Temperature Stresses in a Piecewise-Homogeneous Cylindrical Shell Caused by the Presence of a Longitudinal Crack

By using the method of generalized conjugation problems, we propose a numerical scheme for investigation of the redistribution of temperature stresses in a piecewise-homogeneous cylindrical shell caused by a longitudinal crack. This scheme is based on systems of integral equations (some of them are singular) to determine the unknown jumps of integral characteristics of the disturbed temperature field and displacements and their derivatives on the line of a crack and on the interface as well as the derivatives of these integral characteristics with respect to the longitudinal coordinate at the interface.     

UP-conversion of terahertz radiation induced by photon drag effect

An all-optical approach to convert terahertz radiation (THz, wavelength λ₁) into infrared (IR, peak wavelength λ₂) is presented. We show that this up-conversion process is due to the photon drag effect induced by the THz radiation in intrinsic narrow-gap semiconductors followed by spatial redistribution of current carriers and band-to-band radiative recombination. The process results in non-selective high-speed (ns range rise/fall times) IR imaging of positive (conventional luminescence) and/or negative (negative luminescence) contrasts. Estimates made for an InSb pixelless converter at 300 K and moderate THz intensity (kW/cm²) show that this up-conversion process (with λ₁/λ₂>10²) can be observed with a conventional thermal imaging camera.     

Rigidity of Branch Groups Acting on Rooted Trees

Automorphisms of groups acting faithfully on rooted trees are studied. We find conditions under which every automorphism of such a group is induced by a conjugation from the full automorphism group of the rooted tree. These results are applied to known examples such as Grigorchuk groups, Gupta–Sidki group, etc.     

Temperature-dependent behavior of birefringence and rotation of the optical indicatrix in crystals of deuterated triglycinesulfate

On the basis of a complex null-polarimetric method, the natural birefringence and the rotation of the optical indicatrix in crystals of deuterated triglycinesulfate are measured in the temperature range of 300–340 K. The temperature-dependent behavior of the optical parameters is shown to be close to that observed previously in triglycinesulfate crystals. Changes in them upon the ferroelectric phase transition can be accounted for by the spontaneous quadratic electro-optic effect, with the values of the electro-optic coefficients being larger by a factor of 1.4 than in triglycinesulfate crystals.     

Spectral Properties of Image Measures Under the Infinite Conflict Interaction

We introduce the conflict interaction with two positions between a couple of image probability measures and consider the associated dynamical system. We prove the existence of invariant limiting measures and find the criteria for these measures to be a pure point, absolutely continuous, or singular cotinuous as well as to have any topological type and arbitary Hausdorff dimension.     

A stereoselective synthesis of asymmetrically substituted calix[4]arenecarbamates

Calix[4]arenes bearing a methoxy and an R or S α-phenylethylacetamido group at the narrow rim of macrocycles are stereoselectively acylated with 1 equiv of trichloroacetyl isocyanate to give chiral asymmetrically substituted calix[4]arenecarbamates in preparative yields and high diastereomeric excess.     

Pattern formation in nonextensive thermodynamics: selection criterion based on the Renyi entropy production

We analyze a system of two different types of Brownian particles confined in a cubic box with periodic boundary conditions. Particles of different types annihilate when they come into close contact. The annihilation rate is matched by the birth rate, thus the total number of each kind of particles is conserved. When in a stationary state, the system is divided by an interface into two subregions, each occupied by one type of particles. All possible stationary states correspond to the Laplacian eigenfunctions. We show that the system evolves towards those stationary distributions of particles which minimize the Renyi entropy production. In all cases, the Renyi entropy production decreases monotonically during the evolution despite the fact that the topology and geometry of the interface exhibit abrupt and violent changes.     

Poly[μ2‐chloro‐μ2‐1,4‐oxathiane‐κ2S:S‐copper(I)]

The title complex, [CuCl(C₄H₈OS)]_n, contains infinite spiral (CuS)_n chains linked by bridging Cl atoms into layers. The Cl atoms do not form polymeric fragments with Cu^I, but combine into isolated centrosymmetric Cu₂Cl₂ units. The compound is non‐isomorphous with the Br‐containing analogue, which contains Cu₈S₈ rings linked by Br atoms into chains. The O atom of the 1,4‐oxathiane mol­ecule does not realize its coordination abilities in the known copper(I)–halide complexes, while in copper(II)–halide complexes, oxathiane is coordinated via the S and O atoms. This falls into a pattern of the preferred inter­actions, viz. weak acid (Cu^I atom) with weak base (S atom) and harder acid (Cu^II atom) with harder base (O atom).     

Diastereospecific ring cleavage of bornane-2,3-dione in the Bucherer-Bergs reaction

A novel regio- and diastereospecific ring cleavage of bornane-2,3-dione (camphor quinone) under Bucherer-Bergs reaction conditions has been investigated. The simplicity of this transformation provides a novel and straightforward synthetic pathway to enantiopure derivatives of cyclopentane carboxylic acid as well as functionalized hydantoins in just two steps, starting from inexpensive and easily available camphor.