范畴中态射集的加权减序

利用态射的加权广义逆,引进并讨论态射集中的加权减序和加权星序.给出了态射集中的加权减序的一些刻画和性质以及加权减序和加权星序之间的关系.加权减序和加权星序都是态射集中的新的偏序.所得结果均可应用于矩阵理论中.
关键词：态射;加权广义逆;加权减序;加权星序     

Combinatorial solutions to normal ordering of bosons

We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions — the Stirling and Bell numbers, Bell polynomials and Dobinski relations — lead to calculational tools, which allow to find explicitly normally ordered forms for a large class of operator functions. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Rook numbers and the normal ordering problem

For an element w in the Weyl algebra generated by D and U with relation DU=UD+1, the normally ordered form is w=∑c_i,jUⁱD^j. We demonstrate that the normal order coefficients c_i,j of a word w are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients c_i,j. We calculate the Weyl binomial coefficients: normal order coefficients of the element (D+U)ⁿ in the Weyl algebra. We extend these results to the q-analogue of the Weyl algebra. We discuss further generalizations using i-rook numbers.     

A Tukey decomposition of 𝒫κλ and the tree property for directed sets

Generalizing a result of Todor?evi?, we prove the existence of directed sets D, E such that D ? ??_κλ and E ? ??_κλ but D × E ≥ ??_κλ in the Tukey ordering. As an application, we show that the tree property for directed sets introduced by Hinnion is not preserved under products. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of charge ordering in NaxCoO2

A simple microscopic model of charge ordering in the Na_xCoO₂ system is presented. The model takes into account the interplane interactions between the ordered Na ions and d electrons from the CoO₂ layers as well as the nearest-neighbor intraplane Coulomb interactions between d electrons. It is shown that a driving force of charge ordering in the CoO₂ layers is the interplane interaction that alone is able to describe various types of inhomogeneous charge ordering (e.g., the striped phases) as well as to predict correctly the conducting properties of the system.     

On some measures and distances for positive random variables

A number of conventional measures of risk as real‐valued functions on the space of positive random variables are considered: the expected shortfall, the mean excess over the threshold, the stop‐loss and some others. Ordering of risks, based on these measures and the distances between corresponding distribution functions, are described. The perturbed measures, describing the effect of changing environment, are discussed. These measures are defined by the accelerated life and proportional hazards models widely used in reliability and survival analysis. The case of a random environment is of a prime interest in the paper. The main result states that if, for instance, the stochastic environment is ‘neutral in expectation’ with respect to the baseline one, the distance between the corresponding distribution functions can be still sufficiently large. Copyright © 2003 John Wiley & Sons, Ltd.     

Nd0.5Ca0.5Mn1-xAlxO3 (x=0,0.03)体系中电荷有序态的超声研究

系统研究了Nd0．5Ca0．5Mn1-xAlxO3(x=0,0．03)单相多晶样品在低温下的电磁性质和超声特性．电阻和磁化率测量表明,Nd0．5Ca0.5O3体系在TCO-257 K处发生了电荷有序相变．超声声速从室温开始随着温度的降低逐渐减小,并在TCO附近达到最小,之后,随着温度的进一步降低,声速急刷增加,同时伴随着一个尖锐的超声衰减峰出现.TCO附近的超声异常表明体系中存在着强烈的电-声子相互作用,该电-声子耦合来源于Mn3 的Jahn-Teller效应．在低温下,出现了另一个超声衰减峰,它的出现归结为反铁磁相与顺磁相之间的相分离现象.随着Al在Mn位的掺入,超声声速的最低点和衰减峰向低温移动,表明体系中的电荷有序态和反铁磁相均被部分抑制,     

Phase Separation Driven by a Fluctuating Two-Dimensional Self-Affine Potential Field

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar–Parisi–Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetry of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features.     

Demand variability and incentives in inventory-based contracts

We present some results on the impact of demand variability on stocking policies and incentives to forecast, in the context of single period inventory-based contracts in a manufacturer-retailer channel.     

Microstructural evolution of slowly solidified Cu-Ti-Zr-Ni amorphous alloy

The microstructures of slowly solidified Cu-Ti-Zr-Ni bulk amorphous alloy were identified by X-ray diffractometry (XRD) and transmission electron microscope (TEM). XRD and TEM examinations show that the deep eutectic structures of the tested alloy consist of CuTi₂-Cu₁₀Zr₇、Cu₃Ti-CuZr、Cu₃Ti-Cu₁₀Zr₇-CuZr low-order eutectics. Moreover, short-range ordering clusters in the melt with configuration similar to that of Cu₁₀Zr₇ compound may contribute to the glass forming ability of bulk amorphous Cu-Ti-Zr-Ni alloy.