时变地层仿射变换中扩展Skorokhod问题的显式解

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-02 DOI:10.1155/2021/9992546

M. Slaby

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引用次数: 0

摘要

本文的目的是推广先前关于具有正交反射域的一类特殊约束域的扩展Skorokhod问题解的显式公式。我们研究了仿射变换如何将扩展Skorokhod问题的解转化为变换后的约束系统的新问题的解。对于任意随时间变化的约束集和任意基自然定义的反射场的任意n值函数càdlàg，我们得到了扩展Skorokhod问题解的显式公式。在生成反射场的坐标系中，演化约束集是夹在两个图之间的区域。讨论了扩展Skorokhod映射的Lipschitz性质，并推导了该类约束集的特殊情况下的Lipschitz常数。

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Explicit Solutions of the Extended Skorokhod Problems in Affine Transformations of Time-Dependent Strata

The goal of this paper is to expand the explicit formula for the solutions of the Extended Skorokhod Problem developed earlier for a special class of constraining domains in ℝ n with orthogonal reflection fields. We examine how affine transformations convert solutions of the Extended Skorokhod Problem into solutions of the new problem for the transformed constraining system. We obtain an explicit formula for the solutions of the Extended Skorokhod Problem for any ℝ n - valued càdlàg function with the constraining set that changes in time and the reflection field naturally defined by any basis. The evolving constraining set is a region sandwiched between two graphs in the coordinate system generating the reflection field. We discuss the Lipschitz properties of the extended Skorokhod map and derive Lipschitz constants in special cases of constraining sets of this type.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.