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

In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…

The present paper shows meta-programming turn programming, which is rich enough to express arbitrary arithmetic computations. We demonstrate a type system that implements Peano arithmetics, slightly generalized to negative numbers. Certain…

We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…

In 2023 in (3), Uwe finds the explicit form of the map which is which is settled in ZN of finite functional degree and14 discusses how to compute its usual degree w.r.t to the derivative in the linear form, i.e. the product of ones formed…

We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…

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…

Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…

We consider Mityuk's function and radius which have been proposed in \cite{Mit} as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute Mityuk's…

Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…

Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…

This article demonstrates that convolutional operation can be converted to matrix multiplication, which has the same calculation way with fully connected layer. The article is helpful for the beginners of the neural network to understand…

Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values in a given manner. Such functions are…

This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…

This paper provides a mathematical analysis of optimal algebraic manipulation detection (AMD) codes. We prove several lower bounds on the success probability of an adversary and we then give some combinatorial characterizations of AMD codes…

We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with…

Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…

It is possible to interpret text as numbers (and vice versa) if one interpret letters and other characters as digits and assume that they have an inherent immutable ordering. This is demonstrated by the conventional digit set of the…

In this work, we established symmetric representation of numbers where one can use any of 9 digits giving the same number. The representations of natural numbers from 0 to 1000 are given using only single digit in all the nine cases, i.e.,…

We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are…