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.     

Homotopy analysis method for solving the MHD flow over a non-linear stretching sheet

The problem of the boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is considered. Homotopy analysis method (HAM) is applied in order to obtain analytical solution of the governing nonlinear differential equations. The obtained results are finally compared through the illustrative graphs with the exact solution and an approximate method. The compression shows that the HAM is very capable, easy-to-use and applicable technique for solving differential equations with strong nonlinearity. Moreover, choosing a suitable value of none–zero auxiliary parameter as well as considering enough iteration would even lead us to the exact solution so HAM can be widely used in engineering too.     

Quasi-random Simulation of Linear Kinetic Equations

We study the improvement achieved by using quasi-random sequences in place of pseudo-random numbers for solving linear spatially homogeneous kinetic equations. Particles are sampled from the initial distribution. Time is discretized and quasi-random numbers are used to move the particles in the velocity space. Quasi-random points are not blindly used in place of pseudo-random numbers: at each time step, the number order of the particles is scrambled according to their velocities. Convergence of the method is proved. Numerical results are presented for a sample problem in dimensions 1, 2 and 3. We show that by using quasi-random sequences in place of pseudo-random points, we are able to obtain reduced errors for the same number of particles.     

Adaptation of PTB’s analytical modelling for TDCR–Cherenkov activity measurements at LNHB

Designed for triple to double coincidence ratio measurements based on liquid scintillation, the three-photomultipliers detection system can also be applied for Cherenkov counting using aqueous solutions. For activity determination, a specific modelling of Cherenkov light emission has to be constructed. For that purpose, the analytical modelling first developed at PTB was adapted to account for the physical features of the detection system used at LNHB. The first results are presented in the case of activity measurements of two high-energy β^?-emitters (⁹⁰Y and ⁸⁹Sr). The analytical modelling was also tested for the standardization of ⁶⁸Ge in a solution of ⁶⁸Ge/⁶⁸Ga in equilibrium in the framework of a BIPM international comparison in 2014.     

Investigation of a powerful analytical method into natural convection boundary layer flow

The natural convection boundary layer flow modeled by a system of nonlinear differential equations is considered. By means of similarity transformation, the non-linear partial differential equations are reduced to a system of two coupled ordinary differential equations. The series solutions of coupled system of equations are constructed for velocity and temperature using homotopy analysis method (HAM). Convergence of the obtained series solution is discussed. Finally some figures are illustrated to show the accuracy of the applied method and assessment of various prandtl numbers on the temperature and the velocity is undertaken.     

Exponential stability for some stochastic neutral partial functional integrodifferential equations with delays and Poisson jumps

In this work, we study the existence, uniqueness and exponential stability in mean square of mild solutions for some stochastic neutral partial functional integrodifferential equations with delays and Poisson jumps. Sufficient conditions for the existence and exponential stability in mean square of mild solutions are derived by means of the Banach fixed point principle. We suppose that the linear part has a resolvent operator in the sense given in Grimmer (Trans. Am. Math. Soc., 273(1):333–349, 1982). An example is provided to illustrate the results of this work.