Related papers: Arithmetic Digit Manipulation and The Conway Base-…

This paper investigates two-terminal interactive function computation with reconstruction constraints. Each terminal wants to compute a (possibly different) function of two correlated sources, but can only access one of the sources…

A table of the families of alternating knots formed by conways is presented. The Conway's function is shown with the use of linear algebra in terms of natural numbers, called conways, that represent the number of crossings along a…

The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…

By means of a new technique, we develop further a discrete subordination approach to the functional calculus of power bounded and Ritt operators initiated by N. Dungey in [19]. This allows us to show, in particular, that (infinite) convex…

A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution…

In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the…

For all natural numbers a,b and d > 0, we consider the function f_{a,b,d} which associates n/d to any integer n when it is a multiple of d, and an + b otherwise; in particular f_{3,1,2} is the Collatz function. Coding in base a > 1 with b <…

The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and…

It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using…

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…

We propose a conjecture for the exact expression of the dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer…

We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…

In this paper, we propose a collection of approximations for the 8-point discrete cosine transform (DCT) based on integer functions. Approximations could be systematically obtained and several existing approximations were identified as…

In 1995, Meinardus & Berg presented a reformulation of the Collatz Conjecture in terms of a functional equation in a single complex variable over the open unit disk. This paper generalizes that method to deal with not only a large class of…

Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…

A new incremental algorithm for data compression is presented. For a sequence of input symbols algorithm incrementally constructs a p-adic integer number as an output. Decoding process starts with less significant part of a p-adic integer…

An algorithm is described to convert Lorentz and gauge invariant expressions in non--Abelian gauge theories with matter into a standard form, consisting of a linear combination of basis invariants. This algorithm is needed for computer…

For an integer b>=2, let s_b(n) be the sum of the digits of the integer n when written in base b, and let S_b(N) be the sum of s_b(n) over n=0,...,N-1, so that S_b(N) is the sum of all b-ary digits needed to write the numbers 0,1,...,N-1.…

This short note studies the asymptotic behavior of a generating function associated with the decimal expansion of \(2^n\). Our aims are twofold: (i) to present a problem on the best possible upper bound for this behavior, and (ii) to…

In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant). We also characterize a function…