Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation

We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This yields a semiclassically reduced nonlocal Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semiclassical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross-Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained

Signature Characters for A_2 and B_2

The signatures of the inner product matrices on a Lie algebra's highest weight representation are encoded in the representation's signature character. We show that the signature characters of a finite-dimensional Lie algebra's highest weight representations obey simple difference equations that have a unique solution once appropriate boundary conditions are imposed. We use these results to derive the signature characters of all $A_2$ and $B_2$ highest weight representations. Our results extend, and explain, signature patterns analogous to those observed by Friedan, Qiu and Shenker in the Virasoro algebra's representation theory.Comment: 22 p

Symmetry operators of the two-component Gross–Pitaevskii equation with a Manakov-type nonlocal nonlinearity

We consider an integro-differential 2-component multidimensional Gross-Pitaevskii equation with a Manakov-type cubic nonlocal nonlinearity. In the framework of the WKB-Maslov semiclassical formalism, we obtain a semiclassically reduced 2-component nonlocal Gross- Pitaevskii equation determining the leading term of the semiclassical asymptotic solution. For the reduced Gross-Pitaevskii equation we construct symmetry operators which transform arbitrary solution of the equation into another solution. Constructing the symmetry operator is based on the Cauchy problem solution technique and uses an intertwining operator which connects two solutions of the reduced Gross-Pitaevskii equation. General structure of the symmetry operator is illustrated with a 1D case for which a family of symmetry operators is found explicitly and a set of exact solutions is generated

Neighbor-Dependent Ramachandran Probability Distributions of Amino Acids Developed from a Hierarchical Dirichlet Process Model

Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1) input data size and criteria for structure inclusion (resolution, R-factor, etc.); 2) filtering of suspect conformations and outliers using B-factors or other features; 3) secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included); 4) the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5) whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately) have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp

Analysis of spatial humus distribution in virgin and arable Chernozems in the eroding landscapes

A statistical assessment of data on the content and spatial distribution of humus in virgin and arable Chernozems on slopes in the south of the forest-steppe zone of the Central Russian Upland was performed. The greatest number of statistically significant differences between arable and virgin Chernozems was found for the upper soil layer (0–20 cm

Combined reactive‐separation process epoxidation of natural rubber production waste

Предложена  схема  совмещенного  реакционно‐разделительного  про‐ цесса эпоксидирования скрапа натурального каучука в cреде вода‐ксилол. Дана коли‐ чественная и качественная оценка результатов химической модификации.  The A scheme of combined reactive separation process epoxidation of natu- ral rubber scrap in water‐xylene medium was proposed. A quantitative and qualitative as‐ sessment of the results of chemical modification was given.

Kazakhstani material testing Tokamak KTM. project status

Creation of cost-efficient and safe fusion reactor will require the development of special structural materials for first wall, blanket, reactor components, which will be operated under conditions of the high heat fluxes, superconducting magnets, plasma heating systems and other elements. The existing tokamaks and other fusion facilities do not currently allow for conduction of specialized researches of plasma-facing structural materials. Kazakhstani Material Testing Tokamak (hereinafter - KTM) provides for a unique opportunity to conduct materials research and testing of separate units and components of fusion reactors..

Modeling Risk Reduction in Agriculture Associated with Dangerous Agrometeorological Phenomena

The paper discusses possible approaches to reduce the risks associated with dangerous weather conditions. More specifically, the article considers the problem of reducing agricultural losses from such dangerous agrometeorological phenomena as hailstorm and drought. Within the framework of the decision-making theory, the formulation of the problem of reducing the losses of a considering industry from these phenomena is proposed – the objective is making decisions under risk. The features of the information support of this problem and the main tasks arising in the way of its practical use are discussed. The results of calculations that are carried out to analyze the effectiveness of the proposed method are given. The results of the calculations showed that the method is quite effective and can be used to reduce agricultural losses from hail