Vanishing Viscosity Limit of the Compressible Navier–Stokes Equations for Solutions to a Riemann Problem

We study the vanishing viscosity limit of the compressible Navier–Stokes equations to the Riemann solution of the Euler equations that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a family of smooth solutions to the compressible Navier–Stokes equations that converges to the Riemann solution away from the initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first mathematical justification of this limit for the Navier–Stokes equations to the Riemann solution that contains these two typical nonlinear hyperbolic waves.     

Empirical likelihood for AR-ARCH models based on LAD estimation

By employing the empirical likelihood method,confidence regions for the stationary AR(p)-ARCH(q) models are constructed.A self-weighted LAD estimator is proposed under weak moment conditions.An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained.Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy,especially for relative small size of observation.     

Global well‐posedness of the compressible Euler with damping in Besov spaces

In this paper, we consider the Cauchy problems for compressible Euler equations with damping. In terms of the Littlewood–Paley decomposition and Bony's para‐product formula, we prove the global existence, uniqueness and asymptotic behavior of the solution in the critical Besov space comparing with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

Optical transmission through an interface between subwavelength slits

This paper studies optical transmission through an interface between two slits with different widths in a sheet composed of an ideal conductor. Such a structure is of potential use in fabricating optical diode and may be the simplest one compared to other designs. Our calculations show that there is a critical wavelength. When the light wavelength is below the critical wavelength, the transmissivity is unidirectional. The expression of the stable transmissivity as a function of the ratio of the widths of the two slits was obtained analytically. Particularly, at the critical wavelength, the transmissivities are zero. This phenomenon has great potential for application in the manufacture of wavelength blockers.     

Theoretical studies of the effect of electron-withdrawing dicyanovinyl group on the electronic and charge-transport properties of fluorene-thiophene oligomers

At the quantum-chemical level, we characterize some important parameters that control photoelectronic properties of three π-conjugated fluorene-thiophene oligomers namely, 2,7-di(2-thienyl)-9,9-dihexylfluorene, 2,5-Bis-(9H-fluorene-2-yl)-thieno[3,2-b]thiophene and 2,7-Bis[5-(1,1-dicyanovinyl)thiophene-2-yl]-9,9-di-n-hexylfluorene (FTCN). The geometric and electronic structures of these compounds in the ground and the lowest singlet excited states were studied using density function theory. By employing the incoherent transport model, the electron and hole mobilities were evaluated on a wide variety of nearest-neighbor charge transfer pathways. These results show that the chemical modifications by changing linkage mode or introducing the electron-withdrawing group could improve the charge transfer, especially for FTCN. Meanwhile, it is found that the packing effect weakens the emission intensity to some extent according to the simulations of photoluminescences of dimers.     

CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong s...     

普通物理综合设计实验课教学方法改革初探

开设普通物理综合设计实验课程目的在于培养学生动手能力、分析问题解决问题能力和创新能力。本文以首都师范大学物理系开设的普通物理综合设计实验为例讨论了具体的教学方法和过程,首先通过设计大量的预习思考题提高学生预习的针对性和预习效果,通过分组讨论来理解实验原理,并给出设计思路,最后通过实际实验锻炼学生的动手能力。该方法取得了良好的教学效果。     

含氟二羧酸和含氮配体与过渡金属(Ⅱ)配合物的合成、表征及晶体结构

水热法合成了5个新的配位聚合物:[Cd(TFSA)(2,2’-bpy)2]n(1),[Mn(HFGA)(phen)2]n(2),[Co(TFSA)(bpp)2(H2O)2]n(3),[Zn(TFSA)(bpp)2(H2O)2]n(4)和[Cu(HFGA)(phen)]n(5)(TFSA=四氟丁二酸,HFGA=六氟戊二酸,2,2’-bpy=2,2’-联吡啶,phen=1,10-邻菲啰啉,bpp=1,3-二吡啶基丙烷),通过X射线单晶衍射确定了配合物的晶体结构.配合物1和2具有相似的1D链结构,四氟丁二酸和六氟戊二酸以两个单齿羧基氧原子分别配位于Cd2+和Mn2+离子,2,2’-联吡啶和1,10-邻菲啰啉分别螯合配位于Cd2+和Mn2+离子.配合物3和4具有相似的1D链结构,1,3-二吡啶基丙烷以两个端基氮原子桥联金属离子,四氟丁二酸和六氟戊二酸分别以单齿方式配位.配合物5是具有{4.82}拓扑的2D网结构,六氟丁二酸配体通过单齿/双齿-桥联模式连接Cu2+离子.5个配合物均通过分子间弱作用进一步构筑成3D超分子结构.     

Synthesis and Characterization of Three Vanadium（Ⅴ） Complexes Incorporating Tridentate Hydrazone Ligands of Thiophene-2-carboxylic Hydrazide and 2-Furoic Acid Hydrazide

Divanadium(Ⅴ) complex [VO(aptch)(μ-OCH3)]2(1) and two monovanadium(Ⅴ) complexes [VO(apfah))(OEt)](2a and 2b,H2aptch = 2-hydroxyacetophenone thiophene-2-car-boxylic hydrazone,H2apfah = 2-hydroxyacetophenone 2-furoic acid hydrazone) have been synthesized and characterized.Single-crystal X-ray diffraction studies reveal that 1 is a cen-trosymmetric dimer bridged by two methoxido O-atoms.Complex 1 crystallizes in the monoclinic crystal system,space groups P21/c with a = 7.4825(4),b = 17.0928(11),c = 11.6961(7) ,β = 98.172(4)o,Z = 2,F(000) = 728,μ = 0.829 mm-1,the final R = 0.0457 and wR = 0.1137 for 2654 observed reflections with I > 2(I).The vanadium(V) is coordinated to the tridentate ligand,ethanol molecule to form a distorted square-pyramidal geometry,complexes 2a and 2b.Although 2a and 2b have the same asymmetric unit,they belong to different space groups.Complex 2a crystallizes in the monoclinic crystal system,space groups P21/n with a = 10.2293(2),b = 15.6660(3),c = 10.6298(2) ,β = 116.259(1)o,Z = 4,μ = 0.676 mm-1;complex 2b crystallizes in the triclinic crystal system,space groups P with a = 8.2808(4),b = 9.4704(5),c = 10.0819(5) ,α = 86.133(3),= 81.956(3),γ = 80.248(3)o,Z = 2 and μ = 0.670 mm-1.The hydrogen bonds are found to exist in 2b only.The crystal structure is stabilized by intermolecular hydrogen bonds of C-H···O.