Related papers: Note on star-triangle equivalence in conducting ne…
This article examines the coincidence of the projective and conformal Weyl tensors associated to a given connection D. The connection may be a general Weyl connection associated to a conformal class of metrics [g]. The main result for n>3…
In this article we combinatorially describe the triangles that are present in two types of line arrangements, those which have global cyclicity and those which are infinity type line arrangements. A combinatorial nomenclature has been…
Cellular electrophysiology is often modeled using the cable equations. The cable model can only be used when ionic concentration effects and three dimensional geometry effects are negligible. The Poisson model, in which the electrostatic…
We study variuos homological structures associated with Poisson algebra, the canonical differential complex for singular Poisson structure and the analogue of the star operator for such manifolds. Give the interpretation of the classical…
We prove the existence of a deformation quantization for integrable Poisson structures on R^3 and give a generalization for a special class of three dimensional manifolds.
In the last few decades, lots of universal relations between different global physical quantities of neutron stars have been proposed to constrain the unobservable or hard to be observed properties of neutron stars. But few of them are…
Alternating sign triangles were introduced by Carroll and Speyer in relation to cube recurrence, by analogy to alternating sign matrices for octahedron recurrence. In this paper, we prove the connectivity of alternating sign triangles,…
In this note, we show that the space of all $\varepsilon$-nets in the real line $\mathbb{R}$ with a natural metric, equipped with either Hausdorff or Gromov--Hausdorff distance, is contractible.
In two lectures, we overview the renormalon and renormalon-related techniques and their phenomenological applications. We begin with a single renormalon chain which is a well defined and systematic way to specify the character of…
While for standard percolation directionality is known to increase the combinatorial complexity of percolation, here we show that when connectivity is ensured by paths of length $R\geq 2$, network directionality, impeding backtracking, can…
Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point…
Let $P$ be a set of $N$ points in the Euclidean plane, where a positive proportion of points lies off a single straight line. This note points out two facts concerning the number of equivalence classes of triangles that $P$ determines,…
The significance of stripes in certain high-temperature superconductors has been hotly debated for decades. Now a consensus is emerging that there may, in fact, be two networks of different stripes in which shape resonances play a key role…
Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but…
This note contains some observations on abelian convexity theorems. Convexity along an orbit is established in a very general setting using Kempf-Ness functions. This is applied to give short proofs of the Atiyah-Guillemin-Sternberg theorem…
Recently it was shown by H. Guenancia and M. Paun that a singular metric satisfying the conical Kahler-Einstein equation with a simple normal crossing divisor is equivalent to a conical metric along that divisor. In this note, we present an…
We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous…
The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions---$\epsilon$-approximations and…
In this paper, the author first establish the connections between the selectively $k$-star-ccc properties, the chain conditions and other star-Lindel\"of properties. Secondly, some examples are presented to solve questions raised by Xuan…
Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of…