Cylindrical solitons in a Gödel Universe and their stability

Exact cylindrically symmetric solutions are obtained for a class of interacting scalar and vector fields in a rotating Godel Universe. We select those with the properties of solitons with smooth decrease of the fields to asymptotics and those with sharp boundaries (droplets). It is shown that only some of the droplets are stable with respect to perturbations that preserve cylindrical symmetry.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 24–27, May, 1991.     

Synthesis, structure and reactivity of binuclear metal-metal bonded molybdenum(V) and tungsten(V) thioselenohalides: Molecular structure of Mo2(μ-S2)2Cl6(SeCl2)2 and W2(μ-S2)2Cl6(SeCl2)2

Thioselenohalide complexes Mo₂(μ-S₂)₂Cl₆(SeCl₂)₂ (I), Mo₂(μ-S₂)₂Br₆(SeBr₂)₂ (II), and W₂(μ-S₂)₂Br₆(SeBr₂)₂ (III) were synthesized by the reactions of corresponding metal halides or carbonyls or molybdenum metal with excesses of S₂ X ₂+Se₂ X ₂ mixtures. The complex W₂(μ-S₂)₂Cl₆(SeCl₂)₂ (IV) was obtained by an exchange reaction between (III) and excess of Se₂Cl₂. Coordination of the neutral SeX ₂ ligands to thiohalidesM ₂(μ-S₂)₂ X ₆ results in higher thermal stability, and suggests the possibility to synthesize SeX ₂ complexes of the unstable parent tungsten thiohalides. An unusual oxidative addition reaction of (I) was detected: {fx27-1} Both (I) and (IV) were characterized by X-ray crystal structure analysis. They are isostructural and form discrete molecules. Bridging S ₂ ^2? ligands are coordinated perpendicularly to the metal-metal bond;d(M?M)=2.8066 Å and 2.793 Å for I and IV, respectively. Nonequivalence of chlorine atoms which are bound to the metal atom, relate to nonequivalence of halogen atoms in the complexesM ₂(μ?S₂)₂ X ₈ ^2? . Chlorine atomstrans to SeCl₂ ligands form short bonds with the metal; the corresponding³⁵Cl NQR frequency is increased. The selenium dichloride ligand is ambidentate. The selenium atom binds as a donor to the metal and as an acceptor to two chlorine atoms which are also bound covalently to the same metal atom.     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

Universal measurability of the identity mapping of a Banach space in certain topologies

If X is a Banach space and X is its conjugate, then a subset Y of X is called madmissible for X if a) the topology (X, Y) is Hausdorff, b) the identity embedding of (X, (X, Y)) into X is universally measurable (Ref. Zh. Mat., 1975, 8B 75 8K). If X is separable, then the existence of an m-admissible set is well known. In this note it is shown that there exist nonseparable X having separable m-admissible sets. The properties of spaces with separable m-admissible sets are considered. It is proved, in particular, that a separable normalizing subset Y of X is m-admissible for X if and only if every (X, Y)-compact set is separable in X.Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 305–314, February, 1978.     

4-Hydroxy-2-quinolones 120. Synthesis and structure of ethyl 2-hydroxy-4-oxo-4H-pyrido-[1,2-a]pyrimidine-3-carboxylate

An improved method for the preparation and purification of ethyl 2-hydroxy-4-oxo-4H-pyrido[1,2-a]-pyrimidine-3-carboxylates is proposed. According to ¹H and ¹³C NMR spectroscopic data the synthesized compounds exist in DMSO solution in the 2-hydroxy-4-oxo form while in the crystal (at least for the case of the unsubstituted derivative) X-ray analysis shows that it occurs in the bipolar 2,4-dioxo form. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 6, pp. 864–876, June, 2007.     

8-Spinors and structure of solitons in generalized Mie electrodynamics

A generalization of Mie electrodynamics is considered. It includes a 8-spinor field and higher powers of the Mie invariant A _μ A ^μ . Particular topological properties of 8-spinors are indicated and are associated with the existence of the remarkable Brioschi identity of eight squares, which permits deriving a natural 8-spinor unification of the Skyrme model of baryons and the Faddeev model of leptons, these particles being treated as topological solitons. Two types of soliton configurations admitted by the model are constructed. These are charged static and neutral lightlike (luxons) ones.     

2-Allyloxy/propargyloxypyridines: synthesis,structure, and biological activity

The alkylation (allylation and propargylation) of 3-cyano-6-dialkylamino-2-pyridones containing a d-annulated ring occurs at the oxygen atom. The structures of the starting compounds and their alkylation products were determined by X-ray diffraction. The neurotropic and antimicrobial activity of alkylation products was examined.     

Heterocyclization of electrophilic alkenes with tetranitromethane revisited: regiochemistry and the mechanism of nitroisoxazole formation

Revised regiochemistry for the heterocyclization of electrophilic alkenes with tetranitromethane (TNM) in the presence of triethylamine, providing rapid access to nitroisoxazoles, is reported. The formation of 5-nitroisoxazoles previously incorrectly assigned as 3-nitro regioisomers, has now been established unambiguously by X-ray crystallography. Empirical computations with ACD/CNMR Predictor, based both on hierarchical ordering of spherical environments (HOSE) and an algorithm of artificial neural networks (ANN), and also Density Functional Theory computations of the ¹³C NMR chemical shifts for the 3- versus 5-nitroisoxazoles are shown to consistently match the spectra of the experimentally observed 5-regioisomers.