Criteria for the injectivity of analytic sheaves

It is shown that a moduleL over the sheafO of germs of holomorphic functions on a domain G of Cⁿ is injective if and only if the following conditions are satisfied; a)L is flabby; b) for every closed set S ?G and every point z λ G, the stalk se _z of the sheafS ^L;U1→Γ S ^(U:L) is an injectiveO _z -module. It follows in particular that the sheaf of germs of hyperfunctions is injective over the sheaf of germs of analytic functions.     

Effect of spherically symmetric mass flow from the surface of a particle on the force of interaction with a plane surface

A stationary velocity field of the flow of a gaseous medium generated by uniform radial injection from the surface of a spherical particle near a wall is considered in the Stokes' approximation. Bispherical coordinates are used to write the expression for the stream function. A formula is obtained for the force acting on the spherical particle when there is an arbitrary mass flow from its surface, generalizing earlier results /1, 2/. An expression for the force acting on the particle is obtained for the case of spherically symmetric injection from the surface of the particle, and asymptotic formulas at short and long distances from the wall are studied.

An analogous problem concerning the forces of interaction between two spherical particles of the same radius, when uniform injection of equal intensity takes place from their surfaces, is discussed. This is equivalent to the problem of the interaction of a spherical particle with a free surface. A general expression for the force of interaction, and its asymptotic forms for short and long distances, are obtained.     

Electron paramagnetic resonance in a subsystem of structural defects as a factor in the plasticization of NaCl crystals

A change in the macroplastic deformation rate and an increase in the travel distances of edge dislocations are observed in NaCl single crystals placed in crossed dc and rf magnetic fields. The magnetic-field frequencies at which softening maxima are observed correspond to the resonance frequencies of transitions between Zeeman sublevels in paramagnetic complexes of structural defects. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 5, 400–405 (10 September 1998)     

A review of methods for computer-aided reconstruction of solid models of objects by their orthographic views

The paper contains a review of methods for computer-aided reconstruction of three-dimensional solid models of objects by their orthographic views. This problem arises when passing from engineering 2D-drawings to spatial models of objects in systems of three-dimensional solid modeling. In spite that there exists a large variety of such systems, none of them provides a computer-aided solution of this problem. This is due to the fact that the existing methods for solution are imperfect and require further elaboration. In this paper, we review the existing approaches and compare their application domains.     

Conditions for the spatial flatness and spatial injectivity of an indecomposable CSL algebra of finite width

This paper is concerned with the connection between the geometric properties of the latticeL of subspaces of a Hilbert spaceH and homological properties (flatness and injectivity) ofH regarded as a natural module over the reflexive algebra AlgL that consists of all operators leaving invariant each element of the latticeL. It follows from these results that the cohomology groups with coefficients inB(H) are trivial for a broad class of reflexive algebras.     

Preparation of 4,5-dimethylenecyclohexane-1,2-diamines by the [4+2]-cyclization of 2,3-dimethylene-1,4-bis-(dipropylboryl)butane with 1,2-diimines

N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117913 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 9, pp. 2198–2199, September, 1992.     

Stereospecific coordination ofl-hydroxyproline esters with triosmium clusters

The reactions of cluster (-H)Os₃(CO)₁₀(-OH) with ethyl and isopropyl esters ofl-oxyproline were studied. In the presence of Me₃NO intermediate complex (-H)Os₃(CO)₉(-OH)L (L — isopropyl ester ofl-oxyproline) is formed, which slowly converts to the more stable cluster (-H)Os₃(CO)₉ . Cluster complexes containing chelate-bridging heterocycles were also obtained by heating (-H)Os₃(CO)₁₀(-OH) with esters ofl-oxyproline. In both cases, only one of the possible diastereomeric complexes (-H)Os₃(CO)₉ (R = Et, Prⁱ) is formed, which indicates that the reactions are stereospecific. Based on analysis of Dreiding's models, an attempt to determine the absolute configuration of the obtained clusters was made.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2021–2025, October, 1995.     

Synthesis, characterization, and reactivity of Ti(IV)-monosubstituted Keggin polyoxometalates

Ti(IV)-monosubstituted Keggin-type polyoxometalates (Ti-POMs), mu-oxo dimer [Bu4N]8[(PTiW11O39)2O] (1), and three monomers [Bu4N]4[PTi(L)W11O39], where L = OH (2), OMe (3), and OAr (4, ArOH = 2,3,6-trimethylphenol (TMP)), have been prepared starting from mu-hydroxo dimer [Bu4N]7[(PTiW11O39)2OH] (5) or heteropolyacid H5PW11TiO40 or both. The compounds have been characterized by elemental analysis, IR, UV-vis, and multinuclear (31P, 1H, 183W) NMR. The interaction of 1 and 3-5 with H2O in MeCN produces 2. The hydrolysis constants, estimated from 31P and 1H NMR data, are 0.006 and 0.04 for 1 and 3, respectively. Studies by 31P NMR, IR, potentiometric titration, and cyclic voltammetry revealed that 1-3 and 5 afford the same protonated titanium peroxo complex [Bu4N]4[HPTi(O2)W11O39] (I) upon interaction with aqueous H2O2 in MeCN. The rates of formation of I correlate with the rates of hydrolysis of the Ti-POMs and follow the order of 5 > 1 > 3. A two-step mechanism of the reaction of Ti-POMs with H2O2, which involves hydrolysis of the Ti-L bonds to yield 2 followed by fast interaction of 2 with hydrogen peroxide producing I, is suggested. The equilibrium constant for the reaction of 2 with H2O2 to yield I and H2O, estimated using 31P NMR, is 10. The interaction of the Ti-POMs with TMP follows the trends similar to their interaction with H2O) and requires preliminary hydrolysis of the Ti-L bonds. All of the Ti-POMs catalyze the oxidation of TMP with H2O2 in MeCN to give 2,3,5-trimethyl-p-benzoquinone and 2,2',3,3',5,5'-hexamethyl-4,4'-biphenol. The product distribution is similar for all of the Ti-POMs. The catalytic activities of the Ti-POMs correlate with the rates of formation of I and follow the order of 2 > 5 > 1 > 3. The findings lay a basis for a better understanding of the nature of the reactivity of titanium in Ti-catalyzed oxidations.     

A Femtosecond Pulse Train with a Selectable Carrier–Envelope Offset Phase

Optics and Spectroscopy - A method and a scheme of obtaining a femtosecond pulse train without frequency comb offset and selectable carrier–envelope offset phase are proposed.