An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper. The method is based on the so called transformed field expansion (TFE) coupled with a spectral-Galerkin solver for elliptical domain using Mathieu functions. Numerical results are presented to show the accuracy and stability of the proposed m...

We show that the finite Toda lattice with complex-valued initial data can be integrated by the inverse spectral method. For this goal spectral data for complex Jacobi matrices are introduced and an inverse spectral problem from the spectral data is solved. The time evolution of the spectral data for the Jacobi matrix associated with the solution of the Toda lattice is computed. Using the soluti...

A new model of inflation is described. An unusual form for the inflationary potential is obtained because the inflaton corresponds to a non-trivial path in the configuration space of the two real scalar fields of the model. The model predicts a spectral index n = 1 − 3/2N ≃ 0.97 for the density perturbations and negligible gravitational waves. KUNS 1275 astro-ph/9407040 ∗e-mail address: eds@mur...

We calculate Connes’ invariant χ(M) for certain II1 factors M that can be obtained as inductive limits of subfactors with spectral gap, then use this to answer a question he posed in 1975, on the structure of McDuff factors M with χ(M) = 1.

We present an algorithm for learning a mixture of distributions based on spectral projection. We prove a general property of spectral projection for arbitrary mixtures and show that the resulting algorithm is efficient when the components of the mixture are logconcave distributions in n whose means are separated. The separation required grows with k, the number of components, and logn. This is ...

We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astro-physical problems in the framework of general relativity.

A computation is a temptation that should be resisted as long as possible. "

Three-year data of WMAP implies not only a negative running of the spectral index with large absolute value, but also a large positive running of running of the spectral index with order of the magnitude 10. We calculate the running of running in usual inflation model and noncommutative inflation model. A large tensor-scalar ratio r ≥ 1.23 is needed in order to fit the WMAP data in the noncommu...

Nuclearity of the Hankel operator is a known sufficient condition for convergence of Lyapunov-balanced truncations. We show how a previous result on nuclearity of Hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class D with p ≥ 1 (the case p = 1 being the analytic case). For semigroups that are generated by a Dunford-Schwartz spectral operat...

Remote sensing images with large sizes are usual. They also include several spectral channels, increasing the volume of information. To get valuable information from data automatically, computers need higher amounts of memory and efficient processing techniques. Segmentation is a key technique to deal with remote sensing. It identifies regions in images. Therefore, it deals with large amounts o...