SEARCH · Searcharxiv
Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The theory of numbers was supposed to be the less useful branch of mathematics. At the same time, cryptography was thought to be a military or a diplomatic issue. In this note we show how the two concepts are today strictly related and how this link affects our daily activities.
In this paper we have produced different kinds of bimagic squares based on bimagic squares of order 8x8, 16x16, 25x25, 49x49, etc. A different technique is applied to produce bimagic square of order 16x16, 25x25, 49x49, etc. The bimagic square of order 8x8 used is the already known in the literature. The work is neither based on any programming language nor on mathematical results. Just simple combinations are used to produce these bimagic squares. Moreover, in each case we have used consecutive numbers starting from 1
We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on σ-class is given.
Computational science and engineering (CSE) has been misunderstood to advance with the construction of enormous computers. To the contrary, the historical record demonstrates that innovations in CSE come from improvements to the mathematics embodied by computer programs. Whether scientists and engineers become inventors who make these breakthroughs depends on circumstances and the interdisciplinary extent of their educations. The USA currently has the largest CSE professorate, but the data suggest this prominence is ephemeral.
Traditionally, mathematical knowledge is published in printed media such as books or journals. With the advent of the Internet, a new method of publication became available. To date, however, most online mathematical publications do not employ the full capabilities of the medium. We describe a project to modernize online mathematics presentation and build a community-focused environment in which the lines between "author" and "reader" are blurred, enhancing collaboration and improving publication quality.
In this article (it's only in italian, but I'm translating it) I will try to solve some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given some parallel line segments, is there at least one straight line that passes through all of them? If there were many lines that solve the problem, how can I choose a "better one" among all of them? I fully answer the first question, for the second I'll just give some ideas for future research.
In this article I will address some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given some parallel line segments, is there at least one straight line that passes through all of them? If there were many lines that solve the problem, can I choose a "best one" among all of them? I will fully address the first question. As for the second question, I will illustrate it with some "experimental" examples and suggest an outline for future explorations.
Game versions of the Monty Hall Problem are discussed. The focus is on the principle of eliminating the dominated strategies, both in the zero-sum and noncooperative formulations.
We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the sums of the tetrahedrons, whose calculation is trivial.
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured presentations. References are also provided, as well as a brief discussion of Grassmann spaces and an example showing the relevance and usefulness of affine spaces in Newtonian physics.
Gerhard Hochschild's contribution to the development of mathematics in the XX century is succinctly surveyed. We start with a personal and mathematical biography, and then consider with certain detail his contributions to algebraic groups and Hopf algebras.
We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
Let $n$ be a positive integer. Then cyclic group $Z_n$ of order $n$ is the only group of order $n$ iff g.c.d. $(n,ϕ(n))=1$, where $ϕ$ denotes the Euler-phi function. In this article we have given another proof of this result using the knowledge of semi direct product and induction.
What is an interesting number theoretic or a combinatorial characterization of the divisors of 24 amongst all positive integers? In this paper I will provide one characterization in terms of modular multiplication tables. This idea evolved interestingly from a question raised by a student in my elementary number theory class. I will give the characterization and then provide 5 proofs using various techniques: Chinese remainder theorem, structure theory of units, Dirichlet's theorem on primes in an arithmetic progression, Bertrand-Chebyshev theorem, and results of Erdos and Ramanujan on the pi(x) function.
This paper is base on talks which I gave in May, 2010 at Workshop in Trieste (ICTP). In the first part we present an introduction to knots and knot theory from an historical perspective, starting from Summerian knots and ending on Fox 3-coloring. We show also a relation between 3-colorings and the Jones polynomial. In the second part we develop the general theory of Fox colorings and show how to associate a symplectic structure to a tangle boundary so that tangles becomes Lagrangians (a proof of this result has not been published before). Chapter VI of the book "KNOTS: From combinatorics of knot diagrams to combinatorial topology based on knots will be based on this paper.
Seven mathematicians and one political scientist met at the Cambridge Apportionment Meeting in January 2011. They agreed a unanimous recommendation to the European Parliament for its future apportionments between the EU Member States. This is a short factual account of the reasons that led to the Meeting, of its debates and report, and of some of the ensuing Parliamentary debate.