相关论文: Potpourri, 7
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre…
These are the notes corresponding to the course given at the IAS-Park City graduate summer school in July 2007.
Lecture notes for an introductory course in elementary particles.
We consider a class of linear eigenvalue problems depending on a small parameter epsilon in which the series expansion for the eigenvalue in powers of epsilon is divergent. We develop a new technique to determine the precise nature of this…
These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.
In this note we prove a decomposition related to the affine fundamental group and the projective fundamental group of a line arrangement and a reducible curve with a line component. We give some applications to this result.
We define a category with as objects operational resolutions and with as morphisms - not necessarily deterministic - state transitions. We study connections with closure spaces and join-complete lattices and sketch physical applications…
We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…
This special issue cover the seventh and last conference of the CL&C series, started in 2006 in San Servolo. Topics are the computational content of logics between intuitionistic logic and classical logic, through normalization, and a new…
The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the…
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…
This note derives parametrizations for surfaces of revolution that satisfy an affine-linear relation between their respective curvature radii. Alongside, parametrizations for the uniform normal offsets of those surfaces are obtained. Those…
We present a development of norms and discuss their relationship to factorization. In earlier work, the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
This paper is a contribution to the study of foliations on $\mathbb{CP}^2$ with a unique singularity. We provide an explicit example in degree 7 of such a foliation, in the non dicritical case, having a divergent separatrix, and…