Asphericity of shadows of a convex body

A shadow F of a body K is a parallel projection of K to a plane. The shadow F is said to be ε-aspherical if the boundary ∂F lies in a circular ring with center O and ratio of radii equal to 1 + ε. F is said to be ε-aspherical by a part of α if the same is true for the part of ∂F lying inside an angle of 2α π with vertex at O (or within the union of two vertical angles equal to απ if K is centrally symmetric). It is proved that each convex body K ⊂ ℝ³ has a -aspherical shadow and a shadow that is (sec π/5 − 1)-aspherical by 4/5. If K is centrally symmetric, then K has a -aspherical shadow and a shadow that is (sec π/7 − 1)-aspherical by 6/7. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 67–78.     

Segmentation of Heteropolymer Sequences Specifying Subsequences with Different Composition and Statistical Properties

We have studied the segmentation of two‐letter AB heterosequences composed of subsequences with different composition and distribution of A and B monomer units along the chain. Our approach is based on the segmentation function S(k) introduced in the present work and on the Jensen–Shannon divergence measure determined with respect to the probabilities of the lengths of uniform blocks of A and B monomer units. It is shown that the function S(k) is extremely sensitive to the sequence statistics. Even visual analysis of S(k) allows judgment on some features of sequence statistics. In particular, function S(k) is constant for random copolymers, it is an oscillating function for random block copolymers and shows monotonic growth up to some constant value for proteinlike copolymers. However, due to significant fluctuations observed for short sequences, the function S(k) can be effectively used only for segmentation of a heterosequence composed of very long subsequences. On the other hand, we find that the Jensen–Shannon divergence measure does not allow one to judge the type of statistics, but is extremely efficient for segmentation of a heterosequence. Therefore, the two introduced functions, being mutually complementary, provide an effective approach for recognizing and segmentation of heterosequences. As an example, the methods developed are applied for concatenating sequences of different proteins.

Segmentation function S(k, l, x) as a function of parameter k and starting number x of “window” for a sequence composed of elastin and ribonuclease sequences.     

Macromolecular reaction and interdiffusion in a compatible polymer blend, 2. The role of H‐bonding

A theory describing slow macromolecular reaction and interdiffusion in a compatible polymer blend is extended to consider H‐bonding. The known treatments of H‐bonding influence on the free energy of mixing and chains' mobilities are combined to calculate mutual diffusion coefficients in the framework of linear non‐equilibrium thermodynamics. Numerical calculations are performed for a blend of two random copolymers AC and BC to reveal the effect of H‐bonding (between A and B, B and B units) on the interdiffusion profiles. Then, the transformation of A units into B ones is included and the reaction‐diffusion equations are solved with the parameters corresponding to the blend of poly(tert‐butyl acrylate‐co‐styrene) with poly‐(acrylic acid‐co‐styrene) in which the thermal decomposition of tert‐butyl acrylate units takes place. The numerical calculations show that this system is suitable for the experimental verification of theoretical predictions concerning the interplay between macromolecular reaction and interdiffusion in polymer blends.     

On the stress state of shells penetrating into a deformable solid

The motion of an axisymmetric shell in a deformable solid medium is considered. It is assumed that the medium resistance is described by a two-term expression containing a constant term (the rigidity characteristic) and an inertial term quadratic with respect to the penetration velocity. A model of the impactor penetration with the normal interactions with the resisting medium taken into account is proposed. The membrane forces and the arising stresses are determined for decelerated motions of the impactor.     

Polygons inscribed in a closed curve and a three-dimensional convex body

Here are samples of results obtained in the paper. Let γ be a centrally symmetric closed curve in ℝ ⁿ that does not contain its center of symmetry, O. Then γ is circumscribed about a square (with center O), as well as about a rhombus (also with center O) whose vertices split γ into parts of equal length. If n is odd, then there is a centrally symmetric equilateral 2n-link polyline inscribed in γ and lying in a hyperplane. Let K ⊂ ℝ³ be a convex body, and let x ∈ (0; 1). Then K is circumscribed about an affine-regular pentagonal prism P such that the ratio of the lateral edge l of P to the longest chord of K parallel to l is equal to x. Bibliography: 7 titles.     

Crystallization problem with symmetries of composite lattices in statistical crystal theory as bifurcational symmetry breaking problem

Bifurcation theory methods under group symmetry conditions are applied to crystallization problem with composite lattices in statistical crystal theory. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: A numerical study

Detailed finite element implementation is presented for a recently developed technique (He et al., 2012) to characterize nonlinear shear stress–strain response and interlaminar shear strength based on short-beam shear test of unidirectional polymeric composites. The material characterization couples iterative three-dimensional finite element modeling for stress calculation with digital image correlation for strain evaluation. Extensive numerical experiments were conducted to examine the dependence of the measured shear behavior on specimen and test configurations. The numerical results demonstrate that consistent results can be achieved for specimens with various span-to-thickness ratios, supporting the accurate material properties for the carbon/epoxy composite under study.     

On conditions of flutter onset for elongated plate in supersonic gas flow

The scheme developed in [1] of the investigation of Poincaré–Andronov-Hopf bifurcation on the base of the Lyapounov-Schmidt method is applied to two boundary value problems for nonlinear ordinary differential equation describing the oscillations of an elongated plate in supersonic gas flow. Necessary conditions for the existence of periodic solutions are obtained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Subgroup structure of bifurcation equations with crystallographic group symmetry

For stationary and Andronov-Hopf bifurcation with symmetry of highest crystalline classes of basic syngonies of symmorphic crystallographic groups as semidirect products of translations on basic directions and point symmetry of lattice the subgroup structure of relevant bifurcation equations and bifurcating solutions dual to subgroup structure of such symmetry is investigated. Applications to phase transitions in physics are considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rapidity dependence of charged antihadron to hadron ratios in Au+Au collisions at sqrt[s(NN)]=200 GeV

We present ratios of the numbers of charged antihadrons to hadrons (pions, kaons, and protons) in Au+Au collisions at sqrt[s(NN)]=200 GeV as a function of rapidity in the range y=0-3. While the ratios at midrapidity are approaching unity, the K(-)/K(+) and p;/p ratios decrease significantly at forward rapidities. An interpretation of the results within the statistical model indicates a reduction of the baryon chemical potential from mu(B) approximately 130 MeV at y=3 to mu(B) approximately 25 MeV at y=0.