We define and study quaternionic stochastic areas processes associated with Brownian motions on the rank-one symmetric spaces HHn HPn. The characteristic functions of fixed-time marginals these are computed allow for explicit description their corresponding large-time limits. also obtain exact formulas semigroup densities area using a Doob transform in former case density circular Jacobi proces...

introduction non-invasive fluorescent reflectance imaging (fri) is used for accessing physiological and molecular processes in biological media. the aim of this article is to separate the overlapping emission spectra of quantum dots within tissue-equivalent phantom using svd, jacobi svd, and nmf methods in the fri mode. materials and methods in this article, a tissue-like phantom and an optical...

In his celebrated paper Kontsevich has proved a theorem which manifestly gives a quantum product (deformation quantization formula) and states that changing coordinates leads to gauge equivalent star products. To illuminate his procedure, we make an arbitrary change of coordinates in the Moyal product and obtain the deformation quantization formula up to the third order. In this way, the Poisso...

We present a new flexible wavefront propagation algorithm for the boundary value problem for subRiemannian (SR) geodesics in the roto-translation group SE(2) = R S with a metric tensor depending on a smooth external cost C : SE(2) → [δ, 1], δ > 0, computed from image data. The method consists of a first step where an SR-distance map is computed as a viscosity solution of a Hamilton–Jacobi–Bellm...

This paper is about the role of Planck’s constant, h̄, in the geometric quantization of Poisson manifolds using symplectic groupoids. In order to construct a strict deformation quantization of a given Poisson manifold, one can use all possible rescalings of the Poisson structure, which can be combined into a single “Heisenberg-Poisson” manifold. The new coordinate on this manifold is identified ...

The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function. There are two efficient choices of a set of radial basis functions suitable for discretising the solution of a partial differential equation posed in either such geometry. One choice is methods based on standard C...

In this paper we investigate Donder-Weyl (DW) Hamilton-Jacobi equations and establish the connection between DW Hamilton-Jacobi equations and multi-symplectic Hamiltonian systems. Based on the study of DW Hamilton-Jacobi equations, we present the generating functions for multi-symplectic partitioned Runge-Kutta (PRK) methods.

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F2f . We show how to construct Jacobi forms with various ind...

The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and optics. In this paper, we study the Weil representations of the Jacobi group and their properties. We also provide their applications to the theory of automorphic forms on the Jacobi group and repr...