The paper deals with the existence and nonexistence of positive solutions for a class of p-Laplacian systems. We investigate the effect of the size of the domain on the existence of positive solution for the problem in sublinear cases. We will use fixed point theorems in a cone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted...

This paper introduces a novel shape representation which performs shape analysis in a hierarchical fashion using Gaussian and Laplacian pyramids. A background on hierarchical shape analysis is given along with a detailed explanation of the hierarchical method, and results are shown on natural contours. A comparison is performed between the new method and our proposed approach using Point Distri...

This paper presents a novel reversible data-embedding method for digital images using integer wavelet transform and companding technique. This scheme takes advantage of the Laplacian-like distribution of integer wavelet coefficients in high frequency subbands, which facilitates the selection of compression and expansion functions and keeps the distortion small between the marked image and the o...

In this paper we provide‎ ‎existence results for positive solution to‎ ‎Dirichlet p(t)-Laplacian boundary value problems‎. ‎The sublinear and‎ ‎superlinear cases are considerd‎.

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if φ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition φ , is given by the convolution of φ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation...

Let G be a stratified Lie group and L be the sub-Laplacian on G. Let 0 6= f ∈ S(R). We show that Lf(L)δ, the distribution kernel of the operator Lf(L), is an admissible function on G. We also show that, if ξf(ξ) satisfies Daubechies’ criterion, then Lf(L)δ generates a frame for any sufficiently fine lattice subgroup of G.

Upper and lower bounds are determined for a function which counts the approximation numbers of the Sobolev embedding W 1,p( )/C ↪→ L p( )/C, for a wide class of domains of finite volume in Rn and 1 < p < ∞. Results on the distribution of the eigenvalues of the Neumann Laplacian in L2( ) are special consequences. We dedicate this paper to Jerry Goldstein on his 60th birthday.

We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log likelihood of data is increased. The gradient and Laplacian of a Boltzmann machine admit beautiful mathematical representations, although computing them is in gene...

According to recent advances in digital image processing techniques, interest in high-quality images has been increased. This paper presents a resolution enhancement (RE) algorithm based on the pyramid structure, in which Laplacian histogrammatching is utilized for high-frequency image prediction. The conventional RE algorithms yield blurring near-edge boundaries, degrading image details. In or...

This paper addresses theory and applications of ℓ p -based Laplacian regularization in semi-supervised learning. The graph -Laplacian for > 2 has been proposed recently as a replacement the standard ( = ) learning problems with very few labels, where is degenerate. In first part we prove new discrete to continuum convergence results -Laplace on k -nearest neighbor -NN) graphs, which are more co...