X-ray diffraction investigation of <Emphasis Type="Italic">trans</Emphasis>-2,8-dihydroxy-2,4,4′, 6,6′,8,10,10′,12,12′-decamethyl-5,11-dicarbacyclohexasiloxane and <Emphasis Type="Italic">trans</Emphasis>-1,4-dihydroxy-1,4-dimethyl-1,4-disilacyclohexane

The crystal structures of two organosilicon compounds are studied by X-ray diffraction. Crystals of trans-2,8-dihydroxy-2,4,4′,6,6′,8,10,10′,12,12′-decamethyl-5,11-dicarbacyclohexasiloxane, C₁₂H₃₆O₆Si₆, (I) are studied at 293 K [a = b = 16.310(4) Å, c = 9.849(3) Å, V = 2620(1) ų, d_calcd = 1.128 g/cm³, space group P4(2)/n, Z = 4, 3370 reflections, wR2 = 0.1167, R1 = 0.0472 for 2291 reflections with F > 4σ(F)]. Crystals of trans-1,4-dihydroxy-1,4-dimethyl-1,4-disilacyclohexane, C₆H₁₆O₂Si₂, (II) are studied at 110 K [a = 6.8253(5) Å, b = 9.5495(8) Å, c = 12.0064(10) Å, α = 101.774(2)°, β = 102.203(2)°, γ = 95.068(2)°, V = 741.8(1) ų, d_calcd = 1.184 g/cm³, space group \(P\bar 1\), Z = 3, 6267 reflections, wR2 = 0.1052, R1 = 0.0421 for 3299 reflections with F > 4σ(F)]. It is found that the conformation of the ring in compound I, which contains two methylene groups in the cyclohexasiloxane ring, differs from those in its analogues containing only oxygen atoms or one methylene group in the ring. The noticeable difference between the SiCSi angle [123.0(2)°] and the tetrahedral angle is characteristic of cyclohexasiloxanes. Structure II contains three independent molecules with very close conformations. The cyclohexane rings adopt a chair conformation. The methylene groups in II, in distinction to those in I, are characterized by a standard tetrahedral coordination.     

Air Stable Iridium Catalysts for Direct Reductive Amination of Ketones

Half-sandwich iridium complexes bearing bidentate urea-phosphorus ligands were found to catalyze the direct reductive amination of aromatic and aliphatic ketones under mild conditions at 0.5 mol % loading with high selectivity towards primary amines. One of the complexes was found to be active in both the Leuckart–Wallach (NH₄CO₂H) type reaction as well as in the hydrogenative (H₂/NH₄AcO) reductive amination. The protocol with ammonium formate does not require an inert atmosphere, dry solvents, as well as additives and in contrast to previous reports takes place in hexafluoroisopropanol (HFIP) instead of methanol. Applying NH₄CO₂D or D₂ resulted in a high degree of deuterium incorporation into the primary amine α-position.     

Improved approximations for two-stage min-cut and shortest path problems under uncertainty

Mathematical Programming - In this paper, we study the robust and stochastic versions of the two-stage min-cut and shortest path problems introduced in Dhamdhere et al. (in How to pay, come what...     

Electron effects of the substituents on the structure of 4,4′-dipyridylium dications

The crystal structure of N,N′-di(2-hydroxyethyl)-4,4′-dipyridylium diperchlorate C₁₄H₁₈Cl₂N₂O₁₀ is determined by X-ray diffraction at 293 K. The crystals are monoclinic, a = 6.446(1) Å, b = 14.479(3) Å, c = 9.912(1) Å, β = 99.24(2)°, space group P2₁/c, and Z = 2; 1562 reflections measured; and wR2 = 0.086 and R1 = 0.033 for 1209 reflections with F > 4σ(F). It is found that, in the absence of charge transfer from the counterion to the dication, the planarity of the dipyridylium skeleton of the molecule is primarily due to the conjugation between the lone electron pairs of the hydroxyl groups and the π system of the dication. This inference is supported by the intramolecular O?N contact (2.847 Å).     

DG-resolutions of NC-smooth thickenings and NC-Fourier–Mukai transforms

We give a construction of NC-smooth thickenings [a notion defined by Kapranov (J Reine Angew Math 505:73–118, 1998)] of a smooth variety equipped with a torsion free connection. We show that a twisted version of this construction realizes all NC-smooth thickenings as \(0\) th cohomology of a differential graded sheaf of algebras, similarly to Fedosov’s construction in (J Differ Geom 40:213–238, 1994). We use this dg resolution to construct and study sheaves on NC-smooth thickenings. In particular, we construct an NC version of the Fourier–Mukai transform from coherent sheaves on a (commutative) curve to perfect complexes on the canonical NC-smooth thickening of its Jacobian. We also define and study analytic NC-manifolds. We prove NC-versions of some of GAGA theorems, and give a \(C^\infty \) -construction of analytic NC-thickenings that can be used in particular for Kähler manifolds with constant holomorphic sectional curvature. Finally, we describe an analytic NC-thickening of the Poincaré line bundle for the Jacobian of a curve, and the corresponding Fourier–Mukai functor, in terms of \(A_\infty \) -structures.     

Noncommutative two-tori with real multiplication as noncommutative projective varieties

We define analogues of homogeneous coordinate algebras for noncommutative two-tori with real multiplication. We prove that the categories of standard holomorphic vector bundles on such noncommutative tori can be described in terms of graded modules over appropriate homogeneous coordinate algebras. We give a criterion for such an algebra to be Koszul and prove that the Koszul dual algebra also comes from some noncommutative two-torus with real multiplication. These results are based on the techniques of [Categories of holomorphic bundles on noncommutative two-tori. math.AG/0211262] allowing to interpret all the data in terms of autoequivalences of the derived categories of coherent sheaves on elliptic curves.     

Glass crystallization in the MnNbOF5-BaF2-BiF3 system as probed by Raman spectroscopy

Crystallization of glass samples with compositions of 20MnNbOF₅-40BaF₂-40BiF₃, 20MnNbOF₅-30BaF₂-50BiF₃, and 30MnNbOF₅-30BaF₂-40BiF₃ has been studied using Raman spectroscopy. The study of band formation kinetics in high-frequency and low-frequency regions of the Raman spectrum provided information about the crystallization of the materials. The processes involved in glass crystallization have been found to be strongly dependent on the glass composition and annealing schedule. For 20MnNbOF₅-40BaF₂-40BiF₃ and 20MnNbOF₅-30BaF₂-50BiF₃ glasses, crystallization is accompanied by liquation, whereas for 30MnNbOF₅-30BaF₂-40BiF₃ glass, crystallization does not involve noticeable liquation effects and occurs in one step.     

Complexes of 3<Emphasis Type="Italic">d</Emphasis> Metal Biurates with 4-Phenylthiosemicarbazide

Biurate complexes with 4-phenylthiosemicarbazide, namely, [Mn(HL)₂](Urat)₂, [Co(HL)₃](Urat)₃, and [Ni(HL)₄](Urat)₂ (HL is 4-phenylthiosemicarbazide, Urat is anion of uric acid dissociating at first stage) are synthesized and their physicochemical properties and structures are studied by spectroscopic (IR and diffuse reflection) and DTA methods.__________Translated from Koordinatsionnaya Khimiya, Vol. 31, No. 5, 2005, pp. 358–363.Original Russian Text Copyright © 2005 by Koksharova, Yaroslavskaya, Polishchuk.