We solve the Milne, constant-source and albedo problems for isotropic scattering in a two-dimensional “Flatland” half-space via the Wiener-Hopf method. The Flatland H-function is derived and benchmark values and some identities unique to Flatland are presented. A number of the derivations are supported by Monte Carlo simulation. 1. Intro The study of linear transport theory [1, 2] in lower-dime...

Wireless Sensor Networks (WSNs) are networks of autonomous nodes used for monitoring an environment. In designing WSNs, one of the main issues is limited energy source for each sensor node. Hence, offering ways to optimize energy consumption in WSNs which eventually increases the network lifetime is strongly felt. Gravitational Search Algorithm (GSA) is a novel stochastic population-based meta-...

Data depth is an approach to statistical analysis based on the geometry of the data. Half-space depth has been studied most frequently by computational geometers. The half-space depth of a point x relative to a set of points S = {X1, ..., Xn} in R d is the minimum number of points of S lying in any closed half-space determined by a line through x [2, 11]. Depth contours, enclosing regions with ...

In this paper, we present improvements to half vector space light transport (HSLT) [KHD14], which make this approach more practical, robust for difficult input geometry, and faster. Our first contribution is the computation of half vector space ray differentials in a different domain than the original work. This enables a more uniform stratification over the image plane during Markov chain expl...

It is shown that Witten's star product in string field theory, defined as the overlap of half strings, is equivalent to the Moyal star product involving the relativistic phase space of even string modes. The string field ψ A (x µ [σ]) can be rewritten as a phase space field of the even modes A (x µ 2n , x 0 , p µ 2n) , where x µ 2n are the positions of the even string modes, and p µ 2n are rela...

In this paper, the classical JKR theory of the adhesive contact of isotropic elastic spheres is extended to consider the effect of anisotropic elasticity. The contact area will then generally be non-circular, but in many cases it can reasonably be approximated by an ellipse whose dimensions are determined by imposing the energy release rate criterion at the ends of the major and minor axes. Ana...

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.