In this paper, we prove that the Hodge-Laplace operator on strongly pseudoconvex compact complex Finsler manifolds is a self-adjoint elliptic operator. Then, from the decomposition theorem for self-adjoint elliptic operators, we obtain a Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds. M.S.C. 2010: 53C56, 32Q99.

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is bas...

In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This known as triple Laplace transform decomposition method. generalized in the sense of conformable derivative. Important results and theorems concerning are discussed. A new algorithm proposed to solve linear three dimensions. Moreover, some examples provided verify performance algorithm....

In this article, we present a fractional order HIV-1 infection model of CD4+ T-cell. We analyze the effect of the changing the average number of the viral particle N with initial conditions of the presented model. The Laplace Adomian decomposition method is applying to check the analytical solution of the problem. We obtain the solutions of the fractional order HIV-1 model in the form of infini...

A method of text detection in natural images, to be turned into an effective embedded software on a mobile device, shall be both efficient and lightweight. We observed that a simple method based on the morphological Laplace operator can do the trick: we can construct in quasi-linear time a hierarchical image decomposition / simplification based on its 0-crossings, and search for some text in th...

In this work, the initial-boundary value problems for one-dimensional linear time-dependent Schrödinger parabolic and pseudoparabolic partial differential equations are studied. The modified double Laplace decomposition method is applied to get semianalytic solutions explicit finite difference approximate of problems. von Neumann stability analysis presented also investigated.

This paper provides a computational method to model a three-dimensional static electromagnetic field within a finite source free volume starting from discrete field information on its surface. The method uses the Helmholtz vector decomposition theorem and the differential algebraic framework of COSY INFINITY to determine a solution to the Laplace equation. The solution is locally expressed as a...