Related papers: Canonical Functions: a proof via topological dynam…
The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of length functions to counting problems. Secondly, we use…
In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Let X be an infinite set of regular cardinality. We determine all clones on X which contain all almost unary functions. It turns out that independently of the size of X, these clones form a countably infinite descending chain. Moreover, all…
A clonoid is a set of finitary functions from a set $A$ to a set $B$ that is closed under taking minors. Hence clonoids are generalizations of clones. By a classical result of Post, there are only countably many clones on a 2-element set.…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define…
We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Teorem: any special scroll is the projection of a canonical scroll and…
We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…
Caucal hierarchy is a well-known class of graphs with decidable monadic theories. It were proved by L. Braud and A. Carayol that well-orderings in the hierarchy are the well-orderings with order types less than $\varepsilon_0$. Naturally,…
Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…
If the Continuum Hypothesis is false, it implies the existence of cardinalities between the integers and the real numbers. In studying these "cardinal characteristics of the continuum", it was discovered that many of the associated…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Actually, they provide a uniform and semantic way to axiomatise all extensions of intuitionistic logic and all modal logics above K4. Although the method…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
Any continuous piecewise-linear function $F\colon \mathbb{R}^{n}\to \mathbb{R}$ can be represented as a linear combination of $\max$ functions of at most $n+1$ affine-linear functions. In our previous paper [``Representing piecewise linear…
Some boundedness properties of function spaces (considered as topological groups) are studied.
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…