Analysis of packing factors of crystalline polymers in terms of the glass transition to melting temperature radio

An expression for the ratio of the glass transition temperature to the melting temperature, T _g/T _m, was derived with allowance for fluctuations of the packing factor in the amorphous state. This relationship made it possible to describe the actual range of variation in T _g/T _m depending on a change in the packing factor in the crystalline state k _{o, cr}. The proposed approach forms the basis for the method of determination of increments in the packing ratio k _{o, cr} and formulation of the principles of selection of experimental data for calculations. The glass transition temperatures in polyethylene depending on the type of unit cell were calculated.     

Duality for Finite Hopf Algebras Explained by Corings

We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for finite Hopf algebras and its refinements. This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State University Dominguez Hills. He would like to thank both departments for their hospitality.     

Definition and properties of characteristic frequencies of a linear equation

The definition of the characteristic frequencies of zeroes and changes of sign for solutions is given. It is equal to the upper medium (with respect to the time half-axis) of their number on the half-interval of length π. We also define the main frequencies for a linear homogeneous equation of order n. These main frequencies for an equation with constant coefficients coincide with the absolute values of the imaginary parts of the roots of the corresponding characteristic polynomial. It is proved that for the second-order equation the main frequencies are the same for all solutions and that they are stable with respect to uniformly small and infinitely small perturbations of the coefficients. For the third-order equation they can be different, and for any of the main frequencies an example of nonstability is given. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 249–294, 2005.     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

An unstructured mesh finite volume method for modelling saltwater intrusion into coastal aquifers

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.     

Quadratic data envelopment analysis

Data Envelopment Analysis (DEA) offers a piece-wise linear approximation of the production frontier. The approximation tends to be poor if the true frontier is not concave, eg in case of economies of scale or of specialisation. To improve the flexibility of the DEA frontier and to gain in empirical fit, we propose to extend DEA towards a more general piece-wise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). We show that QDEA gives statistically consistent estimates for all production frontiers with bounded Hessian eigenvalues. Our Monte-Carlo simulations suggest that QDEA can substantially improve efficiency estimation in finite samples relative to standard DEA models.     

A STUDY OF VARIOUS BARRIERS IN ENCLOSED SOUND FIELD BY USING THE COMPUTER PROGRAM—SOFIS

In the study of the behaviors of barriers in an enclosed field, one should take into account such phenomena as sound energy reflection, absorption, scattering and diffraction. Therefore, the study is much more difficult than that in free field. In this paper, sound barriers are classified into four kinds according to their size, number and shape. Each kind of barriers is modelled by a corresponding method based on a computer program—SOFIS. The program combines the ray-tracing technique and statistical method. The impulse response and some acoustical parameters such as sound pressure level at different positions can be calculated by the program, no matter there are a certain kind of barriers in the field or the field is empty. The ray-tracing program and the algorithms for various barriers are validated by the comparison between measurement and prediction of the reverberation room and the anechoic room of the Northwestern Polytechnic University.     

Characteristics of propagation of light beams in gyrotropic crystals

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 5, pp. 815–819, May, 1991.