Lemniscates and inequalities for the logarithmic capacities of continua

It is shown that if P(z) = z ⁿ + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2^?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained.     

代数基本定理的另一证明

在复变函数论中,用了两种不同的方法证明了代数基本定理。文章从另一种角度:用映射的观点证明该定理。     

模糊集合论在矿山控制网布设和图纸质量评定中的应用

应用模糊数学方法研究和处理矿山测量中存在的具有“模糊性”的问题。例如控制网布设方案及矿山测量图纸质量的综合评判。它能更准确地描述用精确数学模型难以描述的问题。     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

Structural determinants of steroids for cytochrome P450 3A4-mediated metabolism

Cytochrome P450 3A4 (CYP3A4), a major member of cytochrome P450 isoenzymes, metabolizes the majority of steroids in 6β-position. For the purpose of determining requisite structural features of a series of structurally related steroids for CYP3A4-mediated metabolism, three-dimensional pharmacophore modeling as well as electrotopological state map were conducted for 15 steroids. Though prior studies speculated that the chemical reactivity of the allylic 6β-position might have a greater influence on CYP3A4 selective 6-hydroxylation than steric constraints in the enzyme, our results reveal that for CYP3A4 steroidal substrates, it is not the chemical reactivity of atoms at 6β-site, but the pharmacophoric features, i.e. the two hydrophobic rings together with two H-bond donors, that act as the key factors responsible for determining the CYP3A4 selective 6-hydroxylation of steroids.     

Dual microband electrodes: current distributions and diffusion layer ‘titrations’. Implications for electroanalytical measurements

The simulation of transport to double microband electrodes in generator–collector mode is reported focusing especially on the ‘titration curve’ approach to electroanalysis in which a titrant is electrogenerated from a redox active precursor on the generator electrode and reacts homogeneously with the target analyte. The current on the detector electrode reflects the amount of titrant ‘surviving’ passage between the two electrodes. The form of the titration curve – plots of detector current as a function of generator current – is shown to be highly sensitive to the electrode kinetics of the redox couple driven at the generator electrode. Accordingly the naïve use of such methodology for analysis without accompanying simulation and kinetic analysis is fraught with danger. Use of the conformal mapping approach in combination with the ADI method for investigation of the ‘titration’ current distributions at the double band system gives fast and precise simulation of this and similar problems. Convergence analysis is described which allows for the automatic selection of the simulation grid size so as to obtain a chosen accuracy (for example 1%) of the current for all experimentally meaningful values of the geometrical and physico-chemical parameters of the system to be investigated.     

Velocity map imaging of the photolysis of n-C4H9Br in UV region

Using velocity map ion imaging technique, the photodissociation of n-C₄H₉Br in the wavelength range 231–267 nm was studied. The results and our ab initio calculations indicated that the absorption of n-C₄H₉Br in the investigated region originated from the excitations to the lowest three repulsive states, as assigned as 1A″, 2A′ and 3A′ in C_s symmetry. Dissociations occurred on the PES surfaces of the three states, terminating in C₄H₉+Br (²P_3/2) or C₄H₉ + Br^* (²P_1/2) as two channels, and being impacted by an avoided crossing between the PES surfaces of the 2A′ and 3A′ states. The transition dipole to the 1A″ state was perpendicular to the symmetry plane, so perpendicular to the C–Br bond. The transitions to the 3A′ state was polarized parallel to the symmetry plane, and also parallel to the C–Br bond. While the transition dipole to the 2A′ state was in the symmetry plane, but formed an angle of about 53.1° with the C–Br bond. We have also determined the avoided crossing probabilities, which affected the relative fractions of the individual pathways, for the photolysis of n-C₄H₉Br near 234 nm and 267 nm.     

Separation of peptides and proteins by capillary electrophoresis using acidic buffers containing tetraalkylammonium cations and cyclodextrins

A method for improving separations of peptides and other positively charged species in capillary zone electrophoresis with untreated capillaries using acidic buffers containing tetraalkylammonium cations is described. Tetramethylammonium and tetrabutylammonium cations dynamically modify the capillary surface, leading to a reversal in the direction of the electroosmotic flow. As a result, the adsorption of positively charged peptides and proteins is minimized, and resolution and peak capacity are improved as the migration of cationic analytes is counterbalanced by the electroosmotic flow. The combining effect of reversing electroosmotic flow and cyclodextrin inclusion complexation on separations of closely related peptides and a protein mixture, as well as tryptic digest of hemoglobin is demonstrated.     

技能映射通过析取模型诱导的多分知识结构

基于程序性知识的评估,提出由项目自身的状态结构诱导多分知识结构的方法,以建立适用于问题解答的多分评估体系.首先,根据各项目的解答或操作步骤设定响应值集,通过项目状态转移函数定义项目状态空间;然后,用操作程序表示技能,由过程函数导出析取的技能映射;最后,讨论技能映射通过析取模型诱导的多分知识结构.结果表明：技能映射通过析取模型诱导的多分知识结构是多分知识空间.