For a cellular algebra A with a cellular basis C, we consider a decomposition of the unit element 1A into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular basis C can be partitioned into some pieces with good properties. Then by using a certain map α, we give a coarse partition of C whose refinement is the original partition....

In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.

A recent development of a parabolic equation method for wave propagation in a non-orthogonal coordinate system is reviewed. A transformation of the full governing equation prior to development of any approximation leads to a model whose results stand in closer agreement to laboratory data for a case of waves propagating into a breakwater harbor. The effect of amplitude dispersion on predicted w...

We present here two extensions of the usual Bingham model in which we account for deformations in the region where the shear is below the threshold τo. In particular, we present two models that consider the material in the above region as a neo-Hookean solid or as a visco-elastic upper convected fluid. Both models are developed in the general 3-D framework of the natural configurations theory. ...

We study a certain one dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary condition, regularity of the generalized solution of such a problem remained unclear. We prove that the generalized solution of the problem is indeed a classic...

In this paper, we first develop a digital shearlet theory which is rationally designed in the sense that it is the digitalization of the existing shearlet theory for continuum data. This shows that shearlet theory indeed provides a unified treatment for the continuum and digital realm. Secondly, we discuss our implementation of the associated digital shearlet transform. This software package ca...

In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally monotone.

Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a th...

A Lyapunov type equation characterizing the spectral dichotomy of a matrix by a parabola is proposed and analyzed. The results can be seen as the analogue of the classical Lyapunov stability theorems.