In this paper we find explicit lower bounds for Dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p-Laplace equation. Also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value.

and Applied Analysis 3 Let L2 Λ be a square integrable function space with inner product and norm as follows:

Sudden cardiac death (SCD) is one of the leading causes of death. T-wave alternans (TWA), beat-tobeat alternation in T-wave amplitude, has been shown to be linked to SCD. As risk stratification methods, current TWA detectors still have bad sensitivity. These detectors focus only on the presence of TWA, but not its spatial heterogeneity on the heart , which is thought to be precursors of SCD. We...

Article history: Received 24 June 2015 Received in revised form 6 October 2015 Accepted 14 October 2015 Available online 20 October 2015

For every k ≥ 1, the k-th cohomology group H(X,Q) of the random flag complex X ∼ X(n, p) passes through two phase transitions: one where it appears and one where it vanishes. We describe the vanishing threshold and show that it is sharp. Using the same spectral methods, we also find a sharp threshold for the fundamental group π1(X) to have Kazhdan’s property (T). Combining with earlier results,...

In this paper we study some boundary value problems for fractional analogue of Helmholtz equation in a rectangular and in a half-band. Theorems about existence and uniqueness of a solution of the considered problems are proved by spectral method.

The celebrated Spectral Element Method (SEM) has appeared to be of great interest to extend the capabilities of spectral methods to complex geometries. However, using quadrangular (hexahedral in 3D) elements may be a severe restriction for the most complex geometries, because requiring a structured mesh. Thus, Finite element meshes are usually based on triangles (tetrahedra in 3D). Efforts have...

Article history: Received 6 November 2009 Received in revised form 3 April 2010 Accepted 26 June 2010 Available online 3 July 2010