Dioxomolybdenum(VI) and dioxotungsten(VI) complexes supported by an amido ligand

Stepwise addition of one equivalent of n-butyllithium and trimethylsilyl chloride to 2-tert-butylmercaptoaniline affords the new ligand 1-(Me3SiNH)-2-(t-BuS)C6H4 (LH), that reacts with one equivalent of butyllithium to its lithium salt LLi. Dioxodichloromolybdenum [MoO2Cl2] and dioxodichlorotungsten dimethoxyethane [WO2Cl2(dme)] react in tetrahydrofuran solution at low temperature with two equivalents LLi to monomeric dioxomolybdenum(VI) [MoO2L2] (1) and dioxotungsten(VI) complex [WO2L2] (2) employing two bidentate amido thioether ligands. The crystallographic determination of the molecular structures of 1 and 2 show evidence for M...S contacts. The reaction of [MoO2Cl2] with LLi in tetrahydrofuran solution at room temperature leads next to 1 to two compounds where silyl group migration from nitrogen to oxygen atoms occurs forming [Mo(=NL')2(OSiMe)2] (3) and [Mo(=NL')2(OSiMe3)L] (4, L' = N-2-t-BuSC6H4) as determined by NMR spectroscopy. Compound 4 was isolated in low yield and its molecular structure determined by X-ray crystallography. Higher yields of a bisimido complex can be obtained by the direct reaction of one equivalent of LLi with [Mo(NAr)2Cl2(dme)] (Ar = 2,6-Me2C6H4) forming [Mo(NAr)2LCl] (5).     

A boundary element method for homogenization of periodic structures

Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation using Steklov–Poincaré operators. The resulting boundary element method only discretizes the boundary of the periodic cell and the interface between the materials within the cell. We prove that the homogenized coefficients converge super-linearly with the mesh size, and we support the theory with examples in two and three dimensions.     

Relation between algebraic and geometric view on nurbs tensor product surfaces

NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.     

Catalytic C-H arylation of SEM-protected azoles with palladium complexes of NHCs and phosphines

[reaction: see text] The synthesis and catalytic evaluation of palladium complexes containing imidazolyl carbene ligand of varying steric and electronic properties is reported. These complexes catalyze the efficient C-H arylation of SEM-protected azole heteroarenes and thus provide a good method for preparation of a wide range of arylated free (NH)-azoles including pyrroles, indoles, imidazoles, and imidazo[1,2-a]pyridines. The reaction is operationally simple; the complexes are insensitive to moisture.     

On uniqueness and time regularity of flows of power‐law like non‐Newtonian fluids

Large class of non‐Newtonian fluids can be characterized by index p, which gives the growth of the constitutively determined part of the Cauchy stress tensor. In this paper, the uniqueness and the time regularity of flows of these fluids in an open bounded three‐dimensional domain is established for subcritical ps, i.e. for p>11/5. Our method works for ‘all’ physically relevant boundary conditions, the Cauchy stress need not be potential and it may depend explicitly on spatial and time variable. As a simple consequence of time regularity, pressure can be introduced as an integrable function even for Dirichlet boundary conditions. Moreover, these results allow us to define a dynamical system corresponding to the problem and to establish the existence of an exponential attractor. Copyright © 2010 John Wiley & Sons, Ltd.     

On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model

We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ?Δ³. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ? > 0.     

A central limit theorem for stationary random fields

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form _Xk=g(_εk−s,s∈Z^d)$X_k=g({\epsilon }_{k-s},s\in {\mathbb{Z}}^d)$, k∈Z^d$k\in {\mathbb{Z}}^d$, where _(εi)i∈Zd${\left({\epsilon }_i\right)}_{i\in {\mathbb{Z}}^d}$ are iid random variables and g$g$ is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established.     

Lagrangian and Hamiltonian formalisms for coupled higher-order elements: theory,modeling, simulation

Nonlinear Dynamics - In this work, the definition of the constitutive relation of a classical higher-order two-terminal element from Chua’s table is extended to the coupled element. The way...