Related papers: Decompositions of functions based on arity gap
For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…
A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of…
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…
We study functions from a unique factorization monoid to a field. The set of all such functions is a commutative ring isomorphic to a ring of formal power series over the field, with indeterminates indexed by the prime elements of the…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Let $\mathbb{F}_p$ be the finite field of prime order $p$. For any function $f \colon \mathbb{F}_p{}^n \to \mathbb{F}_p$, there exists a unique polynomial over $\mathbb{F}_p$ having degree at most $p-1$ with respect to each variable which…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
An alternative definition of the concept is given of functional dependence among the attributes of the relational schema in the Relational Model, this definition is obtained in terms of the set theory. For that which a theorem is…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
A random local function defined by a $d$-ary predicate $P$ is one where each output bit is computed by applying $P$ to $d$ randomly chosen bits of its input. These represent natural distributions of instances for constraint satisfaction…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
In this paper, it is shown that every polynomial function is mixed monotone globally with a polynomial decomposition function. For univariate polynomials, the decomposition functions can be constructed from the Gram matrix representation of…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
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.…
In this note, we introduce a new kind of pair of finite range sets in $\mathbb{C}$ for meromorphic functions corresponding to their uniqueness, i.e., how two meromorphic functions are uniquely determined by their two finite shared sets.