Related papers: Potpourri, 3
In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
This paper deals with a semi-classical limit (Theorem 1) by using traditional mathematical methods, and shows a Hopf theorem as a corollary. A formal discussion of it may be found in [7].
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…
This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal…
We extend the decoupling results of the first two authors to the case of real analytic surfaces of revolution in $\mathbb{R}^3$. New examples of interest include the torus and the perturbed cone.
We build foundations of an approach to study canonical forms of $2$-Calabi--Yau triangulated categories with cluster-tilting objects, using dg algebras and relative singularity categories. This is motivated by cluster theory, singularity…
How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
We define a new condition number adapted to directionally uniform perturbations. The definitions and theorems can be applied to a large class of problems. We show the relation with the classical condition number, and study some interesting…
This paper explains unexpected links between the 3 topics in the title and frames them in a large canvas.
In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and…
Lecture notes for an introductory course in elementary particles.
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
Ornaments aim at taming the multiplication of special-purpose datatype in dependently-typed theory. In its original form, the definition of ornaments is tied to a particular universe of datatypes. Being a type theoretic object,…
In this note we observe that the no two of the three invariants defined for contact structures by Etnyre and Ozbagci -- that is, the support genus, binding number and support norm -- determine the third.