相关论文: Origin of the numerals
We give a hierarchial set of axioms for mathematical origami. The hierachy gives the fields of Pythagorean numbers, first discussed by Hilbert, the field of Euclidean constructible numbers which are obtained by the usual constructions of…
The use of OCR in postal services is not yet universal and there are still many countries that process mail sorting manually. Automated Arabic/Indian numeral Optical Character Recognition (OCR) systems for Postal services are being used in…
Natural numbers from 0 to 11111 are written in terms of 1 to 9 in two different ways. The first one in increasing order of 1 to 9, and the second one in decreasing order. This is done by using the operations of addition, multiplication,…
Algebraic-geometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or,…
We give a brief history of Catalan numbers, from their first discovery in the 18th century to modern times. This note will appear as an appendix in Richard Stanley's forthcoming book on Catalan numbers.
In 1969, H. Davenport and W. M. Schmidt studied the problem of approximation to a real number \xi by algebraic integers of degree at most three. They did so, using geometry of numbers, by resorting to the dual problem of finding…
Recall that repdigit in base $g$ is a positive integer that has only one digit in its base $g$ expansion, i.e. a number of the form $a(g^m-1)/(g-1)$, for some positive integers $m\geq 1$, $g\geq 2$ and $1\leq a\leq g-1$. In the present…
In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the…
Arabic is recognised as the 4th most used language of the Internet. Arabic has three main varieties: (1) classical Arabic (CA), (2) Modern Standard Arabic (MSA), (3) Arabic Dialect (AD). MSA and AD could be written either in Arabic or in…
The Mersenne primes are primes which can be written as some prime power of 2 minus 1. These primes were studied from antiquity in that their close connection with perfect numbers and even to present day in that their easiness for primality…
We present a modern reconstruction of the classical formula, first derived by medieval Arab astronomers, that describes the trajectory of the tip of a gnomon's shadow during the day as a function of latitude, solar declination, and gnomon…
In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce…
We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present…
This is a collection of definitions, notations and proofs for the Bernoulli numbers $B_n$ appearing in formulas for the sum of integer powers, some of which can be found scattered in the large related historical literature in French,…
The hybrid numbers were introduced by Ozdemir [9] as a new generalization of complex, dual, and hyperbolic numbers. A hybrid number is defined by $k=a+bi+c\epsilon +dh$, where $a,b,c,d$ are real numbers and $% i,\epsilon ,h$ are operators…
This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the well-known construction of the real numbers using Dedekind cuts, the idea is…
Our main source of inspiration was a talk by Hendrik Lenstra on harmonic numbers, which are numbers whose only prime factors are two or three. Gersonides proved 675 years ago that one can be written as a difference of harmonic numbers in…
This paper builds on the research initiated by Boyadzhiev, but introduces generalized harmonic numbers, \[ H_n(\alpha)= \sum_{k=1}^n \frac{\alpha^{k}}{k}, \] which enable the derivation of new identities as well as the reformulation of…
Magic squares have always been and are still fascinating for many people, be it only because of their mathematical properties. Their origin is still but certain : we find no magic squares in Greece, and only a 3x3 one in China at the…
Handwritten character recognition is an active area of research with applications in numerous fields. Past and recent works in this field have concentrated on various languages. Arabic is one language where the scope of research is still…