Constraints on the fundamental topological parameters of spatial tessellations

Tessellations of that use convex polyhedral cells to fill the space can be extremely complicated, especially if they are not “facet‐to‐facet”, that is, if the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. In a recent paper 15 , we have developed a theory which covers these complicated cases, at least with respect to their combinatorial topology. The theory required seven parameters, three of which suffice for facet‐to‐facet cases; the remaining four parameters are needed for the awkward adjacency concepts that arise in the general case. This current paper establishes constraints that apply to these seven parameters and so defines a permissible region within their seven‐dimensional space, a region which we discover is not bounded. Our constraints in the relatively simple facet‐to‐facet case are also new.     

Study of the vibrational spectra of SO2, H2O and D2O using the U(4) algebraic model

Using the U(4) algebraic model, in this work we report a study of the vibrational spectra of SO₂, H₂0¹⁸ and D₂O¹⁶. The inclusion of intermode couplings in algebraic models has been stated to give a deep insight into detailed spectroscopy for these bent XY₂ molecules. Improved set of algebraic parameters has been reported to provide improved RMS deviations for these molecules.     

电泳沉积制备ZnO-C60和ZnO-MWCNT合涂层电极及其光电性质

在氧化铟锡( ITO)导电玻璃表面电泳沉积制备ZnO-C60和ZnO-MWCNT复合涂层电极,经后续热处理增强其结合强度,通过SEM观察2种电极复合涂层的表面形貌,并使用CHI 705电化学分析仪和PMI-E电致化学发光系统测定其光电性质.结果表明,ZnO-C60复合涂层电极具有较高的稳定性,在可见光辐照下,该电极显示...     

载有C60的TiO2纳米粒子光催化活性

以水溶性C₆₀和TiO₂粒子为前驱体,采用水热法制备了载有C₆₀的锐钛矿型TiO₂纳米粒子。应用X射线衍射、透射电子显微镜、红外光谱、紫外-可见漫反射光谱、荧光光谱对产物进行了表征。以对-硝基苯酚为模型污染物研究了产物的光催化活性,结果表明适量负载C₆₀可以提高TiO₂纳米粒子的光催化活性,C₆₀起着传输电子、促进TiO₂光生载流子分离的作用,且经7次循环使用后对-硝基苯酚的降解效率仍能达到74%。讨论了载有C₆₀的TiO₂纳米粒子光催化降解对-硝基苯酚的机理。     

Monotonicity of solutions of Fully nonlinear uniformly elliptic equations in the half-plane

In this paper we study the monotonicity of positive (or non-negative) viscosity solutions to uniformly elliptic equations F(∇u,D²u)=f(u) in the half plane, where f is locally Lipschitz continuous (with f(0)?0) and zero Dirichlet boundary conditions are imposed. The result is obtained without assuming the u or |∇u| are bounded.     

Random attractors for stochastic lattice dynamical systems in weighted spaces

In this paper, we first provide some sufficient conditions for the existence of global compact random attractors for general random dynamical systems in weighted space (p?1) of infinite sequences. Then we consider the existence of global compact random attractors in weighted space for stochastic lattice dynamical systems with random coupled coefficients and multiplicative/additive white noises. Our results recover many existing ones on the existence of global random attractors for stochastic lattice dynamical systems with multiplicative/additive white noises in regular l² space of infinite sequences.     

Homogenization of a parabolic model of ferromagnetism

This work deals with the homogenization of hysteresis-free processes in ferromagnetic composites. A degenerate, quasilinear, parabolic equation is derived by coupling the Maxwell-Ohm system without displacement current with a nonlinear constitutive law:

     

Large solution to nonlinear elliptic equation with nonlinear gradient terms

The aim of this paper is to study the qualitative behavior of large solutions to the following problem

     

Riesz means associated with certain product type convex domain

In this paper we study the maximal operators and the convolution operators Tδ associated with multipliers of the form