相关论文: The densest sequence in the unit circle

Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…

We present results of sub-arcsec ALMA observations of CO(2-1) and CO(5-4) toward a massive main sequence galaxy at z = 1.45 in the SXDS/UDS field, aiming at examining the internal distribution and properties of molecular gas in the galaxy.…

Among several things, we find the side density for random triangles circumscribing the unit circle and calculate that its median is 5.5482.... An analogous exact computation for perimeter density remains open.

Recent observations show a large concentration of galaxies at high redshift. At first sight strong clustering of galaxies at high redshifts seems to be in contradiction with the models of structure formation. In this paper we show that such…

We show that in any two-coloring of the positive integers there is a color for which the set of positive integers that can be represented as a sum of distinct elements with this color has upper logarithmic density at least $(2+\sqrt{3})/4$…

A sequence $\{z_n\}_{n\geq0}$ is called ratio log-convex in the sense that the ratio sequence $\{\frac{z_{n+1}}{z_n}\}_{n\geq0}$ is log-convex. Based on a three-term recurrence for sequences, we develop techniques for dealing with the ratio…

We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small…

In this paper we give an example of a closed, strongly one-sided dense set which is not of uniform density type. We also show that there is a set of uniform density type which is not of strong uniform density type.

Let A \subseteq [1,..,N]^2 be a set of density at least 1/(log log log N)^c, where c some constant c>0. We prove that A contains a so-called right-angle triangle, i.e. a triple of the form {(k,m), (k+d,m), (k,m+d)}, where d>0.

For every positive integer $k$, we show that every graph of order $n$ at least $3k$ with more than $$\max\{{2k-1\choose 2}+(2k-1)(n-(2k-1)),{3k-1\choose 2}+(n-(3k-1))\}$$ edges has $k$ vertex disjoint cycles, which is a best possible…

For K a cyclic cubic number field with odd class number containing a unit w such that Norm(w)=Norm(1-w)=-1, we prove that the density of rational primes p that satisfy the given spin relation is equal to 1/2. Furthermore, we prove that this…

In this paper we consider the density of maximal order elements in $\mathrm{GL}_n(q)$. Fixing any of the rank $n$ of the group, the characteristic $p$ or the degree $r$ of the extension of the underlying field $\mathbb{F}_q$ of size…

[ABRIDGED] We present the first results from the largest spectroscopic survey to date of an intermediate redshift galaxy cluster, the z=0.834 cluster RX J0152.7-1357. We use the colors of galaxies, assembled from a D~12 Mpc region centered…

A Universal Cycle for t-multisets of [n]={1,...,n} is a cyclic sequence of $\binom{n+t-1}{t}$ integers from [n] with the property that each t-multiset of [n] appears exactly once consecutively in the sequence. For such a sequence to exist…

An Ulam sequence U(1,n) is defined as the sequence starting with integers 1,n such that n > 1, and such that every subsequent term is the smallest integer that can be written as the sum of distinct previous terms in exactly one way. This…

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter---the total length of all pieces of their boundaries visible from above. We prove that if the centers…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

The vertical as well as horizontal oscillation modes in a thermally excited two-dimensional (2D) dust coulomb cluster were investigated for particle numbers between and using both a box_tree simulation and an analytical method. The…

We consider real sequences $(f_n)$ that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where the sequence has no positive…

Direct numerical simulation of homogeneous isotropic turbulence shows pronounced clustering of inertial particles in the inertial subrange at high Reynolds number, in addition to the clustering typically observed in the near dissipation…