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Author: R. Miron
Publisher: Springer Science & Business Media
ISBN: 9401733384
Category : Mathematics
Languages : en
Pages : 351
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Book Description
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.
Author: R. Miron
Publisher: Springer Science & Business Media
ISBN: 9401733384
Category : Mathematics
Languages : en
Pages : 351
Get Book Here
Book Description
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.
Author: Ronen Eldan
Publisher: Springer Nature
ISBN: 3031263006
Category : Mathematics
Languages : en
Pages : 443
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Book Description
This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
Author:
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 490
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Author: Efstathios Vassiliou
Publisher:
ISBN:
Category : Mechanics, Analytic
Languages : en
Pages : 36
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Author: Mircea Neagu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 42
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Author: M. Boleanţu
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 34
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Book Description
Author: Vladimir G. Ivancevic
Publisher: Taylor & Francis
ISBN: 9781402045448
Category : Language Arts & Disciplines
Languages : en
Pages : 856
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Book Description
Geometrical Dynamics of Complex Systems is a graduate-level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By'complexsystems', inthis book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi-input multi-output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular 'soft complexity philosophy', we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high-dimensional nonlinear systems and processes of 'real life' can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well-known that linear systems, which are completely predictable and controllable by de?nition - live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.
Author: P. Donato
Publisher: Springer Science & Business Media
ISBN: 9780817635817
Category : Mathematics
Languages : en
Pages : 504
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Book Description
This volume contains the proceedings of the conference "Colloque de Goometrie Symplectique et Physique Mathematique" which was held in Aix-en-Provence (France), June 11-15, 1990, in honor of Jean-Marie Souriau. The conference was one in the series of international meetings of the Seminaire Sud Rhodanien de Goometrie, an organization of geometers and mathematical physicists at the Universities of Avignon, Lyon, Mar seille, and Montpellier. The scientific interests of Souriau, one of the founders of geometric quantization, range from classical mechanics (symplectic geometry) and quantization problems to general relativity and astrophysics. The themes of this conference cover "only" the first two of these four areas. The subjects treated in this volume could be classified in the follow ing way: symplectic and Poisson geometry (Arms-Wilbour, Bloch-Ratiu, Brylinski-Kostant, Cushman-Sjamaar, Dufour, Lichnerowicz, Medina, Ouzilou), classical mechanics (Benenti, Holm-Marsden, Marle) , particles and fields in physics (Garcia Perez-Munoz Masque, Gotay, Montgomery, Ne'eman-Sternberg, Sniatycki) and quantization (Blattner, Huebschmann, Karasev, Rawnsley, Roger, Rosso, Weinstein). However, these subjects are so interrelated that a classification by headings such as "pure differential geometry, applications of Lie groups, constrained systems in physics, etc. ," would have produced a completely different clustering! The list of authors is not quite identical to the list of speakers at the conference. M. Karasev was invited but unable to attend; C. Itzykson and M. Vergne spoke on work which is represented here only by the title of Itzykson's talk (Surfaces triangulees et integration matricielle) and a summary of Vergne's talk.
Author: Corina Vernic
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 30
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Author: Mihaela Neamţu
Publisher:
ISBN:
Category : Conservation laws (Mathematics)
Languages : en
Pages : 18
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Book Description
