相关论文: The Rousseau number: an informetric version of the…
Berezovsky number is defined analogously to Erdos number. Berezovsky network is investigated.
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
This is a survey of some of Erd\H os's work on bases in additive number theory.
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.
This essay offers a brief biography of Paul Erd\H{o}s and summarizes his approach to mathematics. This is further elucidated by a discussion of Erd\H{o}s' simple proof of Bertrand's Postulate.
We give an historical account, including recent progress, on some problems of Erd\H os in number theory.
This is a short survey article written for the Erd\H{o}s centennial conference in Budapest in 2013. The main two topics covered are Szemer\'edi's theorem and its ramifications, and the Erd\H{o}s discrepancy problem. There is an emphasis on…
In our effort to find an arithmetically pure proof of the Bertrand postulate, we investigate and solve (using only elementary arithmetical methods) another less usual inequality in positive integers inspired by the classical proof of the…
In this expository note we present simple proofs of the lower bound of Ramsey numbers (Erd\"os theorem), and of the estimation of discrepancy. Neither statements nor proofs require any knowledge beyond high-school curriculum (except a minor…
In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…
This purpose of this paper is to note an interesting identity derived from an integral in Gradshteyn and Ryzhik using techniques from George Boros'(deceased) Ph.D thesis. The idenity equates a sum to a product by evaluating an integral in…
About Conway's surreal numbers: A letter to a friend (written in French). In memoriam John Horton Conway.
It is evident from the literature that many engineers describe the Reynolds number qualitatively as ``the ratio of inertial forces to viscous forces''. Yet it is not immediately obvious that the well known expression Re = LV(rho)/(eta),…
We establish a variety of extensions to the Erdos-Rado Theorem, particularly involving ordinal numbers, and always involving ordinary partition relations. Most of the results can be regarded as consequences of the Ramification Principle,…
Rousseau's simple proof of the quadratic reciprocity law, followed by the proof of its equivalence with Hilbert's product formula. The Hilbert symbol is explained in terms of the reciprocity isomorphism, and the places of Q are determined.
We introduce a concept called refinement and develop two different ways of refining metrics. By applying these methods we produce several refinements of the shortest-path distance on the collaboration graph and hence a couple new versions…
In the article we give an appreciation of Edward Nelson's multifaceted contribution to mathematics, and particularly to foundational theories of infinitesimals.
We define the $m$th-order Eulerian numbers with a combinatorial interpretation. The recurrence relation of the $m$th-order Eulerian numbers, the row generating function and the row sums of the $m$th-order Eulerian triangle are presented. We…
For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd…
We propose a rational version of the classic Rodrigues' rotation formula, which leads to a more accurate and efficient modelling of rotations and their derivatives in finite precision arithmetic. We explain how the rational Rodrigues'…