Motivated by (continuous) facility location, we study the problem of dispersing and grouping points on a set segments (of streets) in plane. In former problem, given n disjoint line plane, investigate computing point each such that minimum Euclidean distance between any two these is maximized. We prove this 2D dispersion NP-hard, fact, it NP-hard even if all are parallel unit length. This contr...

<p style='text-indent:20px;'>We consider dispersing billiard tables whose boundary is piecewise smooth and the free flight function unbounded. We also assume there are no cusps. Such called type D in monograph of Chernov Markarian [<xref ref-type="bibr" rid="b9">9</xref>]. For a class non-degenerate billiards, we prove exponential decay correlation several other statistical pr...

An efficient chamber-induced activation method was applied for the preparation of holey graphene/cellulose nanofiber-based film with high specific surface area (SSA) and multiple channels through graphene nanosheets. With cellulose nanofiber (CNF) simultaneously serving as “dispersing agent,” “spacer,” “activating oxide (GO) nanosheets are perforated by pyrolysis gas from CNF in confined space ...

Spectral dispersion of light on a finite-size surface plasmon polaritonic (SPP) crystal has been studied. The angular wavelength separation of one or more orders of magnitude higher than in other state-of-the-art wavelength-splitting devices available to date has been demonstrated. The two-stage process is responsible for the dispersion value, which involves conversion of the incident light int...

We derive a rigorous estimate of the size of islands (in both phase space and parameter space) appearing in smooth Hamiltonian approximations of scattering billiards. The derivation includes the construction of a local return map near singular periodic orbits for an arbitrary scattering billiard and for the general smooth billiard potentials. Thus, universality classes for the local behavior ar...

Star clusters are formed in molecular clouds which are believed to be the birth places of most stars. From recent observational data, Lada & Lada(2003) estimated that only 4 to 7% of the proto-clusters have survived. Many factors could cause this high infant mortality. Galactic tidal forces, close encounters with molecular clouds and shock heating are among the possible causes but they have a l...

Metapopulation theory for a long time has assumed dispersal to be symmetric, i.e. patches are connected through migrants dispersing bi-directionally without a preferred direction. However, for natural populations symmetry is often broken, e.g. for species in the marine environment dispersing through the transport of pelagic larvae with ocean currents. The few recent studies of asymmetric disper...