Calculations of the Pressure of Polymorphic Transformation in Small Alkali-Halide Crystals

The present paper analyzes the properties of structural phase transitions under the extremal conditions of high pressures. In the context of the theory of density functional (TDF), the pressures of the B1–B2 transitions are calculated for small alkali-halide crystals as functions of the crystal size. The size effect of the B1–B2 transition – an increase in the transition pressure with the decreasing crystal grain radius – has been established for all investigated halides except lithium fluoride for which the dependence is reverse.     

Resummation of the jet broadening in DIS

We calculate the leading and next-to-leading logarithmic resummed distribution for the jet broadening in deep inelastic scattering, as well as the power correction for both the distribution and mean value. A truncation of the answer at NLL accuracy, as is standard, leads to unphysical divergences. We discuss their origin and show how the problem can be resolved. We then examine DIS specific procedures for matching to fixed order calculations and compare our results to the data. One of the tools developed for the comparison is an NLO parton distribution evolution code. When compared to PDF sets from MRST and CTEQ it reveals limited discrepancies in both. Received: 16 October 2001 / Published online: 12 April 2002     

On the Determination of the Absolute Intensities of Vibrational-Rotational Lines of XY3 Molecules with C 3v Symmetry

Analytical formulas are derived that describe the dependences of the transition probabilities in vibrational-rotational spectra of XY₃-type molecules with C _3v symmetry on the rotational quantum numbers.     

Whitham's dynamical principle for parabolic equations and its proof

A generalization of Whitham's asymptotic principle for parabolic equations is stated. An application of this principle to Fisher's one-dimensional nonlinear equation is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 46–51, 1989.     

State space and wave equation for Boson string with nontrivial topology of world sheet

We show that the wave functions of a string with nontrivial topology of the world sheet should be considered as sections of line bundles over the space of conformal classes of Riemann surfaces. We construct a BRST operator for the case of arbitrary topology and give it a geometric interpretation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 107–121, 1988.     

Diffusion from sessile droplets through membranes

We analyze diffusion from a periodic array of hemispherical droplets through a membrane. We find that the multiple sources do not interact strongly, even when the droplets are closely spaced, so that the flux through the membrane appears nearly additive.     

Christoffel-Darboux-type formulae and a recurrence for biorthogonal polynomials

It is proved that biorthogonal polynomials obey two different kinds of Christoffel-Darboux-type formulae, one linking polynomials with a different parameter and one combining polynomials with different degrees. This is used to produce a mixed recurrence relation, which is valid for all biorthogonal polynomials. This recurrence relation establishes several results on interlacing property of zeros of successive biorthogonal polynomials and leads to a new result on the interlace of zeros of orthogonal polynomials (of equal degrees) with respect to two distributionsdψ(x) andx ^p dψ(x), 0<p≤1, with support in either [0, 1] or [1, ∞).     

Angular dependent rayleigh scattering of Mössbauer radiation on proteins

RSMR experiments with⁵⁷Fe radiation were performed on myoglobin. An areasensitive detector was employed for simultaneous angular dependent collection of the scattered quanta up to a maximum angle 2θ of 17‡. Experimental data of polycrystalline and lyophilized myoglobin are compared with computer calculations of the scattering which are based on the atomic coordinates determined by X-ray structure analysis. Special attention has been paid to the influence of coherence effects from collectively moving parts of the protein. A simple model is introduced in order to take into account these segmental motions. Our first results indicate that the sizes of collectively moving segments are comparable with spheres of about 6 å in diameter in dry myoglobin. In myoglobin crystals, where the molecules are surrounded by large hydration shells, the movements appear to be correlated in segments with sizes comparable to helices.