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

This paper describes a hierarchical spectral method for the correspondence matching of point-sets. Conventional spectral methods for correspondence matching are notoriously susceptible to differences in the relational structure of the point-sets under consideration. In this paper we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. ...

In a recent article [2] Dutt, Greengard and Rohklin define two newmethods of deferred correction. Convergence for the the first method, using one step methods, has been proven in Hansen [8]. In this paper we augment the theory presented in [8] and use this to prove convergence for the second deferred correction method in [2] using linear k-step methods. This method has been known as Spectral De...

3 Spectral Method 5 3.1 A Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Toy Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 General Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 Color agreement problems . . . . . . . . . . . . ....

Article history: Received 22 May 2013 Received in revised form 11 October 2013 Accepted 23 October 2013 Available online 31 October 2013

A deviation from the slow roll may shift the spectral index and its running. Such a deviation is very generic in inflationary models since the slow-roll equation is not the exact solution of the field equation. We calculate the spectral index and its running with non-vanishing deviation parameter, showing that the deviation parameter is a “hidden” parameter of the standard calculation. A runnin...