A Novel Tetranuclear Organotin(IV) Carboxylate with Chain Structure: Synthesis,Crystal Structure,and Characterizations

A new tetranuclear organotin carboxylate {[(n‐Bu₂SnO)₂L]₂}_n (complex 1 ) was synthesized by the reaction of di‐n‐butyltin oxide with (p‐carboxymethoxy‐phenoxy) acetic acid (LH₂) and characterized by elemental analyses: IR, UV–visible, ¹H, ¹³C, ¹¹⁹Sn NMR spectroscopy and single crystal X‐ray study. X‐ray crystallography diffraction data revealed that the complex 1 was polymeric fashion with a chain structure containing a ladder‐like tetranuclear organo‐oxotin cluster. In the complex 1 , the ligand LH₂ is coordinated to the central tin(IV) atoms via the carboxylato‐O atoms. The tetranuclear tin system is formed by the bridges through the carbonyl oxygen atom of the carboxylate moieties and making the tin atom of pentacoordinated in distorted trigonal bipyramidal geometry. Single crystal X‐ray data indicate that the complex 1 crystallized in the cubic system with the space group C₂/c.     

Asymptotic normality of recursive estimators under strong mixing conditions

The main purpose of this paper is to estimate the regression function by using a recursive nonparametric kernel approach. We derive the asymptotic normality for a general class of recursive kernel estimate of the regression function, under strong mixing conditions. Our purpose is to extend the work of Roussas and Tran (Ann Stat 20:98–120, 1992) concerning the Devroye–Wagner estimate.     

Development of an optimal hybrid finite volume/element method for viscoelastic flows

A cell‐vertex hybrid finite volume/element method is investigated that is implemented on triangles and applied to the numerical solution of Oldroyd model fluids in contraction flows. Particular attention is paid to establishing high‐order accuracy, whilst retaining favourable stability properties. Elevated levels of elasticity are sought. The main impact of this study reveals that switching from quadratic to linear finite volume stress representation with discontinuous stress gradients, and incorporating local reduced quadrature at the re‐entrant corner, provide enhance stability properties. Solution smoothness is achieved by adopting the non‐conservative flux form with area integration, by appealing to quadratic recovered velocity‐gradients, and through consistency considerations in the treatment of the time term in the constitutive equation. In this manner, high‐order accuracy is maintained, stability is ensured, and the finer features of the flow are confirmed via mesh refinement. Lip vortices are observed for We>1, and a trailing‐edge vortex is also apparent. Loss of evolution and solution asymptotic behaviour towards the re‐entrant corner are also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

On the benefit of cooperation in three-person games

The analysis of stability of heteroclinic solutions to the Korteweg–de Vries–Burgers equation is generalized to the case of an arbitrary potential that gives rise to heteroclinic states. An example of a specific nonconvex potential is given for which there exists a wide set of heteroclinic solutions of different types. Stability of the corresponding solutions in the context of uniqueness of a solution to the problem of decay of an arbitrary discontinuity is discussed.     

Maximum Principle for Nonlinear Cooperative Elliptic Systems on R^N

We investigate in this work necessary and sufficient conditions for having a Maximum Principle for a cooperative elliptic system on the whole R^N. Moreover, we prove the existence of solutions by an approximation method for the considered system.     

Tandem [5+1] annulation-isocyanide cyclization: efficient synthesis of hydroindolones

A new strategy for the rapid construction of functionalized reduced indoles starting from activated methylene isocyanides and 1,5-dielectrophilic 5-oxohepta-2,6-dienoates (and their equivalents) through a [5+1] annulation-isocyanide cyclization cascade under basic conditions has been developed. This strategy allows the synthesis of polysubstituted dihydroindolones and tetrahydroindolones in high to excellent yields under extremely mild conditions in a single step.     

Photoluminescence and X-ray characterisation of Si/Si1−xGex multiple quantum wells

We present an experimental approach to correlate optical and structural properties of Si/Si_1−xGe_x multiple quantum wells as determined by photoluminescence (PL) and X-ray diffraction, respectively. The optical properties of the quantum wells were characterised by studying the dependence of luminescence on temperature and excitation density. An enhanced PL yield and an increased quenching temperature were observed for a sample grown at 650°C as compared to one grown at 600°C. Pronounced interdiffusion across the multiple quantum well interfaces as well as significant lattice distortions within the SiGe layers have been observed.     

An Organotin(IV) Carboxylate Based on Amide Carboxylic Acid: Synthesis,Crystal Structure,and Characterizations

An organotin carboxylate based on amide carboxylic acid (Ph₃Sn)(L)·C₇H₈ (complex 1 ) (HL = 3‐(1,3‐dioxo‐1H,3H‐benzo[de]isoquinolin‐2‐yl)propanoic acid) has been synthesized and characterized by elemental analyses (IR, ¹H, ¹³C, and ¹¹⁹Sn NMR), UV–visible spectroscopies, and X‐ray crystallography diffraction analysis. Complex 1 is a monomeric triphenyltin carboxylate. Ligand HL in complex 1 adopts unidentate coordination mode. Intermolecular hydrogen bonds and C H···π interactions help complex 1 to build fascinating one‐dimensional and two‐dimensional structures, which are discussed in detail.     

Time‐dependent algorithms for viscoelastic flow: Finite element/volume schemes

Hybrid finite volume/element methods are investigated within the context of transient viscoelastic flows. A finite volume algorithm is proposed for the hyperbolic constitutive equation, of Oldroyd‐form, whereas the continuity/momentum balance is accommodated through a Taylor‐Galerkin finite element method. Various finite volume combinations are considered to derive accurate and stable implementations. Consistency of formulation is key, embracing fluctuation distribution and median‐dual‐cell constructs, within a cell‐vertex discretisation on triangles. In addition, we investigate the effect of treating the time‐term in a finite element fashion, using mass‐matrix iteration instead of the standard finite volume mass‐lumping approach. We devise an accurate transient scheme that captures the analytical solution at short and long time, both in core flow and near shear boundaries. In this respect, some difficulties are highlighted. A new method emerges, with the Low Diffusion B (LDB, with or without mass‐matrix iteration) as the optimal choice. We progress to a complex flow application and demonstrate some provocative features due to the influence of true transient boundary conditions on evolutionary flow‐structure in a 4:1 start‐up rounded‐corner contraction problem. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005