单晶硅晶格间距的测量技术进展及应用

单晶硅晶格间距是许多重要物理常数测量的基础。本文介绍了硅晶格间距测量技术的发展历程,包括X射线干涉仪直接测量和晶格比较仪间接测量两种方法,以及影响测量结果不确定度的关键因素。得益于晶格间距测量的进展,在纳米尺度,硅晶格间距被国际计量局(BIPM)批准成为新的米定义复现形式。最后介绍了硅晶格在计量学中的应用,以及基于硅晶格实现纳米几何量测量的溯源体系的研究趋势。     

Efficient Quantum Dot Light-Emitting Diodes Based on Well-Type Thick-Shell CdxZn1−xS/CdSe/CdyZn1−yS Quantum Dots

Device grade quantum dots (QDs) require QDs ensembles to retain their original superior optical properties as in solution. QDs with thick shells are proven effective in suppressing the inter-dot interaction and preserving the emission properties for QDs solids. However, lattice strain–induced defects may form as the shell grows thicker, resulting in a notable photoluminescence quenching. Herein, a well-type Cd_xZn_1−xS/CdSe/Cd_yZn_1−yS QDs is proposed, where ternary alloys CdZnS are adopted to match the lattice parameter of intermediate CdSe by separately adjusting the x and y parameters. The resultant thick-shell Cd_0.5Zn_0.5S/CdSe/Cd_0.73Zn_0.27S QDs reveal nonblinking properties with a high PL QY of 99% in solution and 87% in film. The optimized quantum dot light-emitting diodes (QLEDs) exhibit a luminance of 31547.5 cd m⁻² at the external quantum efficiency maximum of 21.2% under a bias of 4.0 V. The shell thickness shows great impact on the degradation of the devices. The T₅₀ lifetime of the QLEDs with 11.2 nm QDs reaches 251 493 h, which is much higher than that of 6.5 and 8.4 nm QDs counterparts. The performances of the well-type thick-shell QLEDs are comparable to state-of-the-art devices, suggesting that this type of QDs is a promising candidate for efficient optoelectronic devices.     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

An Analogue of Distributivity for Ungraded Lattices

In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim.     

Around Multicolour Disordered Lattice Gas

We consider a system of multicolour disordered lattice gas, following closely the (monocolour) introduced by Faggionato and Martinelli^(3,4). We study the projection on the monocolour system and we derive an estimate of the closeness between grand canonical and canonical Gibbs measures. AMS Classification: Primary: 60K35, 82C20, 82C22     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)