Phosphaniminato-Trichloroselenate(II): Synthese und Kristallstrukturen von [SeCl(NPPh3)2]+SeCl3− und [Me3SiN(H)PMe3]2+[Se2Cl6]2−

Phosphorane Iminato-Trichloroselenates(II): Syntheses and Crystal Structures of [SeCl(NPPh₃)₂]⁺SeCl₃^? and [Me₃SiN(H)PMe₃]₂⁺[Se₂Cl₆]^2? [SeCl(NPPh₃)₂]⁺SeCl₃^? has been synthesized by the reaction of Se₂Cl₂ with Me₃SiNPPh₃ in acetonitrile solution, forming orangered crystals, whereas red crystals of [Me₃SiN(H)PMe₃]₂⁺[Se₂Cl₆]^2? were obtained by the reaction of Me₃SiNPMe₃ with SeOCl₂ in acetonitrile solution. Both complexes were characterized by X-ray structure determinations. [SeCl(NPPh₃)₂]⁺SeCl₃^?: Space group P2₁/n, Z = 4, structure solution with 7 489 observed unique reflections, R = 0.057. Lattice dimensions at ?60°C: a = 1 117.0; b = 2 241, c = 1 407.5 pm, β = 95.61°. In the cation [SeCl(NPPh₃)₂]⁺ the selenium atom is φ-tetrahedrally coordinated by the chlorine atom and by the nitrogen atoms of the phosphorane iminato ligands, whereas the anion SeCl₃^? has a T-shaped structure with φ-trigonal-bipyramidale surrounding of the selenium atom. [Me₃SiN(H)PMe₃]₂⁺[Se₂Cl₆]^2?: Space group P2₁/c, Z = 4, structure solution with 2 093 observed unique reflections, R = 0.080. Lattice dimensions at ?70°C: a = 956, b = 828, c = 1 973 pm, β = 93.80°. The structure consists of [Me₃SiN(H)PMe₃]⁺ ions and planar [Se₂Cl₆]^2? anions, in which the selenium atoms are bridged nearly symmetrically by two chlorine atoms.     

A double arity hierarchy theorem for transitive closure logic

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k–1)-ary fragment of partial fixed point logic by all (2k–1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive closure logic, we show that an extension is possible when we close this logic under congruence.Supported by a grant from the University of Helsinki. This research was initiated while he was a Junior Researcher at the Academy of FinlandThis article was processed by the author using the LATEX style filepljourlm from Springer-Verlag.     

New adaptive mixed finite element method (AMFEM)

The need to develop reliable and efficient adaptive algorithms using mixed finite element methods arises from various applications in fluid dynamics and computational continuum mechanics. In order to save degrees of freedom, not all but just some selected set of finite element domains are refined and hence the fundamental question of convergence requires a new mathematical argument as well as the question of optimality. We will present a new adaptive algorithm for mixed finite element methods to solve the model Poisson problem, for which optimal convergence can be proved. The a posteriori error control of mixed finite element methods dates back to Alonso (1996) Error estimators for a mixed method. and Carstensen (1997) A posteriori error estimate for the mixed finite element method. The error reduction and convergence for adaptive mixed finite element methods has already been proven by Carstensen and Hoppe (2006) Error Reduction and Convergence for an Adaptive Mixed Finite Element Method, Convergence analysis of an adaptive nonconforming finite element methods. Recently, Chen, Holst and Xu (2008) Convergence and Optimality of Adaptive Mixed Finite Element Methods. presented convergence and optimality for adaptive mixed finite element methods following arguments of Rob Stevenson for the conforming finite element method. Their algorithm reduces oscillations, before applying and a standard adaptive algorithm based on usual error estimation. The proposed algorithm does this in a natural way, by switching between the reduction of either the estimated error or oscillations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quenched Normal Approximation for Random Sequences of Transformations

Journal of Statistical Physics - The study and analysis of real-world social, communication, information and citation networks for understanding their structure and identifying interesting patterns...     

Synthese und Kristallstruktur des Selenyl-Phosphaniminato-Komplexes SeO(NPPh3)2

Synthesis and Crystal Structure of the Selenyl-Phosphoraneiminato Complex SeO(NPPh₃)₂ SeO(NPPh₃)₂ has been prepared from SeO₂ and Me₃SiNPPh₃ in a SeO₂ suspension in acetonitrile, forming colourless crystals. The compound is characterized by IR spectroscopy and by a crystal structure determination. Space group P1 , Z = 2, structure solution with 5 344 observed unique reflections, R = 0.064. Lattice dimensions at ?40°C: a = 931.6, b = 947.6, c = 1 762 pm, α = 77.50°, β = 81.78°, γ = 79.23°. The compound forms monomeric molecules in which the selenium atom is φ-tetrahedrally surrounded with bond lengths SeO = 161.7 pm and SeN = 179.9 and 181.6 pm.