相关论文: Potpourri
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
A bibliographic database containing studies on recurrence plots and related methods is analyzed from various perspectives. This allows a detailed view of the field's development, showcasing the continuous growth in the method's popularity,…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
We present a brief overview of Moonshine with an emphasis on connections to physics. Moonshine collectively refers to a set of phenomena connecting group theory, analytic number theory, and vertex operator algebras or conformal field…
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
The import of the magnitude of fourier coefficients of a pitch class set is fairly well known. This paper deals with the angular component of these compelx numbers, the phase. It enables to shed new light on triads, the Tonnetz, and…
We review various simple analytical theories for homopolymers within a unified framework. The common guideline of our approach is the Flory theory, and its various avatars, with the attempt of being reasonably self-contained. We expect this…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
These notes provide an elementary (and incomplete) sketch of the objects and ideas involved in monstrous and umbral moonshine. They were the basis for a plenary lecture at the 18th International Congress on Mathematical Physics, and for a…
This note surveys how the exterior algebra and deformations or quotients of it, gives rise to centrally important notions in five domains of mathematics: Combinatorics, Topology, Lie theory, Mathematical physics, and Algebraic geometry.
We briefly summarise the current status of neutrino masses and mixing, paying special attention to the prospects for observing new leptonic interactions.