Invertible point transformations,Painlevé test,and the second Painlevé transcendent

The techniques of invertible point transformations and the Painlevé analysis can be used to construct integrable ordinary differential equations. We compare both techniques for the second Painlevé transcendent.     

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.     

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.

     

(Ni0.8Zn0.2Fe2O4)epoxy-PZT双层膜中的磁电效应

讨论了Ni_0.8Zn_0.2Fe₂O₄ (NZFO)与锆钛酸铅(PZT)的双层膜结构样品的磁电(ME)效应.NZFO粉料由溶胶-凝胶法制成，再经900℃热压，并高温烧结.在该双层膜中测量到了很强的磁电相互作用.发现横向的磁电效应比纵向效应大一个数量级，并且随NZFO烧结温度的提高而增加.当烧结温度从950℃上升到1380℃时，横向ME电压系数(α_E)的最大值变化范围为25.6 mV Am^-2≤α_E≤199.6 mV Am^-2.理论分析显示NZFO-PZT双层膜样品中ME效应源于NZFO与PZT之间相对良好的磁电耦合. 关键词： 镍铁氧体 PZT 热压法 ME效应     

Sonogashira alkynylation of unprotected 8-brominated adenosines and guanosines: fluorescence properties of compact conjugated acetylenes containing a purine ring

A practical Sonogashira alkynylation protocol for the preparation of 8-alkynylated adenosines and guanosines has been developed. Protection of the sugar hydroxyl substituents is not required; protection hinders the purification of these products. A preliminary fluorescent study is reported, which shows that the presence of a substituent on the phenylene ring influences the fluorescent properties considerably, an outcome that could be utilized in biological applications.     

A modified predictor–corrector scheme for the two-dimensional sine-Gordon equation

A three-time level finite-difference scheme based on a fourth order in time and second order in space approximation has been proposed for the numerical solution of the nonlinear two-dimensional sine-Gordon equation. The method, which is analysed for local truncation error and stability, leads to the solution of a nonlinear system. To avoid solving it, a predictor–corrector scheme using as predictor a second-order explicit scheme is proposed. The procedure of the corrector has been modified by considering as known the already evaluated corrected values instead of the predictor ones. This modified scheme has been tested on the line and circular ring soliton and the numerical experiments have proved that there is an improvement in the accuracy over the standard predictor–corrector implementation. This research was co-funded by E.U. (75%) and by the Greek Government (25%).