Related papers: Old and new applications of Katona's circle
We investigate which aspects of recent developments on Galois corings and comodules admit a formulation in terms of comonads. This approach hopefully will permit of focusing in what is specific in each particular future situation, having…
Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
We provide a short and self-contained argument for the existence of Cartan-Iwahori-Matsumoto decompositions for reductive groups.
Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally symmetric patterns are classified. Circle pattern analogs…
We give a short proof of the well-known Knuth's old sum and provide some generalizations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and…
In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.
Work in progress concerning alternative formalizations of arithmetic.
A counter example to the main result has been communicated to the author by Matei Toma.
An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.
We give several new examples of hexagonal 3-webs of circles in the plane and give a survey on such webs.
We give new examples of terminal and log canonical singularities.
It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended…
Haga's fold in paper folding is generalized. Recent generalization of Haga's theorems and problems in Wasan geometry involving Haga's fold are also generalized.
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.
In this paper we give two different proofs of Bobenko and Springborn's theorem of circle pattern: there exists a hyperbolic (or Euclidean) circle pattern with proscribed intersection angles and cone angles on a cellular decomposed surface…
Observations on rational Chow groups and cycle class maps in equivariant contexts.
A strong quantitative form of Manin's conjecture is established for a certain variety in biprojective space. The singular integral in an application of the circle method involves the third power of the integral sine function, and is…
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.