Related papers: Aryabhata's Mathematics
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
The input and output algebras of an infinite qubit system and their representations are described.
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other…
This paper is now part of the new paper "Series with Hermite polynomials and applications" arXiv:1710.00687.
In this work is proposed a method using orthogonal matrix transform properties to encrypt and decrypt a message. It will be showed how to use matrix functions to create complex encryptions. Because orthogonal matrix are always…
A short survey on applications of algebraic geometry in topological data analysis.
If you only take one thing away from this document I would like it tobe this: Creating accessible documents requires authors have a working understanding of accessibility, and write with accessibility in mind.
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…
We present zbMATH Open, the most comprehensive collection of reviews and bibliographic metadata of scholarly literature in mathematics. Besides our website https://zbMATH.org which is openly accessible since the beginning of this year, we…
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
We discuss several open problems in Diophantine approximation. Among them there are famous Littlewood's and Zaremba's conjectures as well as some new and not so famous problems.
This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to define these invariants with integral coefficients. We describe…
This article gives a brief survey of the theory and applications of anomalies.
We introduce the concept of protometric and present some properties of protometrics.
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…