this work concerns the study of existence and uniqueness to heat equation with fractional laplacian dierentiation in extended colombeau algebra.

We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of the bundle exhibits a cluster of low-energy states. We demonstrate that the orthogonal projectors onto these states are the Fourier components of an operator with the structure of the Szegö projector, i.e. a Fourier in...

The nonlinear reality structure of the derivatives and the differentials for the euclidean q-spaces are found. A real Laplacian is constructed and reality properties of the exterior derivative are given. On leave of absence from P.N.Lebedev Physical Institute, Theoretical Department, 117924 Moscow, Leninsky prospect 53, CIS This work was supported in part by the Director, Office of Energy Resea...

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.

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 the paper, we investigate the least energy sign-changing solution and the ground state solution of a class of (p,q)-Laplacian equations with nonlocal terms on RN . Applying the constraint variational method, the quantitative deformation lemma, and topological degree theory, we see that the equation has one least energy sign-changing solution u. Moreover, we regard c, d as parameters and give...

We present an iterative algorithm for solving a class of nonlinear Laplacian system of equations in Õ(km log(kn/ǫ)) iterations, where k is a measure of nonlinearity, n is the number of variables, m is the number of nonzero entries in the graph Laplacian L, ǫ is the solution accuracy and Õ() neglects (non-leading) logarithmic terms. This algorithm is a natural nonlinear extension of the one by o...

Article history: Received 7 February 2013 Accepted 15 October 2013 Available online 4 November 2013 Submitted by S. Kirkland

Many segmentation algorithms describe images in terms of a hierarchy of regions. Although such hierarchies can produce state of the art segmentations and have many applications, they often contain more data than is required for an efficient description. This paper shows Laplacian graph energy is a generic measure that can be used to identify semantic structures within hierarchies, independently...

Article history: Received 9 March 2015 Received in revised form 15 October 2015 Accepted 10 November 2015 Available online 28 November 2015