Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution in-tegrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this descript...

Article history: Received 12 May 2009 Available online 6 October 2009 Submitted by B.S. Thomson

The Laplace-Beltrami operator for graphs has been been widely used in many machine learning issues, such as spectral clustering and transductive inference. Functions on the nodes of a graph with vanishing Laplacian are called harmonic functions. In differential geometry, the Laplace-de Rham operator generalizes the Laplace-Beltrami operator. It is a differential operator on the exterior algebra...

We investigate capillary pumping in microchannels both experimentally and numerically. Putting two droplets of different sizes at the in/outlet of a microchannel, there will in general be a flow from the smaller droplet to the larger one due to the Laplace pressure difference. We show that an unusual flow from a larger droplet into a smaller one is possible by manipulating the wetting propertie...

The Γ-convergence of lower bounded quadratic forms is used to study the singular operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace operator with Dirichlet boundary conditions; a procedure to obtain the effective Schrödinger operator (in different subspaces) is proposed, generalizing recent results in case of compact tubes. Finally, after scaling cur...

sity of Nevada, Reno Abstract: We introduce a new class of asymmetric circular distributions, obtained by wrapping skewed Laplace distributions on the real line, around a circle. We obtain explicit forms for the densities and distribution functions for this family, as well as their trigonometric moments and related parameters. We derive basic properties of these laws and illustrate their modeli...

— We show that the limit, by rescaling, of the ‘new supersymmetric index’ attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of comple...

Tomasz J. Kozubowski Department of Mathematics, University of Nevada, Reno Abstract: We discuss circular distributions obtained by wrapping the classical exponential and Laplace distributions on the real line around the circle. We present explicit forms for their densities and distribution functions, as well as their trigonometric moments and related parameters, and discuss main properties of t...

The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions on the guide walls. It is proven that there are at least N (resp. N−1) trapped modes in the Neumann case (resp. Dirichlet case) under fairly ge...

Abstract A recent study introduced a novel approach to the exploration of diffusions’ first-passage times (FPTs): selfsimilarity . Specifically, consider general diffusion process that runs over non-negative half-line; initiating at fixed positive levels, further diffusion’s FPTs origin. Selfsimilarity means are spanned by an intrinsic scaling their initial levels. The addressed two types selfs...