Related papers: A Note on Flexion Units

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…

In [10] the third author of this paper presented two conjectures on the additive decomposability of the sequence of ''smooth'' (or ''friable'') numbers. Elsholtz and Harper [4] proved (by using sieve methods) the second (less demanding)…

The famous example of the double-Watt mechanism given by Connelly and Servatius raises some problems concerning the classical definitions of higher-order flexibility and rigidity, respectively. Recently, the author was able to give a proper…

We compute the noncommutative deformations of a family of modules over the first Weyl algebra. This example shows some important properties of noncommutative deformation theory that separates it from commutative deformation theory.

This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…

A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…

We give a constructive, metastable formulation of a theorem about the exchange of limits for convergent sequence $L^1$ functions. A crucial tool is a one-dimensional version of Szemeredi's regularity lemma for $L^1$ functions.

The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…

This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.

We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we…

This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics

This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…

For certain roots of unity, we consider the categories of weight modules over three quantum groups: small, un-restricted and unrolled. The first main theorem of this paper is to show that there is a modified trace on the projective modules…

This is a pedagogical introduction to original Kaluza-Klein theory and its salient features. Most of the technical calculations are given in detail and the nature of gravitons is discussed.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

This is the English translation of Leonhard Euler's Latin paper "De solidis quorum superficiem in planum explicare licet". Euler explains several methods to obtain equations for developable surfaces. Therefore, this paper might be…

In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…

Recently the ``Fluctuation theorem'' has been criticized and incorrect incorrect contents have been atributed to it. Here I reestablish and comment the original statements.

This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.