The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing...

Using the principle of subordination, we obtain some inclusion properties of certain subclasses of analytic functions defined by a generalized multiplier transformation. Also inclusion properties of these classes involving the generalized integral operator are obtained. Mathematical Subject Classification: 30C45

Evolution equations for anomalous diffusion employ fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. This paper develops the mathematical foundations of those operators.

We study regularity of mild and strong solutions for an abstract mathematical model of a flexible space structure under appropriate initial conditions. We apply our results showing qualitative properties of the trajectories in case of the negative Laplacian operator.

In this exposition, we continue the discussions of Dong [D2] and Li [L]. We shall prove an S3-symmetry of the Jacobi identity, construct the contragredient module for a module for a vertex operator algebra and apply these to the construction of the vertex operator map for the moonshine module. We shall introduce the notions of intertwining operator, fusion rule and Verlinde algebra. We shall al...

This paper introduces an anisotropic Laplace-Beltrami operator for shape analysis. While keeping useful properties of the standard Laplace-Beltrami operator, it introduces variability in the directions of principal curvature, giving rise to a more intuitive and semantically meaningful diffusion process. Although the benefits of anisotropic diffusion have already been noted in the area of mesh p...

For a given standard Hamiltonian H with arbitrary complex scalar and vector potentials in one-dimension, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT symmetric Hamiltonian with a real degree of freedom is pseud...

In a previous paper [10] we explored the notion of coherent fuzzy consequence operator. It is well-known that the operator induced by a fuzzy preorder through Zadeh’s compositional rule is always a coherent fuzzy consequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such operator is coherent [7]. Fuzzy closing operators of mathem...

2 While performing the tasks of organizational control there always happen such situations when the initial conditions of decision making are not clearly defined and characterized by insufficient information for the human-operator who makes decisions, particularly in conflict situations or under extreme conditions. For mathematical formalization of processes and systems of this class there appe...

A mathematical description of grinding processes used in powder technologies is developed. A grinding equation, an operator equation, connecting the final particle size distribution function to the particle size distribution function before the grinding process is studied. The mathematical model introduced here can be used to predict the results of grinding, to construct grinding systems with d...