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.     

On the Barzilai and Borwein choice of steplength for the gradient method

In a recent paper, Barzilai and Borwein presented a new choiceof steplength for the gradient method. Their choice does notguarantee descent in the objective function and greatly speedsup the convergence of the method. They presented a convergenceanalysis of their method only in the two-dimensional quadraticcase. We establish the convergence of the Barzilai and Borweingradient method when applied to the minimization of a strictlyconvex quadratic function of any number of variables.     

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.     

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.     

Calculations of the static polarizability and hyperpolarizability of the LiF molecule including vibrational contributions

The static dipole moment, polarizability and first hyperpolarizability of the LiF molecule have been calculated, including vibrational corrections, using Möller—Plesset perturbation theory and coupled cluster methods. The results show that the vibrational corrections, dominated by the nuclear relaxation term, are as important for the calculations of the polarizability and hyperpolarizability as the electronic contribution, and that the electron correlation effects play an important role in the calculations of both electronic and vibrational contributions for these static properties.