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Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52894870733079,"sku":null,"price":16129.82,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030806507.jpg?v=1781258090"},{"product_id":"springer-optimization-and-its-applications-9783030378226","title":"Springer Optimization and Its Applications","description":"\u003cp\u003eThe book is devoted to the study of approximate solutions of optimization problems in the presence of computational errors. It contains a number of results on the convergence behavior of algorithms in a Hilbert space, which are known as important tools for solving optimization problems. The research presented in the book is the continuation and the further development of the author's (c) 2016 book Numerical Optimization with Computational Errors, Springer 2016. Both books study the algorithms taking into account computational errors which are always present in practice. The main goal is, for a known computational error, to find out what an approximate solution can be obtained and how many iterates one needs for this. The main difference between this new book and the 2016 book is that in this present book the discussion takes into consideration the fact that for every algorithm, its iteration consists of several steps and that computational errors for different steps are generally, different. This fact, which was not taken into account in the previous book, is indeed important in practice. For example, the subgradient projection algorithm consists of two steps. The first step is a calculation of a subgradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error and these two computational errors are different in general. It may happen that the feasible set is simple and the objective function is complicated. As a result, the computational error, made when one calculates the projection, is essentially smaller than the computational error of the calculation of the subgradient. Clearly, an opposite case is possible too. Another feature of this book is a study of a number of important algorithms which appeared recently in the literature and which are not discussed in the previous book. This monograph contains 12 chapters. Chapter 1 is an introduction. In Chapter 2 we study the subgradient projection algorithm for minimization of convex and nonsmooth functions. We generalize the results of [NOCE] and establish results which has no prototype in [NOCE]. In Chapter 3 we analyze the mirror descent algorithm for minimization of convex and nonsmooth functions, under the presence of computational errors.  For this algorithm each iteration consists of two steps. The first step is a calculation of a subgradient of the objective function while in the second one we solve an auxiliary minimization problem on the set of feasible points. In each of these two steps there is a computational error. We generalize the results of [NOCE] and establish results which has no prototype in [NOCE].  In Chapter 4 we analyze the projected gradient algorithm with a smooth objective function under the presence of computational errors.  In Chapter 5 we consider an algorithm, which is an extension of the projection gradient algorithm used for solving linear inverse problems arising in signal\/image processing. In Chapter 6 we study continuous subgradient method and continuous subgradient projection algorithm for minimization of convex nonsmooth functions and for computing the saddle points of convex-concave functions, under the presence of computational errors.  All the results of this chapter has no prototype in [NOCE]. In Chapters 7-12 we analyze several algorithms under the presence of computational errors which were not considered in [NOCE]. Again, each step of an iteration has a computational errors and we take into account that these errors are, in general, different. An optimization problems with a composite objective function is studied in Chapter 7. A zero-sum game with two-players is considered in Chapter 8. A predicted decrease approximation-based method is used in Chapter 9 for constrained convex optimization. Chapter 10 is devoted tominimization of quasiconvex functions. Minimization of sharp weakly convex functions is discussed in Chapter 11. Chapter 12 is devoted to a generalized projected subgradient method for minimization of a convex function over a set which is not necessarily convex.The book is of interest for researchers and engineers working in optimization. It also can be useful in preparation courses for graduate students.  The main feature of the book which appeals specifically to this audience is the study of the influence of computational errors for several important optimization algorithms. The book is of interest for experts in applications of optimization  to engineering and economics.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52894896455959,"sku":null,"price":10730.72,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030378226.jpg?v=1781258291"},{"product_id":"geometric-harmonic-analysis-iv-9783031291791","title":"Geometric Harmonic Analysis IV","description":"\u003cp\u003eThis monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. 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The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52895189139735,"sku":null,"price":6072.63,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030258467.jpg?v=1781258877"},{"product_id":"new-trends-in-parameter-identification-for-mathematical-models-9783319708249","title":"New Trends in Parameter Identification for Mathematical Models","description":"\u003cp\u003eThe Proceedings volume contains 16 contributions to the IMPA conference “New Trends in Parameter Identification for Mathematical Models”, Rio de Janeiro, Oct 30 – Nov 3, 2017, integrating the “Chemnitz Symposium on Inverse Problems on Tour”.  This conference is part of the “Thematic Program on Parameter Identification in Mathematical Models” organized  at IMPA in October and November 2017. One goal is to foster the scientific collaboration between mathematicians and engineers from the Brazialian, European and Asian communities. 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The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes-Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach-Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911117992215,"sku":null,"price":5397.75,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319953212.jpg?v=1781260034"},{"product_id":"lebesgue-integral-9783030601638","title":"Lebesgue Integral","description":"\u003cp\u003eThis book presents a compact and self-contained introduction to the theory of measure and integration. The introduction into this theory is as necessary (because of its multiple applications) as difficult for the uninitiated. Most measure theory treaties involve a large amount of prerequisites and present crucial theoretical challenges. By taking on another approach, this textbook provides less experienced readers with material that allows an easy access to the definition and main properties of the Lebesgue integral. The book will be welcomed by upper undergraduate\/early graduate students who wish to better understand certain concepts and results of probability theory, statistics, economic equilibrium theory, game theory, etc., where the Lebesgue integral makes its presence felt throughout. 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It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results.   The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, whichintroduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study.   By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911124742423,"sku":null,"price":6072.63,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783031105982.jpg?v=1781260179"},{"product_id":"applied-mathematics-for-environmental-problems-9783030617950","title":"Applied Mathematics for Environmental Problems","description":"\u003cp\u003eThis book contains some contributions presented at the Applied Mathematics for Environmental Problems minisymposium during the International Congress on Industrial and Applied Mathematics (ICIAM) held July 15-19, 2019 in Valencia, Spain. The first paper addresses a simplified physical wildfire spread model, based on partial differential equations solved with finite element methods and integrated into a GIS to provide a useful and efficient tool. The second paper focuses on one of the causes of the unpredictable behavior of wildfire, fire-spotting, through a statistical approach. The third paper addresses low -level wind shear which represents one of the most relevant hazards during aircraft takeoff and landing. It presents an experimental wind shear alert system that is based on predicting wind velocities obtained from the Harmonie-Arome model. The last paper addresses the environmental impact of oil reservoirs. It presents high-order hybridizable discontinuous Galerkin formulation combined with high-order diagonally implicit Runge-Kutta schemes to solve one-phase and two-phase flow problems through porous media. All the contributions collected in this volume are interesting examples of how mathematics and numerical modelling are effective tools in the field of environmental problems.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911126511895,"sku":null,"price":12080.49,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030617950.jpg?v=1781260227"},{"product_id":"geometric-continuum-mechanics-9783030426835","title":"Geometric Continuum Mechanics","description":"\u003cp\u003eThis contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911149121815,"sku":null,"price":14780.04,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030426835.jpg?v=1781261589"},{"product_id":"harnack-inequalities-and-nonlinear-operators-9783030737788","title":"Harnack Inequalities and Nonlinear Operators","description":"\u003cp\u003eThe book contains two contributions about the work of Emmanuele DiBenedetto and a selection of original papers. The authors are some of the main experts in Harnack’s inequalities and nonlinear operators. These papers are part of the contributions presented during the conference to celebrate the 70th birthday of Prof. Emmanuele DiBenedetto, which was held at “Il Palazzone” in Cortona from June 18th to 24th, 2017. The papers are focused on current research topics regarding the qualitative properties of solutions, connections with calculus of variations, Harnack inequality and regularity theory. Some papers are also related to various applications. Many of the authors have shared with Prof. DiBenedetto an intense scientific and personal collaboration, while many others have taken inspiration from and further developed his field of research.  The topics of the conference are certainly of great interest for the international mathematical community.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911152464151,"sku":null,"price":20179.14,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030737788.jpg?v=1781261678"},{"product_id":"transmutation-operators-and-applications-9783030359140","title":"Transmutation Operators and Applications","description":"\u003cp\u003eTransmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911168946455,"sku":null,"price":12080.49,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030359140.jpg?v=1781262278"},{"product_id":"approximation-theory-xvi-9783030574642","title":"Approximation Theory XVI","description":"\u003cp\u003eThese proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States.  Over 130 mathematicians from 20 countries attended.  The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. 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The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems. The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas. 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It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book \u0026amp;quote;Rational Extended Thermodynamics beyond the Monatomic Gas\u0026amp;quote; by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. 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