Sharp upper bounds on the number of the scattering poles

We study the scattering poles of a compactly supported “black box” perturbations of the Laplacian in Rⁿ, n odd. We prove a sharp upper bound of the counting function N(r) modulo o(rⁿ) in terms of the counting function of the reference operator in the smallest ball around the black box. In the most interesting cases, we prove a bound of the type N(r)?A_nrⁿ+o(rⁿ) with an explicit A_n. We prove that this bound is sharp in a few special spherically symmetric cases where the bound turns into an asymptotic formula.     

Asymptotics of generalized derangements

An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multi-phase image segmentation. This method is also applied to image restoration and similar advantages are observed.     

Special jordan pairs

There are some important Jordan pairs contained in the free associative pair, e.g. the free special Jordan pair and the Jordan pair of all symmetric elements under the reversal involution. We study the connection between these two Jordan pairs in the case when the ring of scalars contains ½.     

Ammonia/desorption chemical ionization mass spectrometry of some cyclopentane iridoid glucosides

The ammonia/desorption chemical ionization (DCI) mass spectra of nine cyclopentane iridoid glucosides were measured. The dependences cf the intensities of different peaks on the structures and stereochemistries of the compounds investigated is discussed.     

Quantitative relations between corruption and economic factors

We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investment per capita. These relations hold for diverse countries, and also remain stable over different time periods. We also observe a negative correlation between level of corruption and long-term economic growth. We find similar results for two independent indices of corruption, suggesting that the relation between corruption and wealth does not depend on the specific measure of corruption. The functional relations we report have implications when assessing the relative level of corruption for two countries with comparable wealth, and for quantifying the impact of corruption on economic growth and foreign investment.     

Multiplicities of the eigenvalues of periodic Dirac operators

Let us consider the Dirac operator

     

A Basis for the Graded Identities of the Matrix Algebra of Order Two over a Finite Field of Characteristic p≠2

Let K be a finite field of characteristic p>2, and let M₂(K) be the matrix algebra of order two over K. We describe up to a graded isomorphism the 2-gradings of M₂(K). It turns out that there are only two nonisomorphic nontrivial such gradings. Furthermore, we exhibit finite bases of the graded polynomial identities for each one of these two gradings. One can distinguish these two gradings by means of the graded polynomial identities they satisfy.     

Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials

Partially supported by Bulgarian Committee of Science, Contract No. 52/1988