Related papers: Certain functions defined in terms of Cantor serie…
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…
This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic…
In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.
By a Cantor group we mean a topological group homeomorphic to the Cantor set. The author earlier proved that every compact metric space of rational cohomological dimension n can be obtained as the orbit space of a Cantor group action on a…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
We characterize normal families in the unit ball as those families of analytic functions whose restrictions to each complex line through the origin are normal. We then generalize this result to a characterization of normal functions…
We define the notion of an indexed profunctor over a 2-category, and use it to develop an abstract theory of limits. The theory subsumes (conical) limits, weighted limits, ends and Kan extensions. Results include an abstract version of the…
The well-known difficulties arising in a classification which is not set-theoretically trivial---involving what is sometimes called a non-smooth quotient---have been overcome in a striking way in the theory of operator algebras by the use…
We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
By a tensor we mean a multidimensional array (matrix) or hypermatrix over a number field. This article aims to set an account of the studies on the permanent functions of tensors. We formulate the definitions of 1-permanent, 2-permanent,…
We give lower bounds for the Hausdorff dimensions of some model Furstenberg sets.
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
It is shown that any continuous function depending on several $p$-adic variables, each of which is defined on $\mathbb{Z}_{p}$, can be represented as a superposition of continuous functions of one $p$-adic variable. This statement is true…
Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.
To illustrate that the notion of convergence of submodular function sequences fits reasonably into the limit theory of graphs, we describe several classes of matroids and other submodular setfunctions for which convergence of appropriate…
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
We study no-signalling correlations over Cantor spaces, placing the product of infinitely many copies of a finite non-local game in a unified general setup. We define the subclasses of local, quantum spatial, approximately quantum and…
We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.