Discrete Laplace–Beltrami operators on polyhedral surfaces play an important role for various applications in geometry processing and related areas like physical simulation or computer graphics. While discretizations of the weak Laplace–Beltrami operator are well-studied, less is known about the strong form. We present a principle for constructing strongly consistent discrete Laplace–Beltrami o...

a two dimensional generalized thermoelastic problem of a thick circular plate of finite thickness and infinite extent subjected to continuous axisymmetric heat supply and an internal heat generation is studied within the context of generalized thermoelasticity. unified system of equations for classical coupled thermoelasticity, lord-shulman and green-lindsay theory is considered. an exact solut...

We report a skew-Laplace statistical analysis of both flow cytometry scatters and cell size from microbial strains primarily grown in batch cultures, others in chemostat cultures and bacterial aquatic populations. Cytometry scatters best fit the skew-Laplace distribution while cell size as assessed by an electronic particle analyzer exhibited a moderate fitting. Unlike the cultures, the aquatic...

We prove C regularity for a thin obstacle problem for the p-laplace equation. Due to the nonlinearity of the p-laplace operator we can not use the same methods used for the Laplace case, instead we use techniques developed by E. de Giorgi. AMS Classification: 35R35, 35J60, 35B65.

The study of the Laplace operator and its corresponding eigenvalue problem is crucial to understand the foundations of 3D shape analysis. For that reason the most important mathematical properties of the Laplace operator in Euclidean spaces, its eigenvalues and eigenfunctions are summarized and explained in this report. The basic definitions and concepts of infinite dimensional function spaces,...

In this article, we have effectively used the Numerical Inversion of Laplace transform to study the time-dependent thin film flow of a second grade fluid flowing down an inclined plane through a porous medium. The solution to the governing equation is obtained by using the standard Laplace transform. However, to transform the obtained solutions from Laplace space back to the original space, we ...

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotiv...

The convergence property of the discrete Laplace–Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose several simple discretization schemes of Laplace–Beltrami operators over triangulated surfaces. Convergence results for these discrete Laplace–Beltra...

Laplace equations were used for modeling of electrotonic potential in three-dimensional isotropic double-space RC medium. Solutions of Laplace equations for the case of rectangular current pulse stimulation using spherical electrode we obtain using Laplace transforms in imaginary space. Solutions in original space we got using numerical invert Laplace transform. It showed that the rising front ...