Related papers: Edward Nelson (1932-2014)
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
In this paper we generalize the well known relation between Heyting algebras and Nelson algebras in the framework of subresiduated lattices. In order to make it possible, we introduce the variety of subresiduated Nelson algebras. The main…
There have been extensive developments recently in modern nonparametric inference and modeling. Nonparametric and semi-parametric methods are especially useful with large amounts of data that are now routinely collected in many areas of…
The present paper shows that Edward Nelson's stochastic mechanics approach for quantum mechanics can be derived from the two classical elastically colliding particles with masses M and m satisfying a collision momentum preserving equation.…
Transcript of G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The notion of randomness is taken from physics and applied to pure mathematics in order to shed light on the…
The prominent Russian mathematician Igor Rostislavovich Shafarevich passed away on February 19, 2017. In this article we supply his biography, discuss his many important contributions to number theory, algebra and algebraic geometry, and…
Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of…
We produce a series of results extending information-theoretical inequalities (discussed by Dembo--Cover--Thomas in 1989-1991) to a weighted version of entropy. The resulting inequalities involve the Gaussian weighted entropy; they imply a…
We discuss the repercussions of the development of infinitesimal calculus into modern analysis, beginning with viewpoints expressed in the nineteenth and twentieth centuries and relating them to the natural cognitive development of…
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…
This article, written in German language, gives a very elementary introduction to infinite sets. It is meant for interested non-mathematicians.
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
This expository article is an introduction to Landau's problem of bounding the derivative, knowing bounds for the function and its second derivative, and some of its variants and generalizations. Connexions with convex and functional…
We propose Edward, a Turing-complete probabilistic programming language. Edward defines two compositional representations---random variables and inference. By treating inference as a first class citizen, on a par with modeling, we show that…
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
We introduce a notion of palindromicity of a natural number which is independent of the base. We study the existence and density of palindromic and multiple palindromic numbers, and we raise several related questions.
In Early Transcendentals (The American Mathematical Monthly, Vol. 104, No 7) Steven Weintraub presents a rigorous justifcation of the "early transcendental" calculus textbook approach to the exponential and logarithmic functions. However,…
This paper aims to provide physics teachers with tools to help deepen the understanding of the laws of electromagnetism. The fundamental contributions of our proposal are: a) to use quotes from mythical characters in the history of science…
This is a preprint of 1992 with some updates. We study sections of the exponential function Taylor series. Interesting inequalities for these sections were considered by G.Hardy, Kesava Menon, W. Gautschi, H.Alzer and others. The main aim…