Related papers: Some remarks about Cantor sets
We give some remarks on limit mixed Hodge structure and spectrum. These are more or less well-known to the specialists, and do not seem to be stated explicitly in the literature. However, they do not seem to be completely trivial to the…
Lecture notes on selected topics in the theory of gravitation.
In this short note we recall the definition of intrinsically harmonic forms, some known results and some open problems.
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
In this survey we discuss some combinatorial aspects of higher cluster categories.
We study properties of the set of subsums for a convergent series $ k_1 \sin x + \dots + k_m \sin x +\dots + k_1\sin x^n +\dots + k_m \sin x^n + \dots $, where $k_1, k_2, k_3,\dots,k_m$ are fixed positive integers and $0<x<1$. Depends on…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.
We introduce a framework for ordinal notation systems, present a family of strong yet simple systems, and give many examples of ordinals in these systems. While much of the material is conjectural, we include systems with conjectured…
We give several partial positive answers to a question of Juhasz and Szentmiklossy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences…
Every element $u$ of $[0,1]$ can be written in the form $u=x^2y$, where $x,y$ are elements of the Cantor set $C$. In particular, every real number between zero and one is the product of three elements of the Cantor set. On the other hand…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
The ternary Cantor set $C$, constructed by George Cantor in 1883, is probably the best known example of a perfect nowhere-dense set in the real line, but as we will see later, it is not the only one. The present article we will explore the…
This communication records some observations made in the course of studying one-relator groups from the point of view of residual solvability. As a contribution to clas- sification efforts we single out some relator types that render the…
These are informal notes written in 2007 that outline the local and global quantum Langlands program. (I decided to make them public in view of the revived interest in the subject.)
A short note that contains some Cliff's notes of the general theory (see math.AG/9905103) but concentrates on one of the stranger aspects of it - existence of other irreducible components.
This brief comment reflects on the historical and current uses of the term "snowball sampling."
We show that the Cantorvals connected with the geometric Cantor sets are not achievement sets of any series. However many of them are attractors of IFS consisting of affine functions.
After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is…