This paper proposes an algorithm to evaluate the probability that d units of data can be sent from the source node to the sink node through a valid group of paths on a network. The conditions of transmission are such that the transmission time of each path belonging to this valid group of paths does not exceed the specified upper bound T, and that the maximal capacity of that path is not less t...

We consider billiard trajectories in a smooth convex body in R and estimate the number of distinct periodic trajectories that make exactly p reflections per period at the boundary of the body. In the case of prime p we obtain the lower bound (d − 2)(p − 1) + 2, which is much better than the previous estimates.

We consider the inverse problem for the second order hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation.

PURPOSE To document and explain the presence, inferior to the optic disc, of a distinct vertical boundary between two retinal areas of different short-wavelength autofluorescence (SW-AF) intensities. METHODS SW-AF images of the inferonasal region were acquired from 32 healthy subjects. Additionally, color, 488-nm reflectance (488-R), near-infrared reflectance (NIR-R), NIR autofluorescence (NI...

Regional species-climate correlations are well documented, but little is known about the ecological processes responsible for generating these patterns. Using the data from over 690,000 individual trees I estimated five demographic rates--canopy growth, understorey growth, canopy lifespan, understorey lifespan and per capita reproduction--for 19 common eastern US tree species, within the core a...

This study presents the nannostratigraphy and nannofossil events in the lower boundary of Kalat Formation in the East and West of the Kopeh- Dagh basin. The Kalat Formation comprises of coarse grained detritus limestone with subordinate sandstone intercalations. In the current study, six sections have been chosen in the East and West of the basin which are as follow: Dobaradar section, Kalat se...

(1.2) (∂t + V ∂k)ρ+ ρdivV = 0, divV = ∂kV k in D, where V k = δvi = vk and we use the summation convention over repeated upper and lower indices. Here the velocity V = (V , ..., V ), the density ρ and the domain D = ∪0≤t≤T {t}× Dt, Dt ⊂ R are to be determined. The pressure p = p (ρ) is assumed to be a given strictly increasing smooth function of the density. The boundary ∂Dt moves with the velo...

The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension x̃. We consider the case when the boundary is a random fractal, specifically a self-avoiding walk or the frontier of a Brownian walk, in two dimensions, and show that the boundary scaling behaviour of the...