Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration
نویسندگان
چکیده
We collect several foundational results regarding the interaction between locally compact spaces, probability spaces and algebras, commutative $C^*$-algebras von Neumann algebras equipped with traces, in “uncountable” setting wh
منابع مشابه
Canonical Duality Theory for Topology Optimization
This paper presents a novel canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. We first show that by using finite element method, this most challenging problem can be formulated as a bi-level mixed integer nonlinear programming problem, i.e. for a given deformation, the upper-level optimization is a typical linear constrained 0-1 prog...
متن کاملDuality and Canonical Transformations
We present a brief review on the canonical transformation description of some duality symmetries in string and gauge theories. In particular, we consider abelian and non-abelian T-dualities in closed and open string theories as well as S-duality in abelian and non-abelian non-supersymmetric gauge theories. THU-96/36 hep-th/9610024 October 1996 Talk given at the Argonne Duality Institute, June 2...
متن کاملCanonical representation for approximating solution of fuzzy polynomial equations
In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness.
متن کاملCanonical Duality Theory: Connections between nonconvex mechanics and global optimization
This paper presents a comprehensive review and some new developments on canonical duality theory for nonconvex systems. Based on a tri-canonical form for quadratic minimization problems, an insightful relation between canonical dual transformations and nonlinear (or extended) Lagrange multiplier methods is presented. Connections between complementary variational principles in nonconvex mechanic...
متن کاملCanonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming
This paper presents a perfect duality theory and a complete set of solutions to nonconvex quadratic programming problems subjected to inequality constraints. By use of the canonical dual transformation developed recently, a canonical dual problem is formulated, which is perfectly dual to the primal problem in the sense that they have the same set of KKT points. It is proved that the KKT points ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2023
ISSN: ['0016-2736', '1730-6329']
DOI: https://doi.org/10.4064/fm226-7-2022