Related papers: Sur l'origine des chiffres arabes
In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
Hilbert's Foundations of Geometry was perhaps one of the most influential works of geometry in the 20th century and its axiomatics was the first systematic attempt to clear up the logical gaps of the Elements. But does it have gaps of its…
Statistical machine translation for dialectal Arabic is characterized by a lack of data since data acquisition involves the transcription and translation of spoken language. In this study we develop techniques for extracting parallel data…
Surreal numbers are created recursively, with the "birthday" being the depth of the recursion. Birthday arithmetic describes how birthdays of surreal numbers are transformed by standard arithemetic operations. This paper shows that birthday…
``Can number and geometric spaces be reconstructed from their symmetries?'' This question, which is at the heart of anabelian geometry, a theory built on the collaborative efforts of an international community in many variants and with the…
Numeral systems across the world's languages vary in fascinating ways, both regarding their synchronic structure and the diachronic processes that determined how they evolved in their current shape. For a proper comparison of numeral…
A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform.…
We present two ways in which an infinite universal alphabet may be generated using a novel rewrite system that conserves zero (a special character of the alphabet and the symbol for that character) at every step. The recursive method…
In the 16th century, Simon Stevin initiated a modern approach to decimal representation of measuring numbers, marking a transition from the discrete arithmetic practised by the Greeks to the arithmetic of the continuum taken for granted…
We present the Manuscripts of Handwritten Arabic~(Muharaf) dataset, which is a machine learning dataset consisting of more than 1,600 historic handwritten page images transcribed by experts in archival Arabic. Each document image is…
In this paper we address the problem of constructing a class of representations of Clifford algebras that can be named "alphabetic (re)presentations". The Clifford algebras generators are expressed as m-letter words written with a…
Over the past three years, the rapid advancement of Large Language Models (LLMs) has had a profound impact on multiple areas of Artificial Intelligence (AI), particularly in Natural Language Processing (NLP) across diverse languages,…
This is an overview of Nasir al-Din al-Tusi's Treatise of the quadrilateral, an invaluable 13th century document on spherical geometry which was translated into French in 1891. The title we are using here is the one given by the translator…
Calligraphy is an essential part of the Arabic heritage and culture. It has been used in the past for the decoration of houses and mosques. Usually, such calligraphy is designed manually by experts with aesthetic insights. In the past few…
The project targets both oral corpus and the rich text resources written in the Maghreb region. It focuses particularly on the continuity, for more than 12 centuries, of a classical still alive Arabic language and on the extreme…
We provide a simple way to add, multiply, invert, and take traces and norms of algebraic integers of a number field using integral matrices. With formulas for the integral bases of the ring of integers of at least a significant proportion…
Classical and some deep learning techniques for Arabic text classification often depend on complex morphological analysis, word segmentation, and hand-crafted feature engineering. These could be eliminated by using character-level features.…
In Babylonian mathematics two Sumerian words of fractions occur, which were originally used in non-mathematical texts. They are igi-n-g\'al "the reciprocal of (the number) n", which is often abbreviated to igi-n, and igi-te-en whose meaning…
Developing robust automatic speech recognition (ASR) systems for Arabic requires effective strategies to manage its diversity. Existing ASR systems mainly cover the modern standard Arabic (MSA) variety and few high-resource dialects, but…
These notes explore three amazing formulas proved by Abel in his 1826 Paris memoir on what we now call Abelian integrals. We discuss the first two formulas from the point of view of symbolic computation and explain their connection to…