Related papers: Aryabhata's Mathematics
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
In this paper we give solutions of certain diophantine equations related to triangular and tetrahedral numbers and propose several problems connected with these numbers. The material of this paper was presented in part at the 11th…
This paper presents new properties of Primitive Pythagorean Triples (PPT) that have relevance in applications where events of different probability need to be generated and in cryptography.
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
In late October 2004 I did a search on Hopf algebras in the database ZMATH to find out where they occur and what use is made of them (I.e. what applications there are). The result is a little astonishing, as can be seen from what follows.
With the rapid development of quantum computers the currently secure cryptographic protocols may not stay that way. Quantum mechanics provides means to create an inherently secure communication channel that is protected by the laws of…
We propose modifications of known quasigroup based stream ciphers. Systems of orthogonal n-ary groupoids are used.
I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
This paper presents an updated biography of Samgamagr\=ama M\=adhava incorporating viewpoints expounded by scholars in the recent past and collecting together in one place more details about his works culled from recent researches into his…
Main purposes of the paper are followings: 1) To show examples of the calculations in domain of QFT via ``derivative rules'' of an expert system; 2) To consider advantages and disadvantage that technology of the calculations; 3) To reflect…
We give a review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains.
This is the first chapter of an introductory text under construction; further chapters are available via the authors' web pages. Our aim is to provide an elementary access to Cox rings and their applications in algebraic and arithmetic…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality.
In 1998, M. S. Baptista proposed a chaotic cryptosystem, which has attracted much attention from the chaotic cryptography community: some of its modifications and also attacks have been reported in recent years. In [Phys. Lett. A 307 (2003)…
In this paper we determine the metric dimension of Andrasfai graphs and some related graphs.
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.