Развивается теория интегралов и производных дробного порядка. Построен аналог операционного исчисления для дифференциального оператора с кусочно-постоянными коэффициентами. Предложены различные конструкции обобщенного преобразования Лапласа. При помощи операторов установлена связь интегральных преобразований Меллина – Лапласа обобщенным интегральным преобразованием Найден изоморфизм пространств...

Two different approaches for describing discrete-time fractional linear systems are presented. The first is based on the nabla and delta derivatives. In this case, suitable exponentials introduced used to define discrete Laplace transforms. second approach bilinear (Tustin) transformations. For both cases, appropriate algorithms obtaining impulse, step, frequency responses state-variable repres...

We present a novel shape representation that characterizes the shape of a surface in terms of a coordinate system based on the eigensystem of the anisotropic Laplace-Beltrami operator. In contrast to the existing techniques, our representation can capture developable transformations and is therefore useful for analysis of cortical folding patterns. This representation has desirable properties i...

Summary A boundary-value problem was formulated for perturbation of an electrostatic field by a coated dielectric sphere made two distinct linear anisotropic (LAD) materials. Specific affine transformations were employed to represent the electric potential inside core and coating in terms solutions Laplace equation. transition matrix found relate source exterior region. The formulation can be s...

We define a notion of determining sets for the discrete Laplacian in a domain Ω. A set D is called determining if harmonic functions are uniquely determined by providing their values on D, and if D has the same size as the boundary of Ω. It is shown that there exist determining sets that are fairly evenly distributed in Ω. A number of basic properties of determining sets are derived.

OF THE DISSERTATION Chip-Firing Games with Dirichlet Eigenvalues and Discrete Green’s Functions

We study spectrum inclusion regions for complex Jacobi matrices that are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.

A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes into flat domains, while preserving the distances measured on the manifold. Recently, attention has been given to embedding shapes into the eigenspace of the Laplace–Beltrami operator. The L...