Related papers: Axiomatizing some small classes of set functions
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…
To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. These maps are based on model functions which can be written as an inner product. The main family of maps discussed is…
Abstract models of computation often treat the successor function $S$ on $\mathbb{N}$ as a primitive operation, even though its low-level implementations correspond to non-trivial programs operating on specific numerical representations.…
We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.
Let $r,\,f$ be multiplicative functions with $r\geqslant 0$, $f$ is complex valued, $|f|\leqslant r$, and $r$ satisfies some standard growth hypotheses. Let $x$ be large, and assume that, for some real number $\tau$, the quantities…
This paper investigates certain classes of entire functions in C^n that, together with their partial derivatives, share a finite set consisting of three elements. By employing normality criteria, we study the behaviour of such functions and…
We give an elementary characterization of rational functions among meromorphic functions in the complex plane.
Given a rational function of degree at least two defined over a number field k, we study the cardinality of the set of rational iterated preimages. We prove bounds for the cardinality of this set as the rational function varies in certain…
We give a new characterization of the class of rational string functions from formal language theory using order-preserving interpretations with respect to a very weak monadic programming language. This refines the known characterization of…
Richard Cox [1] set the axiomatic foundations of probable inference and the algebra of propositions. He showed that consistency within these axioms requires certain rules for updating belief. In this paper we use the analogy between…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
Challenging the standard notion of totality in computable functions, one has that, given any sufficiently expressive formal axiomatic system, there are total functions that, although computable and "intuitively" understood as being total,…
This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…
We propose a notion of iterating functions $f:X^{k}\rightarrow X$ in a way that represents recurrence relations of the form $a_{n+k}=f(a_{n},a_{n+1},...,a_{n+k-1})$. We define a function as $n$-involutory when its $n$th iterate is the…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
We show that there exists a fixed recursive function $e$ such that for all functions $h\colon \mathbb{N}\to \mathbb{N}$, there exists an injective function $c_h\colon \mathbb{N}\to \mathbb{N}$ such that $c_h(h(n))=e(c_h(n))$, i.e.,…