Measurements of cosmic microwave background (CMB) anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. Using the direct boundary element method, we numerically obtain the low-lying eigenmodes on a com...

Structural learning with forgetting is an established method of using Laplace regularization to generate skeletal artificial neural networks. In this paper we develop a continuous dynamical system model of regularization in which the associated regularization parameter is generalized to be a time-varying function. Analytic results are obtained for a Laplace regularizer and a quadratic error sur...

We derive regularity estimates for viscosity solutions to the parabolic normalized p-Laplace. By using approximation methods and scaling arguments p-parabolic operator, we show that gradient of bounded is locally asymptotically Lipschitz continuous when p sufficiently close 2. In addition, establish in Sobolev spaces.

When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary ope...

We prove novel (local) square function/Carleson measure estimates for non-negative solutions to the evolutionary $ p $-Laplace equation in complement of parabolic Ahlfors-David regular sets. In case heat equation, Laplace as well corresponding function have proven fundamental symmetry and inverse/free boundary type problems, particular study (parabolic) uniform rectifiability. Though implicatio...

background & aims of the study: p-chloronitrobenzene is a benzoic compound that widely used in many chemical industrials. p-chloronitrobenzene may be absorbed through the skin and is suspected to causing cancer. so, developing an easy method to remove of it from the environment is necessary. equilibrium isotherms and adsorption kinetics of p-chloronitrobenzene onto modified silk waste were stud...

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...