A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for

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nonderogatory complex matrices up to unitary similarity, and

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pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues.

The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles.     

Ab initio calculations of surface electronic states in indium oxide

A slab approach in the framework of ab initio calculations was applied to study surface electronic states in In₂O₃ crystal. Density functional theory (DFT) calculations were carried out employing the WIEN 2k code and using the full potential method with Augmented Plane Waves + local orbitals (APW+lo) formalism. Total and partial DOS (Density of States) were calculated for In and O atoms in two upper (110) surface layers. Comparison of total and partial DOS allowed determining a contribution of electronic states of different In and O surface atoms into formation of surface electronic spectra and corresponding chemical bonds. A dominant ionic character of chemical bonds in In₂O₃ is found. Calculations were performed for three slab models with different geometry parameters. It was shown that an optimal ratio between the whole vertical size of a supercell and the vertical size of atomic cluster has to be chosen. The size of vacuum region in the slab model influences significantly on the reliability of calculated characteristics of the surface electronic structure. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The inverse spectral problem for a Stieltjes eight-shaped string

We consider a spectral problem generated by the Stieltjes string equation on a metric figure-of-eight graph and the corresponding inverse problem which is stated as follows. Values of the point masses located on one of the loops and the lengths of subintervals on it are given together with the spectrum of the spectral problem on the whole graph, the total length of the second loop and the length of the first subinterval on it, and a certain constant. Values of the masses and the lengths of subintervals on the second loop are to be found. Conditions sufficient for such a problem to be solvable are given in the implicit form. An algorithm for recovering the masses and the subintervals on the second loop is proposed.     

Modeling the motion of a bright spot in jets from black holes M87* and SgrA*

General Relativity and Gravitation - In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these...     

Study of the Physicochemical and Biological Properties of the Lipid Complex of Marine Microalgae Isolated from the Coastal Areas of the Eastern Water Area of the Baltic Sea

The Baltic Sea algae species composition includes marine euryhaline, freshwater euryhaline, and true brackish water forms. This study aimed to isolate a lipid–pigment complex from microalgae of the Baltic Sea (Kaliningrad region) and investigate its antimicrobial activity against Gram-positive and Gram-negative bacteria. Microalgae were sampled using a box-shaped bottom sampler. Sequencing was used for identification. Spectroscopy and chromatography with mass spectroscopy were used to study the properties of microalgae. Antibiotic activity was determined by the disc diffusion test. Lipids were extracted using the Folch method. Analysis of the results demonstrated the presence of antimicrobial activity of the lipid–pigment complex of microalgae against E. coli (the zone diameter was 17.0 ± 0.47 mm and 17.0 ± 0.21 mm in Chlorella vulgaris and Arthrospira platensis, respectively) and Bacillus pumilus (maximum inhibition diameter 16.0 ± 0.27 mm in C. vulgaris and 16.0 ± 0.22 mm in A. platensis). The cytotoxic and antioxidant activities of the lipid complexes of microalgae C. vulgaris and A. platensis were established and their physicochemical properties and fatty acid composition were studied. The results demonstrated that the lipid–pigment complex under experimental conditions was the most effective against P. pentosaceus among Gram-positive bacteria. Antimicrobial activity is directly related to the concentration of the lipid–pigment complex. The presence of antibacterial activity in microalgae lipid–pigment complexes opens the door to the development of alternative natural preparations for the prevention of microbial contamination of feed. Because of their biological activity, Baltic Sea microalgae can be used as an alternative to banned antibiotics in a variety of fields, including agriculture, medicine, cosmetology, and food preservation.     

Difference schrödinger operators with linear and exponential discrete spectra

Using the factorization method, we construct finite-difference Schrödinger operators (Jacobi matrices) whose discrete spectra are composed from independent arithmetic, or geometric series. Such systems originate from the periodic, orq-periodic closure of a chain of corresponding Darboux transformations. The Charlier, Krawtchouk, Meixner orthogonal polynomials, theirq-analogs, and some other classical polynomials appear as the simplest examples forN = 1 andN = 2 (N is the period of closure). A natural generalization involves discrete versions of the Painlevé transcendents.On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia.     

Solving two-Level variational inequality

An approach to solving a mathematical program with variational inequality or nonlinear complementarity constraints is presented. It consists in a variational re-formulation of the optimization criterion and looking for a solution of thus obtained variational inequality among the points satisfying the initial variational constraints.This research was supported by the Russian Fundamental Research Foundation, Grant No. 93-012-842     

Thermodynamic compatibility of thermal and calorific state equations in statistical method of conditional distributions

It is shown that by approximating the potential of mean forces which can be used to complete a network of integrodifferential equations, as distinct from the approximation of a particle distribution function, one is able to obtain thermodynamically matched thermal and calorific state equations.     

Truncation procedure for high order reduced distribution functions: II. The compatibility problem

The problem of the compatibility of the results obtained from approximate expressions for the junior distribution functions is viewed under a broad aspect. This paper concerns the compatibility of the calculated values of not only the energy and pressure but also of the higher-order derivatives of the free energy with respect to the thermodynamic variables (such as the heat capacity) as well as of the chain of integro-differential equations, the normalization relations, and the satisfaction of the correlation weakening conditions. The degree of agreement with the requirements mentioned is suggested to be useful as a possible a priori measure of applicability of a certain approximation adopted for calculating the correlation functions over a wide range of thermodynamic variables. The consideration is made within the framework of the conditional distribution method.