Boundedness and stability criteria for linear ordinary differential equations of the second order

We establish some correlations for solutions of ordinary differential equations and the imaginary part of the complex solution of the corresponding Riccati equation. On the basis of these correlations and the I. M. Sobol’ theorem we prove some new stability and boundedness criteria for linear equations of the second order.     

Global solvability tests for a scalar Riccati equation with complex coefficients

We obtain two global solvability tests for a scalar Riccati equation with complex coefficients. One of them is used to prove a test for the existence of a solution of the Redheffer system, which arises when studying a physical model of electromagnetic wave distribution in a transmission line and in a physical model of diffraction of particles along a rod.     

The Stevens rearrangement of propargyl-containing ammonium salts

The Stevens rearrangement of ammonium salts with two propargyl group at the ammonium nitrogen results in the formation of amines containing acetylene-acetylene and acetylene-allene fragments.     

Dynamical diffraction of X-rays in ADP single crystal under influence of temperature gradient

The dependence of the integrated intensity of X-ray beams diffracted from a single crystal of ammonium dihydrogen phosphate (ADP) in the Laue geometry on the applied temperature gradient has been investigated. It is found that the integrated intensity of the X-ray beam reflected from a single crystal depends almost linearly on the magnitude of the temperature gradient, applied perpendicular to the reflecting atomic planes, up to saturation. For small values of the temperature gradient, in case of antiparallel vectors of diffraction and temperature gradient, integrated intensity of the reflected X-rays is initially reduced by about 10% and then increases monotonically with increasing value of the temperature gradient. Based on the theoretical analysis, an explanation of the observed phenomena is given.     

Structural informatics,modeling, and design with an open‐source Molecular Software Library (MSL)

We present the Molecular Software Library (MSL), a C++ library for molecular modeling. MSL is a set of tools that supports a large variety of algorithms for the design, modeling, and analysis of macromolecules. Among the main features supported by the library are methods for applying geometric transformations and alignments, the implementation of a rich set of energy functions, side chain optimization, backbone manipulation, calculation of solvent accessible surface area, and other tools. MSL has a number of unique features, such as the ability of storing alternative atomic coordinates (for modeling) and multiple amino acid identities at the same backbone position (for design). It has a straightforward mechanism for extending its energy functions and can work with any type of molecules. Although the code base is large, MSL was created with ease of developing in mind. It allows the rapid implementation of simple tasks while fully supporting the creation of complex applications. Some of the potentialities of the software are demonstrated here with examples that show how to program complex and essential modeling tasks with few lines of code. MSL is an ongoing and evolving project, with new features and improvements being introduced regularly, but it is mature and suitable for production and has been used in numerous protein modeling and design projects. MSL is open‐source software, freely downloadable at http://msl‐libraries.org . We propose it as a common platform for the development of new molecular algorithms and to promote the distribution, sharing, and reutilization of computational methods. © 2012 Wiley Periodicals, Inc.     

Crystallization of a flexible-chain polymer in melt in the presence of double-stranded DNA

The behavior of a mixture of short fragments of double-stranded DNA and a flexible-chain polymer is addressed. The role of the DNA double helix in the formation of the crystalline phase in the flexible-chain polymer’s melt is examined. It is shown that the presence of DNA rigid fragments in melt results in increase in the melting temperature. A shift of the melting temperature of a perfect crystal with respect to the pure melt of polymer is calculated.     

Analysis of models for calculating the motion of solids of revolution of minimum resistance in soil media

The solution of problems of searching for the optimal shape of a body when it penetrates into dense media is considered using local interaction models (LIMs) and Grigoryan's model of a soil medium in an axisymmetric formulation. A new LIM is obtained that is improved by taking account of the non-linear compressibility and shear strength in the analytical solution of a problem on the expansion of a spherical cavity. The applicability of an LIM that is quadratic with respect to the velocity in determining the forces resisting penetration of sharp bodies into soft soil is justified theoretically and experimentally and the violation of the conditions for the model to be applicable in the case of blunt bodies is established. It is shown that a solution taking account of non-linear flow effects in a two-dimensional formulation enables both the shape as well as power and kinematic characteristics of the optimal blunt bodies as they pass through soil media to be improved considerably. The ratio of the finite depths of penetration of solids of revolution into soft ground taking account of internal friction is estimated by the ratio of the coefficients in the Rankine–Resal formulae.