Related papers: Basic facts concerning supermodular functions
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
The aim of this work is to provide formulae for the subdifferential and the conjungate function of the supremun function over an arbitrary family of functions. The work is principally motivated by the case when data functions are lower…
We investigate the properties of a modulus of a foliation on a Riemannian manifold. We give necessary and sufficient conditions for the existence of an extremal function and state some of its properties. We obtain the integral formula…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…
We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…
Recent work on the representation of functions on sets has considered the use of summation in a latent space to enforce permutation invariance. In particular, it has been conjectured that the dimension of this latent space may remain fixed…
We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.
Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators. We give a systematic study of nearly convex sets, and construct examples of subdifferentials of lower semicontinuous convex functions…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.
Some notes and observations on analytic functions defined on an annulus
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
Functions whose composition with every metric is a metric are said to be metric-preserving. In this article, we investigate a variation of the concept of metric-preserving functions where metrics are replaced by ultrametrics.
An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…
We present functions that quantify the contribution of a set of arguments in quantitative bipolar argumentation graphs to (the final strength of) an argument of interest, a so-called topic. Our set contribution functions are generalizations…