Study of temperature fields in a rectangular plate with a temperature-dependent internal source with the aid of fast expansions

The approximate analytic solution of the problem of temperature field in a rectangular plate with an internal temperature- dependent source is obtained by the method of fast expansions. The critical value of a parameter characterizing heat release, which fundamentally affects the analytic solution form, is found. The maximum solution error is shown to amount to 0.02 at the consideration of the first three terms of the Fourier series in fast expansion. Temperature fields are presented, and an analysis of the influence of the plate sizes and the heat release magnitude on their formation is given. Recommendations on the plate shape choice are given.     

Transversals in Uniform Hypergraphs with Property (p,2)

Dedicated to the memory of Paul Erdős Let f(r,p,t) (p > t >= 1, r >= 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f(r,p,2) for p = 3, 4, 5, 6 were found in [1] and bounds on f(r,7,2) are given in [3]. Here we prove that for large p and huge r. Received September 23, 1999 RID="*" ID="*" This work was partially supported by the grant 99-01-00581 of the Russian Foundation for Fundamental Research and the Dutch–Russian Grant NWO-047-008-006.     

Characterization and Spatial Matching of Laser Diode Beams

It is shown that the type of lateral waveguide of a laser diode cannot be determined uniquely based on just the measured magnitude of astigmatism. For a unique determination, the K-factor of Petermann, which characterizes the wavefront curvature at the laser output facet, must be measured as well. In order to determine the type of lateral waveguide, a setup for measuring astigmatic distances in the range 0–200 m with an error of ±2 m and a K-factor with an error of 20% was developed. Operational features of the setup were analyzed, and a technique that allows one to minimize the effect of beam ellipticity on the measurement results was found. Using the technique, the optimization of spatial matching of a laser diode with a ring interferometer of the butterfly type was accomplished. For transformation of the astigmatic elliptical beam into the axially symmetric mode of the interferometer, we have used an optical system that consists of two cylindrical and one spherical lenses. The algorithm for designing the matching system was developed, and the 85% injection of radiation of a AlGaAs laser diode into the principal mode of a ring interferometer was experimentally demonstrated.     

An analysis of boundary conditions in heterostructures

General relations satisfied by scattering matrices, matching matrices for coefficients, transfer matrices, and matching matrices for envelope functions are derived for systems with heteroboundaries. It is shown that the relations found for these matrices are fulfilled to good accuracy within the models proposed for the GaAs/AlAs(001) heterostructure. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 39–44, January, 2008.     

Synthesis and characterization of mono beta-diketiminatosamarium amides and hydrocarbyls

Reaction of SmCl3 with 1 eq of KL (L =[DippNC(Me)CHC(Me)NDipp]; Dipp = 2,6-i-Pr2C6H3) in THF afforded the dimeric samarium dichloride LSmCl2(THF)Cl2SmL (1) in high yield. Reactions of 1 with NaN(SiMe3)2, KNHAr (Ar = 2,4,6-t-Bu3C6H2), KBHEt3, and KCp*(Cp*= C5Me5) yielded various new complexes: LSmClN(SiMe3)2 (2), LSm[N(SiMe3)2]2 (3), LSmNHAr(HBEt3) (4), LSm(NHAr)2 (5), and LSmCp*Cl (6). Reaction of 1 with one eq of NaN(SiMe3)2 followed by treatment with excess AlMe3 afforded a unique bimetallic samarium tetramer Cl3L2Sm2(AlMe4)2Sm2L2Cl3 (7). Reaction of 6 with LiMe or LiCH2SiMe3 afforded LSmCp*Me (8) and LSmCp*CH2SiMe3 (9) in excellent yield. Methyl abstraction from with B(C6F5)3 in toluene yielded the cationic borate species (LSmCp*)[MeB(C6F5)3] (10). Molecular structures of 1-7 and 9 were determined by X-ray single crystal analysis.     

Selective synthesis of the C3v isomer of C60h18

[chemical structure: see text]. C60H18 has been produced by hydrogenation of C60 at 100 bar H2 pressure and 673 K for 10 h. We have investigated the crude material without any purification by use of 1H NMR, 13C NMR, and IR spectroscopy and Fourier transform ion cyclotron resonance mass spectrometry. We show that the crude material consists of 95% of the C3v isomer of C60H18.     

A modified HPLC method for the determination of aspartic acid racemization in collagen from human dentin and its comparison with GC

The D/L ratio of aspartic acid enantiomers in proteins of low turnover is generally accepted as a reliable procedure for age determination. In our study, twelve samples of eyetooth dentin were analyzed for age determination. The pure insoluble collagen isolated from eyetooth dentin was obtained by an EDTA demineralization process. Free amino acids obtained after collagen hydrolysis were converted into o-phthaldialdehyde-N-acetyl-L-cysteine (OPA-NAC) derivatives for HPLC analysis under modified conditions and into trifluoroacetic acid isopropyl esters for GC analysis, respectively. The modified HPLC procedure used phosphate buffer and acidified sample matrix prior to injection which resulted in suppression of peak tailing of both diastereomers, thus allowing achievement of both good selectivity and good resolution. To ensure the high accuracy of the developed method the other parameters, i.e. specificity, precision, linearity, LOD, and LOQ, were also determined. Nine collagen samples covering the age range of 18 to 84 years were used for the determination of coefficient of racemization (KR) and calculation of parameters for age estimation. The regression equations for the data set analyzed were as follows: KR= 0.0005 x age + 0.0262 (R2 = 0.9639) for HPLC, and KR= 0.0006 x age + 0.0319 (R2 = 0.9374) for GC, respectively.