A rationale for the development of thermally stable nanostructured CeO_2-ZrO_2-containing mixed oxides

CeO2-ZeO2 solid solutions are extensively used as oxygen storage promoters in the current automotive three-way catalysts. High thermal stability of the textural properties is one of the most important requirements for practical application since temperatures up to 1273 K are easily experienced by these materials under real working conditions. In the present paper, we investigated how hydrothermal treatments applied to cakes of doped and undoped ZrO2-rich CeO2-ZrO2 precursors might improve the thermal stability of the final CeO2-ZrO2 solid solution. A rationale was developed that allowed to correlate the morphology of the hydrothermaUy treated cake with the thermal stability at 1273 K of the final product, which did not depend on the composition of the mixed oxides.

Mixed d/f Complexes Zn(H2L)Ln(NO3)3(Ln=Sm,Tb and Dy)：Crystal Structure,Fluorescence and Thermal Stability

A series of isostructural d/f molecular compounds Zn（H2L）Ln（NO3）3·CH3OH（Ln = Dy（1）, Tb（2） and Sm（3）） were synthesized by the introduction of a designed multifunctional ligand N,N？,N？？,N？？？-tetra（2-hydroxy-3-methoxy-5-methylbenzyl）-1,4,7,10-tetraazacyclododecan（H4L = C（44）H（60）N4O8）. In the isostructural molecules, each crystallographically independent Zn2＋ and Ln3＋ centers are connected by two phenolic oxygen atoms. For the six-coordinate Zn-（2＋） ion, the coordination geometry can be viewed as a regular bicapped square pyramid. While for the ten-coordinate Ln-（3＋） ion, if each O,O？-chelated nitrate ligand is seen as a single coordination site, the coordination geometry can be viewed as a distorted pentagonal bipyramid. The fluorescent spectra show that compounds 2 and 3 exhibited characteristic sharp emissions of Tb-（3＋） and Sm-（3＋）, respectively, while compound 1 was found to be a single-component white-light-emitting complex in the solid state. Thermal stabilities of the three compounds were investigated by using thermal gravimetric analysis. In addition, the thermal decomposition of compound 1 was confirmed by temperature-dependent powder X-ray diffraction technique.

A STABILIZED MIXED FINITE ELEMENT FORMULATION FOR THE NON-STATIONARY INCOMPRESSIBLE BOUSSINESQ EQUATIONS

In this study, we employ mixed finite element （MFE） method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence, uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.

A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS

A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element （SCNMFVE） formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.

Study of Pickering emulsions stabilized by mixed particles of silica and calcite

Picketing emulsions were prepared using mixed particles of silica and calcite as emulsifiers. The effects of the silica content in the mixed particles on the stability and the drop size of the Picketing emulsions were investigated. The results showed that the Picketing emulsions were of the oil-in-water type. With increasing silica content in the mixed partides, the stability and the drop size of the Pickering emulsions decreased. Larger silica particles had more influence on the stability of the emulsions, while smaller ones had more influence on the drop size of the emulsions. The effect of the silica particles on the emulsions was attributed to their adsorptive behavior at the oil-water interfaces of the Picketing emulsions.

Two-grid stabilized mixed finite element method for fully discrete reaction-diffusion equations

Two-grid mixed finite element method is proposed based on backward guler schemes for the unsteady reaction-diffusion equations. The scheme combines with the stabilized mixed finite element scheme by using the lowest equal-order pairs for the velocity and pressure. The space twogrid method is also used to reduce the time consuming. The benefits of this approach are to avoid the higher derivative, but to have more favorable stability, and to get the numerical solution of the two unknown variables simultaneously. Stability analysis and error estimates are given in this work. Finally, the theoretical results are verified by the numerical examples.

A Stabilized Crank-Nicolson Mixed Finite Element Method for Non-stationary Parabolized Navier-Stokes Equations

In this study, a time semi-discrete Crank-Nicolson （CN） formulation with second-order time accu- racy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element （SCNMFE） formulation based on two local Gauss integrals and parameter- free with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided.

A Posteriori Error Estimate for Stabilized Low-Order Mixed FEM for the Stokes Equations

This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization.Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.

CRITERION FOR SL(2,Z)-MATRIX TO BE CONJUGATE TO ITS INVERSE

This paper gives a necessary and sufficient condition for a matrix in SL(2, Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of second degree. It yields an algorithm to determine this conjugation in finite steps based on the elementary number theory.