functions)
* 17 André Blanchard, Groupes algébriques et équations différentielles linéaires, d'après E. Kolchin (differential Galois theory)
* 18 Jean Dieudonné, Géométrie des espaces algébriques homogènes, d'après W. L. Chow (algebraic geometry)
* 19 Roger Godement, Sommes maintains d'espaces de Hilbert, I (functional research, direct integrals)
* 20 Charles Pisot, Démonstration élémentaire du théorème des nombres premiers, d'après Selberg et Erdös (prime quantity theorem)
* 21 Georges Reeb, Propriétés des trajectoires de certains systèmes dynamiques (dynamical systems)
* 22 Pierre Samuel, Anneaux locaux ; creation à l. a. géométrie algébrique (local rings)
* 23 Marie-Hélène Schwartz, Compte-rendu de travaux de M. Heins sur diverses majorations de los angeles croissance des fonctions analytiques et sous-harmoniques (complex research, subharmonic functions)
* 24 Charles Ehresmann, Les connexions infinitésimales dans un espace fibré différentiable (connections on fiber bundles)
* 25 Roger Godement, Sommes maintains d'espaces de Hilbert, II (see 19)
* 26 Laurent Schwartz, Sur un mémoire de ok. Kodaira : "Harmonic fields in riemannian manifolds (generalized strength theory)", I (Hodge theory)
* 27 Jean-Pierre Serre, Extensions de groupes localement compacts, d'après Iwasawa et Gleason (locally compact groups)
* 28 René Thom, Les géodésiques dans les variétés à courbure négative, d'après Hopf (geodesics)
* 29 Armand Borel, Groupes localement compacts, d'après Iwasawa et Gleason (see 27)
* 30 Jacques Dixmier, Facteurs : category, measurement, hint (von Neumann algebras)
* 31 Jean-Louis Koszul, Algèbres de Jordan (Jordan algebras)
* 32 Laurent Schwartz, Sur un mémoire de ok. Kodaira : "Harmonic fields in riemannian manifolds (generalized power theory)", II (see 26)
* 33 Armand Borel, Sous-groupes compacts maximaux des groupes de Lie, d'après Cartan, Iwasawa et Mostow (maximal compact subgroups)
* 34 Henri Cartan, Espaces fibrés analytiques complexes (analytic geometry, fiber bundles)
* 35 Charles Ehresmann, Sur les variétés presque complexes (almost-complex manifolds)
* 36 Samuel Eilenberg, Exposition des théories de Morse et Lusternick-Schnirelmann (Morse concept, Lyusternik-Schnirelmann category)
* 37 Luc Gauthier, Quelques variétés usuelles en géométrie algébrique (algebraic geometry)
* 38 Jean-Louis Koszul, Cohomologie des espaces fibrés différentiables et connexions (Chern-Weil theory)
* 39 Jean Delsarte, Nombre de options des équations polynomiales sur un corps fini, d'après A. Weil (Weil conjectures)
* forty Jacques Dixmier, Anneaux d'opérateurs et représentations des groupes (operator algebras, illustration theory)
* forty-one Roger Godement, Théorie des caractères dans les groupes unimodulaires (unimodular groups)
* forty two Pierre Samuel, Théorie du corps de sessions neighborhood selon G. P. Hochschild (local classification box theory)
* forty three Laurent Schwartz, Les théorèmes de Whitney sur les fonctions différentiables (singularity theory)
* forty four Jean-Pierre Serre, Groupes d'homotopie (homotopy groups)
* forty five Armand Borel, Cohomologie des espaces homogènes (cohomology of homogeneous areas of Lie groups)
* forty six Samuel Eilenberg, Foncteurs de modules et leurs satellites, d'après Cartan et Eilenberg (homological algebra)
* forty seven Marc Krasner, Généralisations non-abéliennes de l. a. théorie locale des corps de periods (local fields)
* forty eight Jean Leray, l. a. résolution des problèmes de Cauchy et de Dirichlet au moyen du calcul symbolique et des projections orthogonales et obliques (Dirichlet difficulties and Cauchy difficulties for partial differential equations, symbolic calculus)
* forty nine Pierre Samuel, Sections hyperplanes des variétés normales, d'après A. Seidenberg (algebraic geometry, hyperplane sections, general type)

Additional resources for Stability of Motion

Example text

10. From what was shown in page 31 it follows that one can always find an entire function U , which does not contain terms Investigation of One of the Singular Cases of Theory of Stability of Motion 39 of an order lower than three or higher than k, and vanishing for x = x1= x2= ... U has the property that in the expression of the derivative d (Y' + U), formed in virtue of Eqs. (18), there are no terms, which vanish for y = x1 -- x 2 = = x, = 0, of an order lower than k 1. The number k can be arbitrarily large.

We have imposed on z the condition z 3 0. However, with the same right we 54 Stability of Motion might impose the condition z GO as well, and we would get the same result. If, however, we consider the function v1 -- + ~ ( 1 +) ~ + ... + ~ ( k f q - 2 )Z k + ¶ - 2 +(-l)k+q-lW, where U"), Ware the previously used functions, we obviously find where S , is an expression of the same type as S. The derivative d VJdt is obviously sign-definite having the same if z satisfies the condition z GO. But under sign as (-1)"'"-'h, the same condition, the function V , is negative definite, if (-l)k + ¶ - ' h> 0.

N). Obviously, the functions U q + ' U ) ,: 2 q )do not depend on the quantities d i ) ,usi), and therefore, they are completely known. The functions U ( 4 - l ), V 4 ' - ) depend only on those d')for which i < 1. Moreover, for I < q 2, these functions and the function V Z q - l ) do not depend on the quantities ~ 5 ' ) . For I 2 q + 2 they can depend only on those u;') for which i < q 1- I, while V ( q + ' - 3certainly ) does not depend on the quantities u : . ~ + ' - ~ ) . Finally, the functions Ui') (for which always I2 2q) can only depend on those u ( ' ) for which i < 1 - 2q 2 and on those ~ 1 .

Download PDF sample

Rated 4.54 of 5 – based on 40 votes