Coherent trace-class operators in Hilbert couples

In this paper it is proved that the ideal of trace-class operators acting in a couple of Hilbert spaces coincides with the ideal of coherent trace-class operators. A new formula is derived for theK-functional in the couple of algebras of all bounded linear operators acting in a Hilbert couple, and new interpolation theorems are proved for trace class operators.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 866–872, June, 1998.This research was partially supported by the International Science Foundation and the Russian Government under grant JD 7100.     

EIS and XPS studies on passive film of AISI 304 stainless steel in dilute sulfuric acid solution

Electrochemical impedance spectroscopy and XPS studies on AISI 304 stainless steel in naturally aerated 0.5 M H₂SO₄ solution were carried out at room temperature. The valuable model of the metal/solution interphase was established, and the reliable equivalent electrical circuits in the solution were presented. The analysis of the chemical composition of passive film on AISI 304 stainless steel was carried out by XPS. The passive film of AISI 304 stainless steel is composed of oxyhydroxides, Fe₂O_3, FeO, Cr₂O₃, NiO, sulfate, sulfite, and sulfide (FeS, NiS). It is reported that the ferrous sulfide film formed on AISI 304 stainless steel in the dilute sulfuric acid solution. The possible process in which sulfuric acid is reduced to sulfite and sulfide is proposed. The galvanic interaction of sulfide inclusions with the base alloy is introduced. Copyright © 2011 John Wiley & Sons, Ltd.     

Enhanced patch test of finite element methods

Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C^0–1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.     

薄膜润滑中的应力偶效应

利用应力偶理论计算了薄膜润滑的膜厚特性.计算结果表明:应力偶的作用相当于增加润滑剂粘度,其可以增加油膜厚度,提高承载能力;同时应力偶作用依赖于油膜尺寸,润滑油膜越低,其影响越明显.     

分子筛修饰电极的研究（Ⅰ）──氢醌／醌电对在分子筛修饰电极上的电化学行为

考察了中性分子电对Ｈ_２Ｑ／Ｑ在１３Ｘ型分子筛修饰电极上的电化学行为。发现Ｈ_２Ｑ／Ｑ电对在修饰电极上电响应迅速，为双电子可逆反应，不受溶液温度及电极与溶液相对运动的影响，而与溶液的ｐＨ值有关。当ｐＨ≤２．０时，修饰电极对Ｈ_２Ｑ／Ｑ电对的氧化／还原有明显的催化作用．     

双光子吸收效应对孤子和孤子对传输的影响

用分步傅立叶变换法求解含双光子吸收效应的光孤子NLS方程,研究了双光子吸收效应对一阶孤子和孤子对传输的影响,发现双光子吸收效应除对孤子产生等效损耗外,还影响了孤子对在传输中的相互作用。在特定的双光子吸收系数条件下双光子吸收效应可以使孤子对平行地向前传输。     

非对称的非局部塑性理论

从非局部连续场论出发，假定形变与局部转动均属微小，当存在体力矩出现非对称应力场时，设对称应力的能量函数和非对称应力的能量函数可以独立计算。基于热力学原理和屈服面的概念，建立了一种新的非对称－非局部弹塑性力学理论。     

一阶脉冲泛函微分方程非线性边值问题

考虑一阶脉冲泛函微分方程非线性边值问题,利用上下解方法和单调迭代技术得到了耦合解和唯一解存在的充分条件.所得结果改进和推广了文献的相关结果.     

瞬态电磁场对多孔洞目标耦合规律的数值研究

 运用时域有限差分（FDTD）方法,用数值方法研究了瞬态电磁场对开有多个孔洞的长方体的耦合规律。分别分析了不同极化方向、不同入射方向及不同带宽的瞬态电磁场的耦合效应。入射波极化方向与孔洞的短边平行时耦合入腔体的能量最多;相同振幅、不同上升前沿和带宽的入射波以窄带、快前沿耦合入的能量为多;多孔洞腔体内场衰减很快。     

Liquid-phase microextraction and fibre-optics-based cuvetteless CCD-array micro-spectrophotometry for trace analysis

Liquid-phase microextraction (LPME) has been investigated for trace analysis in the present work in conjunction with fibre-optic-based micro-spectrophotometry which accommodates sample volume of 1 μL placed between the two ends of optical fibres. Methods have been evolved for the determination of (i) 1-100 μM and 0.5-20 μM of thiols by single drop microextraction (SDME) and LPME in 25 μL of the organic solvent, respectively, involving their reaction with the Ellman reagent and ion pair microextraction of thiolate ion formed; (ii) 70 μg to 7 mg L⁻¹ of chlorine/chlorine dioxide by headspace in-drop reaction with alternative reagents, viz., mixed phenylhydrazine-4-sulphonic acid and N-(1-naphthyl)ethylenediamine dihydrochloride, o-dianisidine, o-tolidine, and N,N-diethyl-p-phenylenediamine; (iii) 0.2-4 mg L⁻¹ of ammonia by reaction with 2,4-dinitro-1-fluorobenzene to give 2,4-dinitroaniline which was diazotized and coupled with 1-naphthylamine, the resulting dye was subjected to preconcentration by solid-phase extraction and LPME; and (iv) 25-750 μg L⁻¹ of iodide/total iodine by oxidation of iodide by 2-iodosobenzoate, microextraction of iodine in organic solvent, and re-extraction into aqueous starch-iodide reagent drop held in the organic phase. LPME using 25-30 μL of organic solvent was found to produce more sensitive results than SDME. The cuvetteless spectrophotometry as used in combination with sample handling techniques produced limits of detection of analytes which were better than obtained by previously reported spectrophotometry.