Stationary Nonlinear Schr\"odinger Equation on Simplest Graphs: Boundary conditions and exact solutions

We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs consisting of three bonds. It is shown that the method can be extended for the case of arbitrary number of bonds of star graphs and for other simplest topologies such as tree and loop graphs. The case of repulsive and attractive nonlinearities are treated separately

Branched Josephson junctions: Current carrying solitons in external magnetic fields

We consider branched Josephson junction created by planar superconductors connected to each other through the Y-junction insulator. Assuming that the structure interacts with the external constant magnetic field, we study static sine-Gordon solitons in such system by modeling them in terms of the stationary sine-Gordon equation on metric graph. Exact analytical solutions of the problem are obtained and their stability is analyzed

Enrichment of the grains from rye wort after shock-activator-disintegrating processing

ArticleIn this study, the mode of obtaining grains (pellets) from wort prepared from rye processed by the shock-activator-disintegrator (SAD), has been developed. Additionally, the enrichment of the grains by proteins using the strain of yeast producing proteins was carried out. For cultivation of a pure culture of a strain of yeasts producing proteins, grains with a concentration of 43.00 g 100 g -1 reducing substances and 62.71 mg g -1 of the total amount of amino acid were used. Different concentrations (10%, 20%, 30% and 40% by weight of the grains) of filtrate 24.90% dry matter, 21.00 g 100 g -1 reducing substances and 10.82 mg g -1 of the total amount of free amino acid was added to the grains. As nitrogen and phosphorus-containing mineral feed, diammonium phosphate was added to the nutrient medium. To obtain a pure culture of Candida tropicalis, SK-4 yeast strain was isolated. The content of crude protein and the concentration of amino acids were determined. The morphological state of the cells was assessed. The results of this study show that to prepare the nutrient medium for a pure culture of a strain of protein microorganisms-producers and its cultivation, it is necessary to add 30% of the filtrate to the grains, while the proportion of crude protein in the protein-containing additive reaches more than 40%. The resulting protein-enriched product has a balanced amino acid composition, which is of interest as a protein-containing feed additive and its fine particle size distribution allows its use for feeding farm animals