Common multiples and common divisors of matrix polynomials, II. Vandermonde and resultant matrices

In this paper explicit formulas are given for least common multiples and greatest common divisors of a finite number of matrix polynomials in terms of the coefficients of the given polynomials. An important role is played by block matrix generalizations of the classical Vandermonde and resultant matrices. Special attention is given to the evaluation of the degrees and other characteristics. Applications to matrix polynomial equations and factorization problems are made.     

Basis sequences in a Montel space

We establish the following theorem: for a Frechet space E to be a Montel space it is necessary and sufficient that any basis sequence in E contains an absolute basis subsequence that spans a non-normable space.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 329–334, September, 1969.The author deeply thanks A. S. Markus for his continuous interest in this work.     

Focusing of Long-Wavelength X-Rays by Means of Spherical and Planar Microchannel Plates

JETP Letters - The possibility of focusing (concentration) of long-wavelength X-rays by thick spherically bent and planar microchannel plates has been studied experimentally and theoretically. The...     

Tobramycin and Nebramine as Pseudo‐oligosaccharide Scaffolds for the Development of Antimicrobial Cationic Amphiphiles

Antimicrobial cationic amphiphiles derived from aminoglycoside pseudo‐oligosaccharide antibiotics interfere with the structure and function of bacterial membranes and offer a promising direction for the development of novel antibiotics. Herein, we report the design and synthesis of cationic amphiphiles derived from the pseudo‐trisaccharide aminoglycoside tobramycin and its pseudo‐disaccharide segment nebramine. Antimicrobial activity, membrane selectivity, mode of action, and structure–activity relationships were studied. Several cationic amphiphiles showed marked antimicrobial activity, and one amphiphilic nebramine derivative proved effective against all of the tested strains of bacteria; furthermore, against several of the tested strains, this compound was well over an order of magnitude more potent than the parent antibiotic tobramycin, the membrane‐targeting antimicrobial peptide mixture gramicidin D, and the cationic lipopeptide polymyxin B, which are in clinical use.     

Diffraction of Electromagnetic Waves by Multilayer Graphene Metasurfaces in the Terahertz Frequency Band

Radiophysics and Quantum Electronics - We perform mathematical modeling of diffraction of plane electromagnetic waves by multilayer metasurfaces comprised by elements of graphene nanoribbons. The...     

Generalized Bezoutian and the inversion problem for block matrices,I. General scheme

The unified approach to the matrix inversion problem initiated in this work is based on the concept of the generalized Bezoutian for several matrix polynomials introduced earlier by the authors. The inverse X^–1 of a given block matrix X is shown to generate a set of matrix polynomials satisfying certain conditions and such that X^–1 coincides with the Bezoutian associated with that set. Thus the inversion of X is reduced to determining the underlying set of polynomials. This approach provides a fruitful tool for obtaining new results as well as an adequate interpretation of the known ones.