Local description of homogeneous real hypersurfaces of the two-dimensional complex space in terms of their normal equations

In the paper, a classification of real hypersurfaces of the space ℂ² that admit transitive actions of local Lie groups of holomorphic transformations is constructed. Any nonspherical Levi nondegenerate homogeneous surface is determined by the triple of real coefficientsN ₅₂₀ ² ,N ₄₄₀, ImN ₄₂₁ of a Moser normal equation. All such surfaces are described by several quadratic curves in the space of above coefficcients. This work was partially supported by RFBR grant 96-01-01002. Voronezh State Academy of Architecture and Civil Engineering. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 34, No. 2, pp. 33–42, April–June, 2000. Translated by A. V. Loboda     

Each Holomorphically Homogeneous Tube in \mathbb{C}^2 Has an Affine-Homogeneous Base

We study aspherical tube hypersurfaces of the two-dimensional complex space which satisfy the local homogeneity condition. We prove that the holomorphic homogeneity of such a surface in the analytic case is equivalent to its affine homogeneity. The proof bases on the properties of the holomorphic invariants of tube hypersurfaces which are constructed by means of the Moser normal form.     

Itô Method for Proving the Feynman–Kac Formula for the Euclidean Analog of the Stochastic Schrödinger Equation

For a stochastic differential equation of the heat equation type, we obtain a Feynman–Kac formula to which the method of analytic continuation with respect to a parameter can be applied under certain assumptions.     

Natural Science Studies of the Ceramics from Eski-Kermen

Crystallography Reports - The results of comprehensive study of the roofing ceramics fragments found during excavations on the Eski-Kermen plateau (headed by Aibabin and Khairedinova, Bakhchisarai...     

ChemInform Abstract: Isomorphous Substitution of Rare‐Earth Elements in Lacunary Apatite Pb8Na2(PO4)6.

Pb_8‐xLn_xNa₂(PO₄)₆ (x = 0—2.0; Ln: Y, La, Pr—Ho, Tm—Yb) with void structural channels are prepared by solid state reaction of PbO, Na₂CO₃, (NH₄)₂HPO₄, and Ln oxides (Al₂O₃ crucible, 800 °C, 2—10 d).     

Contact Zone Approach for a Moving Interface Crack in a Piezoelectric Bimaterial under Thermoelectromechanical Loading

An interface crack of a finite length moving with a constant subsonic speed v along an interface of two semi-infinite piezoelectric spaces is considered. It is assumed that the bimaterial compound is loaded by a remote mixed mode mechanical loading and a thermoelectrical field and that a frictionless contact zone arises at the leading crack tip. Electrically permeable and electrically insulated cases of the open part of the crack are involved into the consideration. By introducing a moving coordinate system at the crack tip the problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved exactly. For both cases of the electrical conditions the transcendental equations are obtained for the determination of the real contact zone length, and moreover, the associated closed form asymptotic formulas are found for small values of this parameter. Variations of the contact zone length and the stress intensity factor with respect to the crack speed and the loading have been investigated both for electrically permeable and electrically insulated cases.     

X-ray spectroscopy diagnostic of a plasma produced by femtosecond laser pulses irradiating a cluster target

The parameters of a plasma produced upon the interaction of ultrashort laser pulses with cluster targets are measured by the methods of X-ray spectroscopy. The dependence of the plasma parameters on the initial properties of a cluster target (the design of a supersonic nozzle, the average size of clusters, the spatial inhomogeneity) and the laser pulse properties (its duration and contrast) is studied. The plasma diagnostics is performed using the model of formation of emission spectra, which was proposed earlier and includes a number of fitting parameters, which provide good agreement with experimental spectra. The systematic experimental studies performed by us showed that our model of cluster heating by ultrashort pulses is indeed a physical model, and the fitting parameters represent the average values of plasma parameters in the corresponding space-time regions.     

Formation of (b<Subscript><Emphasis Type="Italic">n</Emphasis>−1</Subscript> + H<Subscript>2</Subscript>O) ions by collisional activation of maldi-formed peptide [M + H]<Superscript>+</Superscript> ions in a QqTOF mass spectrometer

Collisional activation of [M + H](+) parent ions from peptides of n amino acid residues may yield a rearrangement that involves loss of the C-terminal amino acid residue to produce (b(n-1) + H(2)O) daughters. We have studied this reaction by a retrospective examination of the m/z spectra of two collections of data. The first set comprised 398 peptides from coat protein digests of a number of plant viruses by various enzymes, where conditions in the tryptic digests were chosen so as to produce many missed cleavages. In this case, a large effect was observed-323 (b(n-1) + H(2)O) daughter ions (approximately 81%), including 185 (approximately 46%) "strong" decays with ratios (b(n-1) + H(2)O)/(b(n-1)) > 1. The second set comprised 1200 peptides, all from tryptic digests, which were carried out under more stringent conditions, resulting in relatively few missed cleavages. Even here, 190 (b(n-1) + H(2)O) ions (approximately 16%) were observed, including 87 (> 7%) "strong" decays, so the effect is still appreciable. The results suggest that the tendency for (b(n-1) + H(2)O) ion formation is promoted by the protonated side chain of a non-C-terminal basic amino acid residue, in the order arginine > lysine > or = histidine, and that its (non-C-terminal) position is not critical. The results can be interpreted by a mechanism in which hydrogen bonding between the protonated side chain and the (n - 1) carbonyl oxygen facilitates loss of the C-terminal amino acid residue to give a product ion having a carboxyl group at the new C-terminus.     

Isomorphous substitution of europium for strontium in the structure of synthetic hydroxovanadate

Polycrystalline strontium-europium hydroxovanadates Sr_10−xEu_x(VO₄)₆(OH)_2−xO_x were synthesized and studied by X-ray powder diffraction, infrared absorption and diffuse-reflectance spectroscopies and also thermogravimetry. The single-phase region of isomorphous substitution of Eu for Sr in hydroxovanadate has been found to lie in the compositional interval 0?x?0.18 at 800 °C. Refinement of X-ray diffraction (XRD) patterns by the Rietveld method shows that Eu substitutes for Sr preferentially at the Sr(1) sites of the apatite structure. The substitution results in a more uniform distribution of Sr-O bond lengths in coordination polyhedra both around Sr (1) and Sr (2) sites and also in a slight contraction of the vanadate anion VO₄³⁻. Synthetic Sr hydroxovanadates absorb a considerable amount of water in two forms: capillary condensed and chemically combined. The latter form may be absorbed at temperatures as high as 500 °C.