The phase transition of two-dimensional Ising model on random point patterns is investigated using Monte Carlo simulation and the critical temperature is calculated using the Bethe approximation. We find a linear relation between the critical temperature and the structural characteristics of the random point pattern, as described by Aboav's parameter. Numerical results and analytical calculatio...

In this paper we present a G2 end-point interpolation of offset curves using rational Bézier curves of degree seven. The method is based on a G2 end-point interpolation of circular arcs using biquadratic Bézier curves. We also prove the invariance of the Hausdorff distance between two compatible curves under convolution. Using this result, we obtain the exact Hausdorff distance between an offse...

Given a label shape L and a set of n points in the plane, the 2-label point-labeling problem consists of placing 2n non-intersecting translated copies of L of maximum size such that each point touches two unique copies—its labels. In this paper we give new and simple approximation algorithms for L an axis-parallel square or a circle. For squares we improve the best previously known approximatio...

The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order 2 > 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic s...

In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and m...