Related papers: A canonical form for some piecewise defined functi…
Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
We extend the known piecewise linear parametrization of the canonical basis of the plus part of an enveloping algebra of type ADE to the nonsimplylaced case.
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…
We study functions which are the pointwise limit of a sequence of holomorphic functions. In one complex variable this is a classical topic, though we offer some new points of view and new results. Some novel results for solutions of…
We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
Consider a Henselian rank one valued field $K$ of equicharacteristic zero along with the language $\mathcal{L}^{P}$ of Denef--Pas. Let $f: A \to K$ be an $\mathcal{L}^{P}$-definable (with parameters) function on a subset $A$ of $K^{n}$. We…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
We give an elementary characterization of rational functions among meromorphic functions in the complex plane.
In this paper, we extend an available neural network verification technique to support a wider class of piece-wise linear activation functions. Furthermore, we extend the algorithms, which provide in their original form exact respectively…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…
Piecewise affine functions on subsets of $\mathbb R^m$ were studied in \cite{Ovchinnikov:02,Aliprantis:06a,Aliprantis:07a,Aliprantis:07}. In this paper we study a more general concept of a locally piecewise affine function. We characterize…
Methods for choosing from a set of options are often based on a strict partial order on these options, or on a set of such partial orders. I here provide a very general axiomatic characterisation for choice functions of this form. It…
This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of the interpretation. In this way we are able to generalise…