Related papers: Application and issues in abstract convexity
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
Approximations during program analysis are a necessary evil, as they ensure essential properties, such as soundness and termination of the analysis, but they also imply not always producing useful results. Automatic techniques have been…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
We define, in the frame of an abstract Wiener space, the notions of convexity and of concavity for the equivalence classes of random variables. As application we show that some important inequalities of the finite dimensional case have…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also associate with that family of functions a dual pair of problems…
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
By applying the perturbation function approach, we propose the Lagrangian and the conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The main tools are the $\Phi$-convexity theory and minimax…
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional…
The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…