Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

The Asymptotics of Spectral Gaps of a 1D Dirac Operator with Cosine Potential

Letters in Mathematical Physics -     

Enhanced specificity of bacterial spore identification by oxidation and mass spectrometry

Addition of an oxidizing agent (e.g., hydrogen peroxide) to intact spores selectively and completely oxidizes Met-containing biomarker proteins by formation of Met sulfoxides. This reaction increases the masses of the biomarker proteins observed in matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) of Bacillus spores by Deltam = (16 x n) Da, where n is the number of Met residues in the sequence of each individual protein. The procedure is very rapid, and can be performed in situ (i.e., on the MALDI target). It confirms the identity of individual biomarkers by comparing the number of Met amino acids from the experimentally determined mass shifts with predictions for n from the tentative amino acid sequence for each protein. In turn, accurate determination of n for several biomarkers allows rapid validation of the initial spore identification by MALDI-MS.     

CTI: A novel charge-related topological index with low degeneracy

A new type of topological index is proposed. Its definition is based on the concept of atomic charge distributions in organic molecules. Introduction of electronic in addition to purely topologic factors allows consideration of heteroatom-containing structures as well. It is demonstrated that the index has a low degree of degeneracy, thus suggesting it can be used for coding chemical structures, discrimination of redundancies in structure generation programs, and studies of quantitative structure-activity relationships for heteroatom-containing structures.     

Kinetic Isotope Effect as a Tool To Investigate the Oxygen Reduction Reaction on Pt-based Electrocatalysts – Part II: Effect of Platinum Dispersion

We investigated the oxygen reduction reaction (ORR) mechanism on Pt nanoparticles (NPs) dispersed on several carbon blacks with various physicochemical properties (i. e. specific surface ranging from 80 to 900 m² g⁻¹, different graphitization degree, etc.). Using the kinetic isotope effect (KIE) along with various electrochemical characterizations, we determined that the rate determining step (RDS) of the ORR is a proton-independent step when the density of Pt NPs on the surface of the carbon support is high. Upon decrease of the density of Pt NPs on the surface, the RDS of the ORR starts involving a proton, as denoted by an increase of the KIE >1. This underlined the critical role played by the carbon support in the oxygen reduction reaction electrocatalysis by Pt supported on high surface area carbon.     

Travel Time Tomography

We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary by measuring for every point and direction of entrance of a geodesic the point of exit and direction of exit and its length. The linearization of these two problems is tensor tomography. The question is whether one can determine a symmetric two-tensor from its integrals along geodesics. We emphasize recent results on boundary and lens rigidity and in tensor tomography in the partial data case, with further applications.     

New class of level statistics in correlated disordered chains

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size, the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.     

Accurate SVDs of weakly diagonally dominant M-matrices

Summary. We present a new O(n³) algorithm which computes the SVD of a weakly diagonally dominant M-matrix to high relative accuracy. The algorithm takes as an input the offdiagonal entries of the matrix and its row sums.Mathematics Subject Classification (1991): 65F15Revised version received September 19, 2003This material is based in part upon work supported by the LLNL Memorandum Agreement No. B504962 under DOE Contract No. W-7405-ENG-48, DOE Grants No. DE-FG03-94ER25219, DE-FC03-98ER25351 and DE-FC02-01ER25478, NSF Grant No. ASC-9813362, and Cooperative Agreement No. ACI-9619020.     

Spectral triangles of Schrödinger operators with complex potentials

Consider the Schrödinger operator with a complex-valued potential v of period Let and be the eigenvalues of L that are close to respectively, with periodic (for n even), antiperiodic (for n odd), and Dirichelet boundary conditions on [0,1], and let be the diameter of the spectral triangle with vertices We prove the following statement: If then v(x) is a Gevrey function, and moreover