每个算子都是两个强不可约算子的和

本文证明了可分无穷维 Hilbert空间上每个有界线性算子均可写成两个强不可约算子之和 .这回答了文献 [9]中提出一个公开问题     

Proton-exchanged optical waveguides fabricated by glutaric acid

In this paper, we first report that a new proton source, glutaric acid, has been used to fabricate optical waveguides in Z-cut lithium niobate crystals. The relationship was experimentally established between proton-exchanged (PE) waveguide parameters and fabrication conditions. It is shown that this new organic acid can be used to obtain deep PE waveguides in fast diffusion speed (0.275 μm²/h at 221°C) and with low loss (0.2 dB/cm). It provides an alternative approach for fabricating PE waveguides in lithium niobate substrate.     

The magnetization behavior of nanocrystalline permanent magnets based on the Stoner–Wohlfarth Model

The magnetization behavior in nanocrystalline permanent magnets has been investigated using mean field Stoner–Wohlfarth model. The model is comparatively simple but allows the numerical treatment of extended nanostructures. The predominant intergrain exchange coupling is expressed by a mean field constant N_m in spite of no explicit relationship between N_m and the microstructure. By this model, the experimental phenomena, such as the remanence enhancement, the shape of demagnetization curve, the irreversible magnetization, the exchange bias field and their respective temperature dependence, can be well explained. The N_m dependence of magnetic properties has been extensively discussed in the present paper.     

Preparation of Phosphoric-Carboxylic Cation Exchangers from Wood Cellulose

Phosphorus-containing cellulose cation exchangers were synthesized by reaction of wood cellulose with orthophosphoric acid and the ternary polymer from glycidylmethacrylate, styrene, and maleic anhydride. The effects of the ratio of reactants, temperature, and duration of the reaction on the phosphorylation and exchange capacity of the modified cellulose material were studied.     

高电荷态Ar^q＋与Ne碰撞中入射离子电荷交换截面的研究

报道Ar^q Ne(q=8，9，11，12)碰撞体系中多电子转移过程，得到了多组实验测量电荷交换截面数据，讨论入射离子电荷交换截面、反冲离子产生截面与入射离子电荷态、能量以及散射离子电荷态的关系，并且将实验结果与Ar^q Ar碰撞体系进行对比研究。在修正分子库仑过垒模型的基础上，对实验现象做了合理的解释。     

Speciation Analysis of Inorganic Tin (Sn(II)/Sn(IV)) by Graphite Furnace Atomic Absorption Spectrometry Following Ion-Exchange Separation

A new method based on anion exchange resin separation and graphite furnace atomic absorption spectrometry (GFAAS) detection is proposed for the determination of inorganic tin species. The result showed that Sn(IV) was quantitatively retained on the resin when [HCl] = 9.0 mol · L⁻¹, but Sn(II) could not be adsorbed on the resin under the same condition. Thus, a separation of Sn(II) and Sn(IV) has been realized. When the concentration of NaOH solution was between 2.0–7.0 mol · L⁻¹, Sn(IV) that adsorbed on the resin could be eluated from the resin completely. Meanwhile, under the atmosphere and the nitrogen states, the translation between Sn(II) and Sn(IV) was investigated. Under the optimal conditions, the detection limit of Sn(IV) is 0.40 μg · L⁻¹ with RSD of 2.3% (n = 5, c = 2.0 μg · L⁻¹). The proposed method was applied to the speciation analysis of tin in different water samples and the recovery of total Sn was in the range of 98.7–101.7%. In order to verify the accuracy of the method, a certified reference water sample was analyzed and the results obtained were in good agreement with the certified value.     

A note on strongly π-regular rings

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x ⁿ=x ^{n +1} y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x ^m=x ⁿ. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

On co-semihereditary rings

A ringR is left co-semihereditary (strongly left co-semihereditary) if every finitely cogenerated factor of a finitely cogenerated (arbitrary) injective leftR-module is injective. A left co-semihereditary ring, which is not strongly left co-semihereditary, is given to answer a question of Miller and Tumidge in the negative. If _R U _S defines a Morita duality,R is proved to be left co-semihereditary (left semihereditmy) if and only ifS is right semihereditary (right co-semihereditary). Assuming thatS⩾R is an almost excellent extension,S is shown to be (strongly) right co-semihereditary if and only ifR is (strongly) right co-semihereditary. Project supported by the National Natural Science Foundation of China.     

耗散准模腔场与激子相互作用的量子统计性质

研究了耗散准模腔场与激子相互作用的量子统计特性 ,给出了当腔场初始处于真空态而激子处于真空态与粒子数态大于 2的叠加态时的腔场与激子能量交换的表达式。研究结果表明 ,激子和腔场可以呈现亚泊松分布状态 ,激子与腔场之间的关联是经典的 ,不存在Cauchy Schwartz不等式的偏离现象。