Quantitative Correlations for the Estimation of Thermodynamic and Molecular Properties of Pyridines and 2,2′-Bipyridyines

Standard heats of formation, entropies, ionization potentials, and molecular dipole moments of a series of pyridines have been calculated by MNDO, AM1 and PM3 methods. Linear relationship have been established which permit a priori estimation of thermodynamic and molecular characteristics of pyridines. Correlation have been found between the values of pK_a for 2,2′-bipyridines for aqueous solutions and their gas phase proton affinities.__________Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, 391–402, March, 2005.     

Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]

An elementary majorant-minorant method to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1,..., n}, where n is the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known results are proved easily by this method. Further, the inequalities in terms of all the lower moments are completely solved by the method. As examples, the most stringent new inequalities of degrees three and four are obtained. Simpler expressions of Mrgritescu's inequality (1987, Stud. Cerc. Mat., 39, 246–251), improving Galambos' inequality, are given.     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.     

Some exact expressions for the mean and higher moments of functions of sample moments

Examples of exact expressions for the moments (mainly of the mean) of functions of sample moments are given. These provide checks on alternative developments such as asymptotic series for n, and simulation processes. Exact expressions are given for the mean of the square of the sample coefficient of variation, particularly in uniform sampling; Frullani integrals studied by G. H. Hardy arise. It should be kept in mind that exact results for (joint) moment generating functions (mgfs) are of interest as they produce a means of obtaining exact results for (cross) moments—including moments with negative indices. Thus an exact expression for the joint mgf of the 1st two noncentral moments can be used to obtain the mean of the (c.v.)² (but not for the mean of the c..). A general expression is given for the moment generating function of the sample variance. The limitations of Fisher's symbolic formula for the characteristic function of sample moments (or more general statistics) are noted.This research was sponsored by the Applied Mathematical Sciences Research program, Office of Energy Research, U. S. Department of Energy under contract DE-AC0584OR21400 with the Martin Marietta Energy Systems. Inc.     

Transference numbers for ultra concentrated solutions of aqueous hydrochloric acid at 25°C

Transference numbers of HCl(aq) solutions at 25°C, from 0.01 to 13.6 mol-kg^–1(m) have been obtained by measuring the emf of cells with transference using hydrogen gas/platinum electrodes. Good agreement is obtained at concentrations up to 1 m with all previous data, and our results strongly corroborate those of King and Spiro over the 2–8m concentration range. The transference numbers of the hydronium ion fit the empirical equation, _H ^HCl = 0.821 + 0.0457m ^1/2 – 2.476×10^–2m – 1.90×10^–4 m ² – 1.45×10^–5 m ³ the maximum deviation in T _H ^HCl being 0.003.     

Comparative Characteristics of Some Physicochemical Properties of Azoles

We have carried out a correlation analysis of some physicochemical characteristics of pyrrole, pyrazole, imidazole, triazole, and tetrazole, calculated by the semiempirical quantum-chemical AM1 method. We have found the linear dependences of the ionization potential, the dipole moment, and the acidity on the -electron excess, and also the dependence of the ionization potential on the enthalpy of formation of the studied azoles.     

Mechanism and kinetics of the reduction of In(III) ions at a polycrystalline gold electrode from highly concentrated ZnCl2 solutions

Summary The mechanism of the cathodic reduction of In(III) at gold has been studied by rotating disc and ring-disc voltammetry in highly concentrated aqueous ZnCl₂ solutions. At concentration of the base electrolyte higher than 7 mol dm^–3, the voltammetric curves recorded at the disc electrode split into two well-separated waves which correspond to the successive charge transfer reactions: In(III) + 2e^– In(I) and In(I) + e^– In. By the use of coulometric and potentiometric techniques, the formal potentials of the In(III)/In(I), In(III)/In and In(I)/In redox couples as well as the equilibrium constants of the reproportionation reaction In(III) + 2 In 3 In(I) has been determined and discussed. The kinetic parameters of the In(III)/In(I) electrode reaction have been also evaluated and discussed.

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Mechanismus und Kinetik der Reduktion von In(III)-Ionen an der Goldelektrode in hochkonzentrierten wäßrigen ZnCl₂-Lösungen

Zusammenfassung Es wird der Mechanismus der Reduktion von In(III)-Ionen in hochkonzentrierten ZnCl₂ Lösungen mittels der Scheiben- und Ring-Scheiben-Elektrode aus Gold untersucht. Wenn die Konzentration des Grundelektrolyten 7 mol dm^–3 übersteigt, verteilen sich die erhaltenen Stromspannungskurven auf zwei gut gestaltete Stufen, die den konsekutiven Durchtrittsreaktionen In(III) + 2e^– In(I) und In(I) + e^– In entsprechen. Aufgrund der coulometrischen und potentiometrischen Messungen werden die Formal-Standardpotentiale der In(III)/In(I)-, In(III)/In-und In(I)/In-Redoxpaare, die Gleichgewichtskonstanten der Reproportionierungsreaktion In(III) + 2 In 3 In ermittelt. Die kinetischen Parameter der Durchtrittsreaktion In(III)/In(I) werden bestimmt und diskutiert.

     

Solvatochromism of 3-[2-(aryl)benzoxazol-5-yl]alanine derivatives

The photophysical properties of N-Boc-3-[2-(9-anthryl)benzoxazol-5-yl]-l-alanine methyl ester (BoxAnt) and N-Boc-3-[2-[4-(9′-(10′-butyl)anthryl)phenyl]benzoxazol-5-yl]-l-alanine methyl ester (BoxPhAnt) were studied in a series of solvents. Their absorption spectra are less sensitive to the solvent polarity than the corresponding fluorescence spectra which show a pronounced solvatochromic effect leading to large Stokes shifts. Using an efficient solvatochromic method, based on the empirical solvent polarity parameter , a large change of the dipole moment on excitation for BoxPhAnt has been found. From an analysis of the solvatochromic behaviour of the absorption and fluorescence spectra in terms of bulk solvent polarity functions, f(_r, n) and g(n), a larger excited-state dipole moment (about 8 D, ψ = 56) was obtained for BoxPhAnt than for BoxAnt (about 3 D, ψ = 0). Both applied methods gave similar values of the excited-state dipole moments for both compounds studied.     

利用全元素矩张量反演方法识别地下核爆炸

将震源矩张量中的各分量作为权重因子,利用基本Green函数的线性组合可以对地震波场进行描述,本文利用水平分层模型下的广义反射-透射系数方法的地震波场正演公式,反演了苏联东哈萨克斯坦地下核试验场的7次地下核爆炸、3次震中位置相近的天然地震的震源矩张量,反演结果表明地下核爆炸震源明显含有爆炸源成分,同时包含双力偶成分（DC）和线性偶极补偿源成分（CLVD）,且CLVD成分比重大,CLVD的存在可用层裂机制来解释;天然地震震源矩张量的反演结果表明,DC源为主要成分,符合剪切位错震源模式。

     

直剪试验过程中剪切面上法向应力变化规律分析

首先推导出不同剪切位移下试样截面惯性矩表达式,然后计算得到试样剪切面上归一化最大、最小法向应力随剪切位移变化的关系曲线,发现两法向应力及其差值随剪切位移的增大而增大,随试样剪切面直径或剪切边长的增大而减小。当试样剪切面直径和边长相同时,圆形试样剪切面上的法向应力要比方形上均匀些。当试样剪切面为矩形,沿矩形长边方向剪切时,其上法向应力的分布要比沿短边方向剪切时均匀些。建议尽量使用剪切面为圆形的大样进行直剪试验。