T his chapter represents the culmination of multivariable calculus. We investigate the remarkable physical applications of vector calculus that provided the original motivation for the development of this subject in the seventeenth, eighteenth, and nineteenth centuries. The vector fields that we examine ...
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Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall,...
A necessary condition for the central limit theorem on spaces of stable type Michael B. Marcus, Wojbor A. Woyczynski Pages 327-339 1 2 Nextpage Back to top Bibliographic Information Book TitleVector Space Measures and Applications I Book SubtitleProceedings, Dublin, 1977 ...
Structure-preserving discretization of fractional vector calculus using discrete exterior calculus Alon Jacobson, Xiaozhe Hu1 January 2024 Pages 186-196 Article preview select article Numerical solutions of an option pricing rainfall weather derivatives model Research articleOpen access Numerical solutions of ...
Abstract In the present paper, we investigate Hölder-type norm inequalities in terms of div and curl of the vector-valued functions in variable exponent Lebesgue spaces Lp(x)(Ω), where Ω⊂R3. Moreover, by using the obtained results we give some applications for magnetostatics problems....
In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) is preordered by a not necessarily solid (and not necessarily pointed) convex cone. It is well-known that there are many examples where the ordering cone of the image space ha...
In such settings, data points are vertices of the graph and are connected by edges if sufficiently close in a certain ground metric. Using discrete vector calculus1,8,9, one defines finite difference operators which are analogous to the differential operators in the continuous setting. This mimeti...
Table of contents (8 chapters) Front Matter Pages i-xi Download chapter PDF Topology Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu Pages 1-39 Banach Spaces and Differential Calculus Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu Pages 40-140 Manifolds and Vector Bundles Ralph ...
The theory of trees and applications to vector-based numerical methods can be found, for example, in [2]. The order of the method in [3] was studied in [4]. 2. Trees, Elementary Differentials, and B-Series Trees are graphs such as , , , , , , , . The “root” of a tree ...