Related papers: Density of Visible Lattice Points on Hyperplanes a…
The focus of this paper is on a thin obstacle problem where the obstacle is defined on the intersection between a hyper-plane $\Gamma$ in $\mathbb{R}^n$ and a periodic perforation $\mathcal{T}_\varepsilon$ of $\mathbb{R}^n$, depending on a…
The hypermetric cone $HYP_n$ is the set of vectors $(d_{ij})_{1\leq i< j\leq n}$ satisfying the inequalities $\sum_{1\leq i<j\leq n} b_ib_jd_{ij}\leq 0 with b_i\in\Z and \sum_{i=1}^{n}b_i=1$. A Delaunay polytope of a lattice is called…
Several models of physics beyond the Standard Model predict neutral particles that decay into final states consisting of collimated jets of light leptons and hadrons (so-called "lepton jets"). These particles can also be long-lived with…
A point visibility graph is a graph induced by a set of points in the plane, where every vertex corresponds to a point, and two vertices are adjacent whenever the two corresponding points are visible from each other, that is, the open…
In 1978, Makai Jr. established a remarkable connection between the volume-product of a convex body, its maximal lattice packing density and the minimal density of a lattice arrangement of its polar body intersecting every affine hyperplane.…
We determine the maximal hyperplane sections of the regular $n$-simplex, if the distance of the hyperplane to the centroid is fairly large, i.e. larger than the distance of the centroid to the midpoint of edges. Similar results for the…
A series of simulated maps showing the appearance in total intensity of flows computed using a recently developed relativistic hydrodynamic code (Duncan \& Hughes 1994: ApJ, 436, L119) are presented. The radiation transfer calculations were…
This paper presents the asymptotic analysis of random lattices in high dimensions to clarify the distance properties of the considered lattices. These properties not only indicate the asymptotic value for the distance between any pair of…
Our view of the high velocity cloud (HVC) system is changing dramatically with new observations from the Far Ultraviolet Spectroscopic Explorer mission and the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope. In…
The concept of a visible point of a convex set relative to a given point is introduced. A number of basic properties of such visible point sets is developed. In particular, it is shown that this concept is useful in the study of best…
In a recent paper we have discussed the higher order singularities in gravitational lensing. We have shown that a singularity map, comprising of $A_3$-lines and unstable (point) singularities ($A_4$ and $D_4$), is a compact representation…
Jet quenching in the hot and dense medium created in ultra-relativistic heavy ion collisions is a well-established experimental phenomenon at RHIC. It has long been anticipated that the LHC heavy ion program would substantially advance the…
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…
We give some sufficient conditions of separation of two sets of integer points by a hyperplane. Our conditions are related to the notion of convexity of sets of integer points and are weaker than existing notions.
We state the formula for the critical number of vertices of a convex lattice polygon that guarantees that the polygon contains at least one point of a given sublattice and give a partial proof of the formula. We show that the proof can be…
We define an operational integer-$n$ lattice observable for state-dependent spatial entanglement in QCD hadrons and a falsifiable local-window analysis of its radius dependence. The observable is the vacuum-subtracted logarithmic radius…
We study the entropy of a set of identical hard objects, of general shape, with each object pivoted on the vertices of a d-dimensional regular lattice of lattice spacing a, but can have arbitrary orientations. When the pivoting point is…
Many high velocity HI clouds (HVCs) are now believed to be scattered throughout the Galactic halo on scales of tens of kiloparsecs. Some of these clouds appear to contain substantial HI masses (>10^6 Msun). It has been suggested that these…
The superfluid density is calculated theoretically for incompressible vortex lattices in two dimensions that have isolated dislocations quenched in by a random arrangement of pinned vortices. The latter are assumed to be sparse and to be…
If a body of inviscid fluid is disturbed, it will typically eject a jet of fluid. If the effects of gravity and surface tension are negligible, these jets travel in straight lines, with the tips approaching a constant velocity. It has been…