Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

2000 Mathematics Subject Classification: 35J05, 35C15, 44P05

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

The Stein-Weiss Type Inequality for Fractional Integrals, Associated with the Laplace-Bessel Differential Operator

2000 Math. Subject Classification: Primary 42B20, 42B25, 42B35

On q-Laplace Transforms of the q-Bessel Functions

Mathematics Subject Classification: 33D15, 44A10, 44A20

Hyperbolic Double-Complex Laplace Operator

2010 Mathematics Subject Classification: 35G35, 32A30, 30G35.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

The Impact of Hurricane Georges on Soft-Bottom, Back Reef Communitites: Site- and Species-Specific Effects in South Florida Seagrass Beds

Seagrass beds are the dominant benthic marine communities in the back reef environment of the Florida Keys. At a network of 30 permanent monitoring stations in this back reef environment, the seagrass Thalassia testudinum Banks & Soland. ex Koenig was the most common marine macrophyte, but the seagrasses Syringodium fi liforme Kuetz., and Halodule wrightii Aschers., as well as many taxa of macroalgae, were also commonly encountered. The calcareous green macroalgae, especially Halimeda spp. and Penicillus spp., were the most common macroalgae. The passage of Hurricane Georges on September 25, 1998 caused an immediate loss of 3% of the density of T. testudinum, compared to 19% of the S. fi liforme and 24% of the calcareous green algae. The seagrass beds at three of the stations were completely obliterated by the storm. Stations that had little to moderate sediment deposition recovered from the storm within 1 yr, while the station buried by 50 cm of sediment and the two stations that experienced substantial erosion had recovered very little during the 3 yrs after the storm. Early colonizers to these severely disturbed sites were calcareous green algae. Hurricanes may increase benthic macrophyte diversity by creating disturbed patches with the landscape, but moderate storm disturbance may actually reduce macrophyte diversity by removing the early successional species from mixed-species seagrass beds.

Le poids des mots : étude du thème de la souveraineté chez Georges Bataille

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Le poids des mots : étude du thème de la souveraineté chez Georges Bataille

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

The Uses of Print and Writing in Eighteenth Century European Ballet: the Case of The Letters on Dancing and Ballets by Jean-Georges Noverre

This article aims to study the uses of print, especially the Letters on Dancing and Ballets by Jean-Georges Noverre, throughout the emergence of pantomime ballet in the late eighteenth century. Noverre’s discourse is directly associated with a project to revitalize the art of dance. In this sense, books as an object are not only a support for the new aesthetic discourse, but a tool with multiple uses. It simultaneously seeks to modify the spectator’s view of the scene, legitimize the success of the new theatrical genre and value the ballet master profession.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

La pintura que no se deja ver. La pintura avergonzada, la pintura escondida (a propósito de los escritos de Ángela de La Cruz, Georges didi-Huberman y Honoré de Balzac)

El artículo «La pintura que no se deja ver: la pintura avergonzada, la pintura escondida» relaciona una de las primeras obras de la artista Ángela de la Cruz ashamed (1995), con La pintura encarnada (1984) de Georges Didi-Huberman, ensayo que a su vez analiza La obra maestra desconocida (1837) de Honoré de Balzac. Entre Ángela de la Cruz, didi-Huberman y Balzac se establece un triángulo en torno al concepto cuadro-cuerpo. A través de una pintura, un ensayo filosófico y un relato, tres autores de tres tiempos distintos recuperan las mismas ideas de carne y piel pictórica y cuadro humanizado. Su objetivo: superar las barreras de representación en la pintura para crear un ser más allá del objeto pictórico. Sin embargo, cuanto más idealizan la pintura y más pretenden superar la pantallapictórica, más se desvanece el concepto de «cuadro»; cuanto más acercan el cuadro a ser, más se aleja de ser un cuadro y menos se permite el acceso a lo que representa. La persecución del ideal implica que el cuadro se vea sometido a su ocultación, al deterioro y a la destrucción de su imagen.

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.