Related papers: Tables of record gaps between prime constellations

Starting with Zhang's theorem on the infinitude of prime doubles, we give an inductive argument that there exists an infinite number of prime $k$-tuples for at least one admissible set $\mathcal{H}_k=\{h_1,\ldots,h_k\}$ for each $k$.

The kappa-space three-dimensional parameter system was originally defined for the physical properties of dynamically hot galaxies. Here we define self-consistent kappa-parameters for disk galaxies, galaxy groups and clusters, and globular…

Motivated by recent observational and numerical studies suggesting that collapsing protostellar cores may be replenished from the local environment, we explore the evolution of protostellar cores submerged in the external counter-rotating…

Planets can carve gaps in the surface density of protoplanetary discs. The formation of these gaps can reduce the corotation torques acting on the planets. In addition, gaps can halt the accretion of solids onto the planets as dust and…

If galaxy clusters contain intracluster dust, the spectra of galaxies lying behind clusters should show attenuation by dust absorption. We compare the optical (3500 - 7200 \AA) spectra of 60,267 luminous, early-type galaxies selected from…

Suppose one has a collection of disks of various sizes with disjoint interiors, a packing in the plane, and suppose the ratio of the smallest radius divided by the largest radius lies between $1$ and $q$. In his 1964 book Regular Figures…

We present a semi-analytical population synthesis model of protoplanetary clumps formed by disk instability at radial distances of 80 - 120 AU. Various clump density profiles, initial mass functions, protoplanetary disk models, stellar…

Let $\mathcal{P}$ be a set of $n=2m+1$ points in the plane in general position. We define the graph $GM_\mathcal{P}$ whose vertex set is the set of all plane matchings on $\mathcal{P}$ with exactly $m$ edges. Two vertices in…

We study the gaps between products of two primes in imaginary quadratic number fields using a combination of the methods of Goldston-Graham-Pintz-Yildirim \cite{GGPY}, and Maynard \cite{MAY}. An important consequence of our main theorem is…

The presence of multiple luminous galaxies in clusters can be explained by the finite time over which a galaxy sinks to the center of the cluster and merges with the the central galaxy. The simplest measurable statistic to quantify the…

We study the luminosity gap, dm12, between the first and second ranked galaxies in a sample of 59 massive galaxy clusters, using data from the Hale Telescope, HST, Chandra, and Spitzer. We find that the dm12 distribution, p(dm12), is a…

Rings and gaps are among the most widely observed forms of substructure in protoplanetary disks. A gap-ring pair may be formed when a planet carves a gap in the disk, which produces a local pressure maximum following the gap that traps…

Many protostellar disks show central cavities, rings, or spiral arms likely caused by low-mass stellar or planetary companions, yet few such features are conclusively tied to bodies embedded in the disks. We note that even small features on…

We study the orbital architecture of multi-planet systems detected by the Kepler transit mission using N-body simulations, focusing on the orbital spacing between adjacent planets in systems showing four or more transiting planets. We find…

Given a fixed number field K, we give non-trivial lower bounds for the distance between the conjugates of any number a from K in terms of the Mahler measure M(a) of a. In the case that K is a cubic field, our bound is best possible in terms…

Bertrand's postulate establishes that for all positive integers $n>1$ there exists a prime number between $n$ and $2n$. We consider a generalization of this theorem as: for integers $n\geq k\geq 2$ is there a prime number between $kn$ and…

We show that the Gaussian primes $P[i] \subseteq \Z[i]$ contain infinitely constellations of any prescribed shape and orientation. More precisely, given any distinct Gaussian integers $v_0,...,v_{k-1}$, we show that there are infinitely…

The Galactic bulge is a tumultuous dense region of space, packed with stars separated by far smaller distances than those in the Solar neighborhood. A quantification of the frequency and proximity of close stellar encounters in this…

We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a "typical" knapsack problem is drastically smaller than the integrality…

A 1-planar graph is a graph which has a drawing on the plane such that each edge is crossed at most once. If a 1-planar graph is drawn in that way, the drawing is called a {\it 1-plane graph}. A graph is maximal 1-plane (or 1-planar) if no…