Tensor valuations

张量估值

• 批准号: 196778596
• 负责人: Professor Dr. Daniel Hug
• 金额: --
• 依托单位: Institut für Stochastik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/196778596?language=en
• 关键词: Tensor; valuations

This project aims at a thorough study of integral geometric results and morphological properties of tensorial functionals of various classes of sets. One main focus will be on translative, kinematic and rotational integral geometric formulas for tensor valuations and for not necessarily additive tensor functionals. We will introduce tensor-valued functionals for quite general classes of sets and with respect to different generating measures. This will enable us to apply tensor valuations as morphological measures that are relevant to the physical processes in anisotropic microstructured materials, and for the thermodynamics of ensembles of non-spherical particles. Tensor functionals will play an important role as geometric descriptors in all projects of the proposal. A particular emphasis in this project will be on foundational problems.

该项目旨在全面研究各类集合的张量泛函的积分几何结果和形态特性。主要焦点之一是用于张量评估以及不一定是可加张量泛函的平移、运动学和旋转积分几何公式。我们将为相当一般的集合类以及不同的生成度量引入张量值泛函。这将使我们能够应用张量评估作为与各向异性微结构材料的物理过程以及非球形粒子集合的热力学相关的形态测量。张量泛函将作为几何描述符在该提案的所有项目中发挥重要作用。该项目将特别强调基础问题。