Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern

The problem considered is that of determining the shape of aplane acoustically sound-soft obstacle from the knowledge ofthe far-field pattern for one time-harmonic incident field.An iterative procedure is proposed based on two boundary integralsrepresenting the incident field and the far-field pattern, respectively.Numerical examples are included which show that the proceduregives accurate numerical approximations in relatively few iterations.     

Photochemical reactions of Ru3(CO)12 involving metalmetal bond fission

Photolysis of Ru₃(CO)₁₂ in the presence of donor ligands rapidly produces monomeric ruthenium species.     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.     

Metal to ligand group transfer reactions : II. Reactions of some π-allylrhodium(I) complexes with trifluoroacetic acid and alkyl,acyl and trimethyltin halides

Rh(π-C₃H₅)(PF₃)₃ (I), reacts with trifluoroacetic acid to form propene and [Rh(CF₃COO)(PF₃)₂]₂ (II). I reacts with t-butyl bromide to give [RhBr(PF₃)₂]₂ and a mixture of propene and 2-methyl-1-propene and with n-propyl bromide to give propene and [RhBr(PF₃)₂]₂. Rh(π-C₃H₅)(PPh₃)₂ (III), and t-butyl bromide yield propene and 2-methyl-1-propene. In these reactions a mechanism involving β-hydrogen abstraction and hydrogen migration via the metal to carbon is proposed. When III reacts with Me₃SnCl the Me₃Sn—moiety migrates intact to the π-allyl group. I reacts with acetyl chloride to give propene, [RhCl(PF₃)₂]₂ and the carbonyl rhodium complex Rh₂Cl₂(PF₃)₃(CO). II does not apparently undergo phosphine ligand exchange unlike the analogous halogeno-bridged dimers.     

High-resolution spectroscopy of induced chiral dimers: a study of the dimers of ethanol by Fourier transform microwave spectroscopy

We present the first recording of the high-resolution spectrum of an induced chiral dimer. Three conformers of the induced chiral dimers of ethanol have been observed using a pulsed molecular-beam Fourier transform microwave spectrometer. The rotational constants of the normal isotopomers of the three species have been determined to be (a) A=5113.826(5), B=1329.7214(4), and C=1257.5151(3) MHz, (b) A=5086.459(5), B=1316.6508(4), and C=1243.6329(4) MHz, and (c) A=4851.608(5), B=1369.7558(6), and C=1243.4184(4) MHz. The observed species have been assigned to calculated structures via Kraitchman double substitution analyses and ab initio calculations. The Kraitchman analyses and the fitted centrifugal distortion parameters suggest that the deuterium bond is significantly stronger than the hydrogen bond in the dimers of ethanol.     

Chemische Vitamin D<Subscript>3</Subscript>-Bestimmung in Lebertran

The different aspects of Vitamin D₃ determination and the data reported in the literature are discussed. The spectrophotometric determination of Vitamin D₃ in cod-liver oil is carried out after the alkaline saponification, extraction of unsaponified parts, precipitation of accompanying sterols and the column- and thin-layer chromatographic purification and separation of vitamin D₃ on 40 cm plates from other vitamins. The dyestuff α-naphtholbenzein is suited well as standard substance for the better location and identification of vitamin D₃ zone on the thin-layer plate. The results obtained from the chemical method were checked through the simultaneous biological determination.     

Consistent propagator approximations

A propagator approximation scheme is presented in the context of an abstract*-algebra approach. The representation theory of such algebras is shown to play a crucial role in the definition of consistent approximations, i.e., approximate propagators based on model time evolutions and states. This procedure places superoperator methods of approximation on a sound Hilbert space footing. A generalization of the Fock vacuum property is introduced which leads to a simplification in the form of the model propagators. Finally a concrete example is considered that fulfills the conditions developed in this article showing that a consistent approximation to the electron propagator results in the Hartree–Fock–Boguliubov equations.