The Geometry of Higher-Order Lagrange Spaces, R. Miron
Автор: R. Miron Название: The Geometry of Higher-Order Lagrange Spaces ISBN: 9048147891 ISBN-13(EAN): 9789048147892 Издательство: Springer Рейтинг: Цена: 30327.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph is mostly devoted to the problem of the geome- trizing of Lagrangians which depend on higher order accelerations. It naturally prolongs the theme of the monograph "The Geometry of La- grange spaces: Theory and Applications," written together with M. Anastasiei and published by Kluwer Academic Publishers in 1994. The existence of Lagrangians of order k > 1 has been contemplated by mechanicists and physicists for a long time. Einstein had grasped their presence in connection with the Brownian motion. They are also present in relativistic theories based on metrics which depend on speeds and accelerations of particles or in the Hamiltonian formulation of non- linear systems given by Korteweg-de Vries equations. There resulted from here the methods to be adopted in their theoretical treatment. One is based on the variational problem involving the integral action of the Lagrangian. A second one is derived from the axioms of Analytical Mechanics involving the Poincare-Cartan forms. The geometrical methods based on the study of the geometries of higher order could invigorate the whole theory. This is the way adopted by us in defining and studying the Lagrange spaces of higher order. The problems raised by the geometrization of Lagrangians of order k > 1 investigated by many scholars: Ch. Ehresmann, P. Libermann, J. Pommaret; J.T. Synge, M. Crampin, P. Saunders; G.S. Asanov, P.Aringazin; I. Kolar, D. Krupka; M. de Leon, W. Sarlet, P. Cantrjin, H. Rund, W.M. Tulczyjew, A. Kawaguchi, K. Yano, K. Kondo, D.
Автор: P.L. Antonelli; R. Miron Название: Lagrange and Finsler Geometry ISBN: 0792338731 ISBN-13(EAN): 9780792338734 Издательство: Springer Рейтинг: Цена: 23053.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The differential geometry of a regular Lagrangian is more involved than that of classical kinetic energy and consequently is far from being Riemannian. This collection of papers covers higher order Lagrange geometry, the theory of -Lagrange manifolds, electromagnetic theory and neurophysiology.
Автор: R. Miron Название: The Geometry of Higher-Order Hamilton Spaces ISBN: 940103995X ISBN-13(EAN): 9789401039956 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Asisknown, theLagrangeandHamiltongeometrieshaveappearedrelatively recently 76, 86]. Since 1980thesegeometrieshave beenintensivelystudied bymathematiciansandphysicistsfromRomania, Canada, Germany, Japan, Russia, Hungary, e.S.A. etc. PrestigiousscientificmeetingsdevotedtoLagrangeandHamiltongeome- tries and their applications have been organized in the above mentioned countries and a number ofbooks and monographs have been published by specialists in the field: R. Miron 94, 95], R. Mironand M. Anastasiei 99, 100], R. Miron, D. Hrimiuc, H. Shimadaand S.Sabau 115], P.L. Antonelli, R. Ingardenand M.Matsumoto 7]. Finslerspaces, whichformasubclassof theclassofLagrangespaces, havebeenthesubjectofsomeexcellentbooks, forexampleby: Yl.Matsumoto 76], M.AbateandG.Patrizio 1], D.Bao, S.S. Chernand Z.Shen 17]andA.BejancuandH.R.Farran 20]. Also, wewould liketopointoutthemonographsofM. Crampin 34], O.Krupkova 72] and D.Opri, I.Butulescu 125], D.Saunders 144], whichcontainpertinentappli- cationsinanalyticalmechanicsandinthetheoryofpartialdifferentialequa- tions. Applicationsinmechanics, cosmology, theoreticalphysicsandbiology can be found in the well known books ofP.L. Antonelliand T.Zawstaniak 11], G.S. Asanov 14]' S. Ikeda 59]: VI. de LeoneandP.Rodrigues 73]. TheimportanceofLagrangeandHamiltongeometriesconsistsofthefact that variational problems for important Lagrangiansor Hamiltonians have numerous applicationsinvariousfields, such asmathematics, thetheoryof dynamicalsystems, optimalcontrol, biology, andeconomy. Inthisrespect, P.L. Antonelli'sremark isinteresting: "ThereisnowstrongevidencethatthesymplecticgeometryofHamilto- niandynamicalsystemsisdeeplyconnectedtoCartangeometry, thedualof Finslergeometry," (seeV.I.Arnold, I.M.GelfandandV.S.Retach 13]). The above mentioned applications have also imposed the introduction x RaduMiron ofthe notionsofhigherorder Lagrangespacesand, ofcourse, higherorder Hamilton spaces. The base manifolds ofthese spaces are bundles ofaccel- erations ofsuperior order. The methods used in the construction ofthese geometries are the natural extensions ofthe classical methods used in the edification ofLagrange and Hamilton geometries. These methods allow us to solvean old problemofdifferentialgeometryformulated by Bianchiand Bompiani 94]morethan 100yearsago, namelytheproblemofprolongation ofaRiemannianstructure gdefinedonthebasemanifoldM, tothetangent k bundleT M, k> 1. Bymeansofthissolutionofthe previousproblem, we canconstruct, for thefirst time, goodexamplesofregularLagrangiansand Hamiltoniansofhigherorder.
Автор: Author Unknown Название: Handbook of the Geometry of Banach Spaces,2 ISBN: 0444513051 ISBN-13(EAN): 9780444513052 Издательство: Elsevier Science Рейтинг: Цена: 27791.00 р. Наличие на складе: Поставка под заказ.
Описание: Encouraged by new perspectives in Banach space theory, the editors present this second volume that opens with an introductory essay that explains the basics of the theory. The rest of the chapters focus on specific directions of Banach space theory or its applications.
Автор: R. Miron; Dragos Hrimiuc; Hideo Shimada; Sorin V. Название: The Geometry of Hamilton and Lagrange Spaces ISBN: 0792369262 ISBN-13(EAN): 9780792369264 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: It reveals new concepts and geometrical objects of Hamilton spaces that are dual to those which are similar in Lagrange spaces. Following this duality Cartan spaces introduced and studied in [98], [99],..., are, roughly speaking, the Legendre duals of certain Finsler spaces [98], [66], [67].
Автор: Alexander M. Rubinov; Xiao-qi Yang Название: Lagrange-type Functions in Constrained Non-Convex Optimization ISBN: 1461348218 ISBN-13(EAN): 9781461348214 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimiza- tion problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints.
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