Mass spectrometric identification of cyclic polysulfides in sediment of the Eastern Gulf of Finland. I

Structures of six cyclic polysulfides, previously unknown as organic environmental pollutants, were analyzed from a sediment sample from the Eastern Gulf of Finland. The determinations were done by gas chromatography connected to mass spectrometry. High resolution (HRMS) measurements of the isotopic composition of four compounds could be done to confirm their molecular formulae. Total low resolution (LRMS) spectra were used to elucidate structures of all six compounds by thermochemical approach, application of fragmentation rules and by ICLU simulation of the spectra. The compounds were deduced to be (in the order of GC- retention) 1,2,4-trithiacycloheptane, tetrathiacyclopentane, 1,2,4,5-tetrathia-cyclohexane, 1,2,3,4- tetrathiacycloheptane, 1,2,3,4-tetrathiacyclohexane and 1,2,4,6-tetrathiacyclooctane.     

Oligosilanylated Silocanes

A number of mono- and dioligosilanylated silocanes were prepared. Compounds included silocanes with 1-methyl-1-tris(trimethylsilyl)silyl, 1,1-bis[tris(trimethylsilyl)silyl], and 1,1-bis[tris(trimethylsilyl)germyl] substitution pattern as well as two examples where the silocane silicon atom is part of a cyclosilane or oxacyclosilane ring. The mono-tris(trimethylsilyl)silylated compound could be converted to the respective silocanylbis(trimethylsilyl)silanides by reaction with KO^tBu and in similar reactions the cyclosilanes were transformed to oligosilane-1,3-diides. However, the reaction of the 1,1-bis[tris(trimethylsilyl)silylated] silocane with two equivalents of KO^tBu leads to the replacement of one tris(trimethylsilyl)silyl unit with a tert-butoxy substituent followed by silanide formation via KO^tBu attack at one of the SiMe₃ units of remaining tris(trimethylsilyl)silyl group. For none of the silylated silocanes, signs of hypercoordinative interaction between the nitrogen and silicon silocane atoms were detected either in the solid state. by single crystal XRD analysis, nor in solution by ²⁹Si-NMR spectroscopy. This was further confirmed by cyclic voltammetry and a DFT study, which demonstrated that the N-Si distance in silocanes is not only dependent on the energy of a potential N-Si interaction, but also on steric factors and through-space interactions of the neighboring groups at Si and N, imposing the orientation of the p_z(N) orbital relative to the N-Si-X axis.     

A Reduction Theorem for Highest Weight Modules over Toroidal Lie Algebras

Let be a toroidal Lie algebra corresponding to a semisimple Lie algebra We describe all Borel subalgebras of which contain the Cartan subalgebra where is a fixed Cartan subalgebra of We show that each such Borel subalgebra determines a parabolic decomposition where is a proper toroidal subalgebra of and Our first main result is that, for any weight which does not vanish on , an arbitrary subquotient of the Verma module is induced from its submodule of invariant vectors. This reduces the study of subquotients of to the study of subquotients of Verma modules over . We then introduce categories and and their respective blocks and corresponding to a central charge which is nonzero on . Our second main result is that the functors of induction and invariants are mutually inverse equivalences of the category and the full subcategory of whose objects are generated by their invariants.     

Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric,skew-symmetric,or Hermitian forms

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field of characteristic different from 2.     

Actions of Pointed Hopf Algebras on Quantum Torus

Actions of finite dimensional pointed Hopf algebras on generic quantum torus are classified.

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Sunto Vengono classificate le azioni delle algebre di Hopf puntate di dimensione finita sul toro quantico generico.

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Research partially supported by grants RFBR 03-01-00167, NSh-1910.2003.1 and INTAS00-566     

Comparative analysis of Reaction-Diffusion Manifold based reduced models for Head-On- and Side-Wall-Quenching flames

In this study, multi-dimensional molecular transport phenomena during Flame-Wall-Interactions (FWI) and their effects on model reduction strategies are investigated. In order to access the problem, the standard configurations of a two-dimensional Side-Wall Quenching (SWQ) flame and a one-dimensional Head-On Quenching (HOQ) flame are used and compared. In the case of the SWQ configuration it is shown that the gradients of the species scatter significantly both in the physical space and in the state space. Moreover, the gradient vector of the specific enthalpy describing energy losses towards the wall is not aligned with the gradient vectors of the species, which can be considered as a typical case while a flame in application might approach to the wall at any arbitrary transversal direction. This observation motivates to take the gradients’ scattering and multi-dimensional transport phenomena into account during model reduction to describe reliably the quenching process.The Reaction-Diffusion Manifold (REDIM) method is applied in this work. The method allows to take into account multi-dimensional transport in a very generic way. In order to generate the REDIM, gradient estimates are approximated by using a Singular-Value Decomposition (SVD) of SWQ detailed gradients fields. Two-dimensional REDIMs for both cases are constructed and compared to each other. Different transport (diffusion) models are implemented to compare quantitatively the manifolds with HOQ and SOQ gradients estimates. The comparison shows that the differences between reduced models with varying transport models is significantly larger than the differences for varying configurations (multidimensional gradient estimates). This justifies the use of a relatively simple REDIM for more complicated geometries and configurations. This simplifies the treatment and model reduction procedure significantly for such complicated transient phenomena.     

Different Complexation Behavior of P‐Functionalized Ferrocene Derivatives Towards SnCl2, SnCl4 and SnPh2Cl2: Auto‐ionization and Redox‐Type Reactions

The novel phosphonyl‐substituted ferrocene derivatives [Fe(η⁵‐Cp)(η⁵‐C₅H₃{P(O)(O‐iPr)₂}₂‐1,2)] ( Fc^1,2 ) and [Fe{η⁵‐C₅H₄P(O)(O‐iPr)₂}₂] ( Fc^1,1′ ) react with SnCl₂, SnCl₄, and SnPh₂Cl₂, giving the corresponding complexes [(Fc^1,2)₂SnCl][SnCl₃] ( 1 ), [{(Fc^1,1′)SnCl₂}_n] ( 2 ), [(Fc^1,1′)SnCl₄] ( 3 ), [{(Fc^1,1′)SnPh₂Cl₂}_n] ( 4 ), and [(Fc^1,2)SnCl₄] ( 5 ), respectively. The compounds are characterized by elemental analyses, ¹H, ¹³C, ³¹P, ¹¹⁹Sn NMR and IR spectroscopy, ³¹P and ¹¹⁹Sn CP‐MAS NMR spectroscopy, cyclovoltammetry, electrospray ionization mass spectrometry, and single‐crystal as well as powder X‐ray diffraction analyses. The experimental work is accompanied by DFT calculations, which help to shed light on the origin for the different reaction behavior of Fc^1,1′ and Fc^1,2 towards tin(II) chloride.