Origin and meaning of the Fermi contact interaction

The Fermi-contact interaction (FCI) can easily be derived from 1st order perturbation theory applied to the non-relativistic wave equation for a spin-(1/2) particle of Lévy-Leblond, with the nuclear spin described by the field of an external magnetic dipole, and it results from the fact that the turn-over-rule for the operator is only valid if the derivatives implicit in are taken in the distribution sense. If one avoids to apply the turn-over-rule, the FCI is obtained without the need to introduce a -function. It is also shown that the formulation of a magnetic point dipole as the limit of an extended nucleus directly leads to the FCI. Traditional methods of the derivation of the FCI are analyzed in the light of this new interpretation. It is then explained why the perturbation expansions in powers of the magnetic moment of the nucleus necessarily diverges, but that the expression for the 1st order energy on which the concept of the FCI is based, can nevertheless be justified by means of the Hellmann-Feynman theorem with a correction term if singular wave functions are involved. Finally some comments on a theory beyond first order are made.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Carbon dioxide supercritical fluid chromatography-Fourier transform infrared spectrometry

Summary The coupling of carbon dioxide supercritical fluid chromatography with Fourier transform infrared spectrometry (SFC-FTIR) is a powerful tool for the separation and on-line identification of non-volatile compounds. The IR transparency of carbon dioxide in the Fermi resonance bands region versus its density has been studied. Functional groups with stretching vibrations outside the transparent window of carbon dioxide are examined. SFC-FTIR separations allow Gram-Schmidt reconstruction chromatograms or IR window chemigrams with high quality spectra to be obtained. This SFC-FTIR lightpipe (flow cell, beam condensing optics, narrow band detector) has allowed detection limits of 250ng for benzonitrile and 70ng for methyl benzoate to be reached. The feasibility of very rapid SFC-FTIR separations is shown along with the subsequent peak spectra.     

微量元素锌在治疗Bell麻痹中的作用

为探讨急性早期应用补锌和综合疗法治疗Bell麻痹 ,将 1 5 8例Bell麻痹患者 ,随机分成两组 :(1 )补锌组 (补锌 +综合疗法 ) ;(2 )对照组 (单纯综合疗法 )。对其进行了观察对比治疗 ,同时检测了所有患者治疗前后自身对照发锌值 ,还对所有患者进行了定位诊断、面神经电反应测试、并对面肌功能进行评分。结果表明 ,对定位诊断其病变在D段、面肌功能评分在 1 1分以下、面神经无电反应患者 ,即使给予早期综合治疗 ,效果仍较差 ,而早期给予补锌加综合治疗效果优于对照组 ,其它段内患者治疗次数和治愈天数也均优于对照组。可见微量元素锌在发挥免疫应答、免疫调控中的重要作用     

绿色供应链中消费者信用支付策略研究

本文考虑了一个由单一供应商和单一电商平台组成的绿色供应链,分析了三种不同支付策略(立即支付策略、分期付款策略以及最低还款策略)对供应链成员最优决策和利润的影响。研究表明:(1)免息期敏感系数对绿色营销水平和供应链成员利润均有正向影响。(2)信用支付会使产品产生溢价现象。但在一定条件下,信用支付策略可同时提高供应链成员利润和绿色营销水平,实现经济绩效和环境绩效的双赢。(3)手续费率较高时,若信用期限系数较小,立即支付策略最优;若信用期限系数适中,分期付款策略最优;否则最低还款策略最优。手续费率较低且信用期较小时,最低还款策略最优,否则立即支付策略最优。在此基础上,针对两种信用支付模型设计了成本分担和收益共享的组合契约,实现了供应链协调。     

Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynomial identities for finitizations of the Virasoro characters as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Dedicated to the memory of Piet Kasteleyn.     

Quantitative stability of variational systems: III.ε-approximate solutions

We prove that the-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that the-subgradient mapping is Lipschitz continuous.Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research.     

Synthesis and electronic properties of pentacene derivatives as promising n-type semiconductor candidates

Two pentacene derivatives 1 and 2 were synthesized from the Diels-Alder reactions of furan derivatives with 1,4-benzoquinone. They were characterized by the methods of ¹H — nuclear magnetic resonance spectroscopy (¹H-NMR), matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF MS), ultraviolet and visible spectrophotometry (UV-VIS), photoluminescence (PL) spectrometry and cyclic voltammetry (CV). The energy gaps of 1 and 2, taken directly from spectroscopic measurements, are broad as 2.72 and 2.46 eV, leading to blue and greenish blue photoluminescence, respectively. The LUMO and HOMO energy levels are −2.77 and −5.49 eV for 1, and −2.91 and −5.37 eV for 2, respectively. The low energy levels make both 1 and 2 good air-stabilities and promising n-type semiconductor candidates for use in organic electronics.     

Simultaneous quantitative analysis of ketanserin and ketanserinol in plasma by RP-HPLC with fluorescence detection

A sensitive and selective high-performance liquid chromatographic assay for the quantification of ketanserin and ketanserinol in human plasma was developed and validated. The procedure involves extraction of ketanserin and ketanserinol from plasma using an Extrelut NT-1 solid-phase extraction column. The chromatograph was equipped with a Hypersil BDS column (100 x 4.5 mm, 3 micro m particle size). Separation was performed with a mixture of acetate buffer 0.01 M, pH 4.9-methanol-acetonitrile (52:40:8, v/v/v). Detection was performed with fluorescence detection (lambda(ex) = 332 nm and lambda(em) = 410 nm). Calibration curves were linear (r(2) = 0.999) in the range 0-400 ng/mL for both ketanserin and ketanserinol. The repeatability coefficient for ketanserin and ketanserinol was 3.1 and 3.0%, respectively. The reproducibility coefficient for ketanserin and ketanserinol was 10.5 and 9.1%, respectively. The limit of quantification for both ketanserin and ketanserinol was 2.0 ng/mL. The mean recovery yield for both ketanserin and ketanserinol was 60%. In an 8 h work day approximately 60 samples, including calibration and reference standards, could be processed.     

由NO分子从头计算结果和紫外光电子能谱确定NO的分子结构

对于NO分子轨道的能级次序现有两种不同的说法,不少人根据NO与O_2~+是等电子体,由O_2~+分子的能级次序确定NO分子组态。本文用NO和O_2~(+)从头计算结果以及NO的紫外光电子能谱相结合的方法说明NO的5σ轨道是弱成键轨道,5σ的轨道能稍高于1π轨道能,也就是说NO的能级次序是与N_2分子相同的;NO与O_2~+虽是等电子体,但是能级次序并不相同,因此由O_2~+的能级次序确定NO分子的电子组态是不妥的。     

Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing ?ω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ?ω at the closed shells. These discontinuities diminish as N increases. For large N, ?ω becomes simply: ?ω?c₁N^?1/3+c₂N^?1. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001