Related papers: A note on lattice coverings
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
A counter example to the main result has been communicated to the author by Matei Toma.
In this paper, using compute-and-forward as an example, we provide an overview of constructions of lattices from codes that possess the right algebraic structures for harnessing interference. This includes Construction A, Construction D,…
Some topics from recent progresses in lattice QCD are reviewed.
In this note I describe some modification of the Langlands correspondence and explain why it is more natural. I will also discuss its significance to the theory of automorphic L-functions.
A theory of light diffraction from planar quasicrystalline lattice with resonant scatterers is presented. Rich structure, absent in the periodic case, is found in specular reflection spectra, and interpreted as a specific kind of Wood…
We analyze the nonabelian surface holonomy on a bipartite hypercubic lattice following a proposal in arXiv:1002.4636 [hep-th]. The bipartite structure of the lattice enables us to introduce spike string configurations. These spikes play a…
In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of which curves have simple elevations, weakening the…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
We give a simple example showing that a knot or link diagram that lies in the ${\mathbb{Z}}^2$ lattice is not necessarily the projection of a lattice stick knot or link in the ${\mathbb{Z}}^3$ lattice, and we give a necessary and sufficient…
This article gives a brief survey of the theory and applications of anomalies.
This paper has been withdrawn by the authors since it was discovered that most of its content was already known.
The illumination conjecture is a classical open problem in convex and discrete geometry, asserting that every compact convex body~$K$ in $\mathbb R^n$ can be illuminated by a set of no more than $2^n$ points. If $K$ has smooth boundary, it…
An technically interesting proof of a known theorem.
The aim of this note is to prove an analog of the flattening decomposition theorem for reflexive hulls. The main applications are: the construction of the moduli space of varieties of general type, improved flatness conditions and criteria…
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
The aim of this note is to describe a geometric relation between simple plane curve singularities classified by simply laced Cartan matrices and cluster varieties of finite type also classified by the simply laced Cartan matrices. We…
We examined the effect of a complete suppression of a lattice artifact, the negative plaquettes, on physical quantities, such as the critical temperature, the string tension, the topological charge, glueball masses, and their ratios.