相关论文: Plinths and Pedestals

The straight-line flow on almost every staircase and on almost every square tiled staircase is recurrent. For almost every square tiled staircase the set of periodic orbits is dense in the phase space.

The problem of classifying the convex pentagons that admit tilings of the plane is a long-standing unsolved problem. Previous to this article, there were 14 known distinct kinds of convex pentagons that admit tilings of the plane. Five of…

An alternate definition of the box-counting dimension is proposed, to provide a better approximation for fractals involving rotation such as the 'Bradley Spiral' structure. A curve fitting comparison of this definition with the box-counting…

In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our…

This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…

A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to…

We calculate the dimension of the locus of elliptic surfaces over P^1 with a section and a given Picard number, in the corresponding moduli space.

We define spinors for pairs of tangent disks in the Euclidean plane and prove a number of theorems, one of which may be interpreted as a "square root of Descartes Theorem". In any Apollonian disk packing, spinors form a network. In the…

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

We establish some new theorems on pentagon and pentagram.

This paper describes how commercially available spectrographs can be used to identify and measure some basic characteristics of planetary nebulae.

A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our…

In this paper, we further investigate the orthogonally connected sets and establish necessary and sufficient conditions for a set to be staircase connected.

Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for…

We describe the tensors and spinor-tensors included in the $\theta$-expansion of the ten-dimensional chiral scalar superfield. The product decompositions of all the irreducible structures with $\theta$ and the $\theta^2$ tensor are provided…

After constructing a splitting tower for separable commutative ring objects in tensor-triangulated categories, we define and study their degree.

In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…

Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject.…

In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.