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.     

Application of Homotopy Perturbation Method and Variational Iteration Method to Nonlinear Oscillator Differential Equations

In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are applied to solve nonlinear oscillator differential equations. Illustrative examples reveal that these methods are very effective and convenient for solving nonlinear differential equations. Moreover, the methods do not require linearization or small perturbation. Comparisons are also made between the exact solutions and the results of the homotopy perturbation method and variational iteration method in order to prove the precision of the results obtained from both methods mentioned.     

On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium

Homotopy analysis method (HAM) is employed to investigate the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generation fluid driven by a continuously moving permeable surface immersed in a fluid saturated porous medium. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Prandtl number, Darcy number, the dimensionless inertia coefficient, the dimensionless heat generation/absorption coefficient and the dimensionless suction/blowing coefficient. A parametric study of all governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for velocity and temperature distributions as well as the local friction coefficient and local Nusselt number. Finally, a proper discussion is derived on the obtained results and some remarkable conclusions are mentioned.     

Exponential Behavior of Solutions to Stochastic Integrodifferential Equations with Distributed Delays

In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C₀-semigroup.     

Weak solutions to stochastic 3D Navier-Stokes-α model of turbulence: α-Asymptotic behavior

We study the asymptotic behavior of weak solutions to the stochastic 3D Navier-Stokes-α model as α approaches zero. The main result provides a new construction of the weak solutions of stochastic 3D Navier-Stokes equations as approximations by sequences of solutions of the stochastic 3D Navier-Stokes-α model.     

Micromechanical modeling of linear viscoelastic behavior of heterogeneous materials

Study of effective behavior of heterogeneous materials, starting from the properties of the microstructure, represents a critical step in the design and modeling of new materials. Within this framework, the aim of this work is to introduce a general internal variables approach for scale transition problem in linear viscoelastic case. A new integral formulation is established, based on the complete taking into account of field equations and differential constitutive laws of the heterogeneous problem, in which the effects of elasticity and viscosity interact in a representative volume element. Thanks to Green’s techniques applied to space convolution’s term, a new concentration relation is obtained. The step of homogenization is then carried out according to the self-consistent approximation. The results of the present model are illustrated and compared with those provided by Hashin’s and Rougier’s ones, considered as references, and by internal variables models such as those of Weng and translated fields.     

A remark on the Kazhikhov–Smagulov type model: The vanishing initial density

This work deals with the global existence of weak solutions for a Kazhikhov–Smagulov type system with a density which may or not vanish. Our model is formally equivalent to the physical compressible model with Fick’s law, in contrast to those in previous works. This model may be used for addressing environmental problems such as propagation of pollutants and avalanche modelling. We also explain why this system may be seen as a physical regularization of the standard nonhomogeneous incompressible Navier–Stokes equations and we give an existence result with an initial density less regular but away from the vacuum.