The surface partition of large clusters is derived analytically for a simple statistical model by using the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested "hills and dales model" reproduces the leading term of the Fisher result for the surface entropy to within a few percent. The model also gives the degeneracy prefactor of large clusters. The s...

An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach. The star-triangle relation between these systems is introduced, and the Darboux transformations for both linear problems from the Moutard transformation of the B-(Moutard) quadrilateral lattice are obtained. A geometric int...

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

We study in this paper a TCP-like linear-increase multiplicative-decrease flow control mechanism. We consider congestion signals that arrive in batches according to a Poisson process. We focus on the case when the transmission rate cannot exceed a certain maximum value. We write the Kolmogorov equations and we use Laplace Transforms to calculate the distribution of the transmission rate in the ...

A model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the material change. The problem is solved using two separate techniques. Primary, by applying Laplace and Fourier transformation,...