相关论文: The densest sequence in the unit circle

Let $G$ denote a distance-regular graph with diameter $D\ge 3$, valency $k$, and intersection numbers $a_i$, $b_i$, $c_i$. By a {\it pseudo cosine sequence} of $G$ we mean a sequence of real numbers $s_0, s_1, ..., s_D$ such that $s_0=1$…

Let $ex(Q_n, H)$ be the largest number of edges in a subgraph $G$ of a hypercube $Q_n$ such that there is no subgraph of $G$ isomorphic to $H$. We show that for any integer $k\geq 3$, $$ex(Q_n, C_{4k+2})= O(n^{\frac{5}{6} +…

In this paper, we study VC-density over indiscernible sequences (denoted VC_ind-density). We answer an open question in [1], showing that VC_ind-density is always integer valued. We also show that VC_ind-density and dp-rank coincide in the…

In this paper we study the length of the longest induced cycle in the unitary Cayley graph $X_n = Cay(\mathbb Z_n; U_n)$, where $U_n$ is the group of units in $\mathbb Z_n$. Using residues modulo the primes dividing $n$, we introduce a…

A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes depending on the strength of the oscillation and the global packing density. For intermediate packing density and oscillation…

We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon…

An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique. On a finite graph, the density of a code is…

In this note we extend a theorem from [13] about uniform circle random coverings

Based on the ROSAT All-Sky Survey we have conducted a large redshift survey as an ESO key programme to identify and secure redshifts for the X-ray brightest clusters found in the southern hemisphere. We present first results for a highly…

We prove a generalization of the author's work to show that any subset of the primes which is `well-distributed' in arithmetic progressions contains many primes which are close together. Moreover, our bounds hold with some uniformity in the…

In this paper I will approach the computation of the maximum density of regular lattices in large dimensions using a statistical mechanics approach. The starting point will be some theorems of Roger, which are virtually unknown in the…

Let g be the element that is the sum of x^(n^2) for n >= 0 of A=Z/2[[x]], and let B consist of all n for which the coefficient of x^n in 1/g is 1. (The elements of B are the entries 0, 1, 2, 3, 5, 7, 8, 9, 13, ... in A108345; see The…

We present a photometric investigation into recent star formation in galaxy clusters at z ~ 0.1. We use spectral energy distribution templates to quantify recent star formation in large X-ray selected clusters from the LARCS survey using…

The upper density of an infinite graph $G$ with $V(G) \subseteq \mathbb{N}$ is defined as $\overline{d}(G) = \limsup_{n \rightarrow \infty}{|V(G) \cap \{1,\ldots,n\}|}/{n}$. Let $K_{\mathbb{N}}$ be the infinite complete graph with vertex…

We calculate the vector spin chirality for $S=1/2$ zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the…

A complete sample of $7.7\times 10^4$ galaxies with five-band imaging and spectroscopic redshifts from the Sloan Digital Sky Survey is used to determine the fraction of the optical luminosity density of the Local Universe (redshifts…

A finite set of real numbers is called convex if the differences between consecutive elements form a strictly increasing sequence. We show that, for any pair of convex sets $A, B\subset\mathbb R$, each of size $n^{1/2}$, the convex grid…

X-ray observations of clusters at different redshifts are presented and compared. For the nearest cluster -- the Virgo cluster -- we show a comparison of the galaxy distribution and the distribution of the intra-cluster gas. Although the…

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…

We study thick subcategories defined by modules of complexity one in $\underline{\md}R$, where $R$ is the exterior algebra in $n+1$ indeterminates.