Tag: Variational

Free Download Svetlin G. Georgiev, "Variational Calculus on Time Scales "
English | ISBN: 1536143235 | 2018 | 297 pages | PDF | 4 MB
This book encompasses recent developments of variational calculus for time scales. It is intended for use in the field of variational calculus and dynamic calculus for time scales. It is also suitable for graduate courses in the above fields. This book contains eight chapters, and these chapters are pedagogically organized. This book is specially designed for those who wish to understand variational calculus on time scales without having an extensive mathematical background.

Free Download Variational Methods in Image Segmentation: with seven image processing experiments By Jean Michel Morel, Sergio Solimini (auth.)
1995 | 248 Pages | ISBN: 1468405691 | PDF | 7 MB
This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image: in the variational seg mentation energies, "edge" terms compete with "region" terms in a way which is supposed to impose regularity on both regions and boundaries. This fact was an experimental guess in perception phenomenology and computer vision until it was proposed as a mathematical conjecture by Mumford and Shah. The third part of the book presents a unified presentation of the evi dences in favour of the conjecture. It is proved that the competition of one-dimensional and two-dimensional energy terms in a variational for mulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves con cepts from geometric measure theory, which proves to be central in im age processing theory. The second part of the book provides a fast and self-contained presentation of the classical theory of rectifiable sets (the "edges") and unrectifiable sets ("fractals").

Free Download Lectures on Geometric Variational Problems By Seiki Nishikawa, Richard Schoen (auth.), Seiki Nishikawa, Richard Schoen (eds.)
1996 | 154 Pages | ISBN: 4431701524 | PDF | 3 MB
In this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon’s notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya’s notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments.

Free Download Variational Principles in Physics: From Classical to Quantum Realm (SpringerBriefs in Physics) by Tamás Sándor Biró
English | March 23, 2023 | ISBN: 3031278755 | 124 pages | MOBI | 10 Mb
This book is an English translation from a Hungarian book designed for graduate and postgraduate students about the use of variational principles in theoretical physics. Unlike many academic textbooks, it dashes across several lecture disciplines taught in physics courses. It emphasizes and demonstrates the use of the variational technique and philosophy behind the basic laws in mechanics, relativity theory, electromagnetism, and quantum mechanics. The book is meant for advanced students and young researchers in theoretical physics but, also, more experienced researchers can benefit from its reading.

Free Download Abderrahim Elmoataz, "Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021, Virtual Event, May 16-2"
English | ISBN: 3030755487 | 2021 | 596 pages | PDF | 118 MB
This book constitutes the proceedings of the 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, which took place during May 16-20, 2021. The conference was planned to take place in Cabourg, France, but changed to an online format due to the COVID-19 pandemic.

Free Download Variational Methods for Structural Optimization by Andrej Cherkaev
English | PDF (True) | 2000 | 561 Pages | ISBN : 0387984623 | 45.4 MB
In recent decades, it has become possible to turn the design process into computer algorithms. By applying different computer oriented methods the topology and shape of structures can be optimized and thus designs systematically improved. These possibilities have stimulated an interest in the mathematical foundations of structural optimization. The challenge of this book is to bridge a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in a sufficiently simple form to make them available for practical use and to allow their critical appraisal for improving and adapting these results to specific models. Special attention is to pay to the description of optimal structures of composites; to deal with this problem, novel mathematical methods of nonconvex calculus of variation are developed. The exposition is accompanied by examples.

Free Download Generative NLP with Variational AutoEncoders
Published 6/2024
MP4 | Video: h264, 1280×720 | Audio: AAC, 44.1 KHz, 2 Ch
Language: English | Duration: 4h 44m | Size: 700 MB
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Free Download Variational Methods: In Imaging and Geometric Control
English | 2017 | ISBN: 3110439239 | 540 Pages | EPUB (True) | 64 MB
With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents:Part ISecond-order decomposition model for image processing: numerical experimentationOptimizing spatial and tonal data for PDE-based inpaintingImage registration using phase・amplitude separationRotation invariance in exemplar-based image inpaintingConvective regularization for optical flowA variational method for quantitative photoacoustic tomography with piecewise constant coefficientsOn optical flow models for variational motion estimationBilevel approaches for learning of variational imaging modelsPart IINon-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problemsThe Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controlsControllability of Keplerian motion with low-thrust control systemsHigher variational equation techniques for the integrability of homogeneous potentialsIntroduction to KAM theory with a view to celestial mechanicsInvariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometryTime-optimal control for a perturbed Brockett integratorTwist maps and Arnold diffusion for diffeomorphismsA Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part IIndex

Free Download Variational Calculus with Engineering Applications by Constantin Udriste, Ionel Tevy
English | October 24, 2022 | ISBN: 1119944368 | 224 pages | MOBI | 23 Mb
VARIATIONAL CALCULUS WITH ENGINEERING APPLICATIONS

Free Download Variational Convergence and Stochastic Homogenization of Nonlinear Reaction-Diffusion Problems by Omar Anza Hafsa, Jean-Philippe Mandallena, Gerard Michaille
English | July 20, 2022 | ISBN: 9811258481 | 320 pages | MOBI | 16 Mb
A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.