Spectral synthesis in Banach modules over commutative banach algebras

Mathematical Notes -     

A reinvestigation of o-phenylenemercurials : IV. Adducts of perfluorotribenzo[b,e,b][1,4,7]trimercuronin and the crystal and molecular structure of its 1 : 1 4-phenylpyridine solvate

Perfluorotribenzo[b,e,h][1,4,7]trimercuronin forms adducts of 1 : 1, 1 : 2 and 1 : 3 stoicheiometry with a variety of polar organic molecules. The structure of the 1 : 1 adduct with 4-phenylpyridine was solved by X-ray methods to an R factor of 7.4% for 3528 observed reflections.     

Chemoenzymatic synthesis of HIV-1 V3 glycopeptides carrying two N-glycans and effects of glycosylation on the peptide domain

[structure: see text] A highly efficient chemoenzymatic synthesis of HIV-1 V3 domain glycopeptides carrying two N-linked core tri- and pentasaccharides was achieved. The synthesis consisted of two key steps: a solid-phase synthesis of the cyclic, 47-mer V3 domain peptide containing two GlcNAc residues and a novel endoglycosidase-catalyzed transglycosylation that simultaneously added two N-glycan moieties to the peptide precursor from the oligosaccharide oxazoline donor substrates. The availability of the synthetic glycopeptides allowed the probing of the effects of glycosylation on the HIV-1 V3 domain. It was demonstrated that glycosylation influenced the global conformations of the V3 domain and provided protection of the V3 domain against protease digestion.     

Spectral Analysis of Differential Operators with Involution and Operator Groups

We study the spectral properties of differential operators with involution of the following two types: operators with involution multiplying the potential and operators with involution multiplying the derivative. The similar operator method is used to obtain a refined asymptotics of the eigenvalues and eigenvectors of such operators. These asymptotics are used to derive asymptotic formulas for the operator groups generated by the operators in question. These operator groups can be used to describe mild solutions of the corresponding mixed problems.     

Comparative analysis of side-illumination methods of measurement of emission decay of fluorescent polymer fibers

The fluorescence decay constant of a fluorescent polymer optical fiber is measured by two different side illumination methods. Comparative analysis of these methods is performed. It is shown that the difference in the measured parameters is caused by different conditions of energy exchange between the core, cladding, and radiation modes of the fiber waveguide.     

Spectral Properties of Classical Dirac Operators and Operators with Involution in Homogeneous Function Spaces

Differential Equations - We present spectrum localization theorems for Dirac operators and operators with involution in a class of function spaces introduced in [Contemp. Math., 2018, vol. 706, pp....