Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities

We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111: 431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory 111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of the proposed method to a solution of the general mixed monotone variational inequality.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

The solution existence of general variational inclusion problems

We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.     

列修正拟Newton法在并行算法中的应用

本文利用解非线性方程组的列修正拟Newton法给出了常微分方程数值解法中的Adams内插公式的并行计算方法,并证明了该方法的收敛性     

Development of a mild mercaptoethanol extraction method for determination of mercury species in biological samples by HPLC–ICP-MS

A mild, efficient and convenient extraction method of using 2-mercaptoethanol contained extractant solution combined with an incubator shaker for determination of mercury species in biological samples by HPLC–ICP-MS has been developed. The effects of the concentration of 2-mercaptoethanol, the composition of the extractant solution and the shaking time on the efficiency of mercury extraction were evaluated. The optimization experiments indicated that the quantitative extraction of mercury species from biological samples could be achieved by using 0.1% (v/v) HCl, 0.1% (v/v) 2-mercapoethanol and 0.15% (m/v) KCl extractant solution in an incubator shaker for shaking overnight (about 12 h) at room temperature. The established method was validated by analysis of various biological certified reference materials, including NRCC DOLT-3 (dogfish liver), IAEA 436 (tuna fish), IAEA MA-B-3/TM (garfish filet), IAEA MA-M-2/TM (mussel tissue), GBW 08193 (bovine liver) and GBW 08572 (prawn). The analytical results of the reference materials were in good agreement with the certified or reference values of both methyl and total mercury, indicating that no distinguishable transformation between mercury species had occurred during the extraction and determination procedures. The limit of detection (LOD) for methyl (CH₃Hg⁺) and inorganic mercury (Hg²⁺) by the method are both as 0.2 μg L⁻¹. The relative standard deviation (R.S.D.s) for CH₃Hg⁺ and Hg²⁺ are 3.0% and 5.8%, respectively. The advantages of the developed extraction method are that (1) it is easy to operate in HPLC–ICP-MS for mercury species determination since the extracted solution can be directly injected into the HPLC column without pH adjustment and (2) the memory effect of mercury in the ICP-MS measurement system can be reduced.     

H-quadrupolar coupling-based analysis of stereochemical and regiochemical memory in the Pd-catalysed allylic alkylation of iso-cinnamyl type substrates employing the chiral monophosphine ligands ‘MOP’ and ‘MAP’

The reaction of iso-cinnamyl acetate with NaC(Me)(CO₂Me)₂, catalysed by Pd-‘MOP’ (MOP=2-methoxy-2′-diphenylphosphino-1,1′-binaphthalene) is known to proceed with a regiochemical memory effect that results in the predominant generation of the branched alkylation product. The analogous reaction employing ‘MAP’ as ligand (MAP=2-N,N-dimethylamino-2′-diphenylphosphino-1,1′-binaphthalene) proceeds with ‘normal’ regioselectivity to generate predominantly the linear isomer of product. A ²H-NMR based analysis, employing quadrupolar coupling in a chiral liquid crystal matrix, has been developed to facilitate the simultaneous study of the regiochemical and stereochemical outcome of the reaction of both enantiomers of iso-cinnamyl ester substrates in ²H-labelled but racemic samples. The analysis allows the comparison of relative rates of two competing isomerisation processes occurring in the π-allyl intermediates in the Pd-catalysed reaction, one of which facilitates asymmetric induction, the other resulting in loss of regiochemical memory. It is demonstrated that the two processes are partially coupled and that this then limits the attainment of high global enantiomeric excess in the branched product to reactions that proceed with low regiochemical retention. A key factor for the observation of high regiochemical memory is found to be the nucleophilicity of the malonate anion and the electrophilicity of the Pd-π-allyl intermediate with reduction in the reactivity of either partner resulting in the onset of substantial loss of memory.     

An implicit function theorem: Comment

In Ref. 1, Jittorntrum proposed an implicit function theorem for a continuous mappingF:R ⁿ ×R ^m R ⁿ, withF(x ⁰,y ⁰)=0, that requires neither differentiability ofF nor nonsingularity of _x F(x ⁰,y ⁰). In the proof, the local one-to-one condition forF(·,y):A R ⁿ R ⁿ for ally B is consciously or unconsciously treated as implying thatF(·,y) mapsA one-to-one ontoF(A, y) for ally B, and the proof is not perfect. A proof can be given directly, and the theorem is shown to be the strongest, in the sense that the condition is truly if and only if.     

Variational reactive scattering calculations: computational optimization strategies

Summary We have developed efficient and accurate techniques for the calculation of quantum mechanical reaction probabilities of atom-diatom exchange reactions in the gas phase, and we have optimized a computer code employing these techniques and applied it sucessfully to several systems. In this paper we consider further strategies for improving the algorithm to allow even more demanding applications. In this context, improvement means that equivalent results can be obtained using fewer computational resources (computer time or storage) or that an equivalent expenditure of resources can yield higher accuracy. The new strategies discussed here lead to improvement in both of these areas. Two areas of special focus in the present paper are (i) the finite difference boundary value method used for calculating distorted wave Green's functions and regular solutions for scattering by the distortion potential and (ii) the choice of the distortion potential itself. Among other results included here is the first application of the outgoing wave or scattered wave variational principle to reactive scattering.     

Freon (CHF<Subscript>3</Subscript>)-assisted atomization for the determination of titanium using ultrasonic slurry sampling–graphite furnace atomic absorption spectrometry (USS–GFAAS): a simple and advantageous method for solid samples

A simple and advantageous method for the determination of titanium using graphite furnace atomic absorption spectrometry with slurry sampling has been developed. Titanium is one of the refractory elements that form thermally stable carbides in the graphite tube, which leads to severe memory effects. Trifluoromethane (Freon-23) was applied in the purge gas during the atomization step or alternatively just prior to the atomization to successfully eliminate the problems of carbide formation and increase the lifetime of the furnace tube which could be used for more than 600 heating cycles. A flow rate of 40 mL min^–1 (5% of Freon in argon) was used to obtain symmetrical peaks with no tailing. However, when the gas flow rate was too high (250 mL min^–1) the peak-tailing and memory effects reappeared. Ti was determined in various materials covering a wide range of concentrations, from 2.8 g g^–1 to 12% (m/m) Ti. The accuracy of the method was confirmed by analyzing certified reference materials (CRMs) or by comparing the results with those obtained using inductively coupled plasma–atomic emission spectrometry (ICP–AES) after decomposition of the samples. The materials analyzed were soil, plant, human hair, coal, urban particulate matters, toothpaste, and powdered paint.     

YD-601型彩色液晶显示器的接口设计

介绍了YD-601型彩色液晶显示器的工作原理,采用计算机接口及内存映射等技术,实现了320×240的16色位图彩色图像显示。