Effects of π bond type,backbone size,and halogen on structural and spectroscopic properties of hydrogen‐bonded complexes of the X?H … π type between alkenes or alkynes and haloacids (HF and HCl)

The effects of CC bond type (double or triple), substituent (H or methyl), and halogen (F and Cl) on three properties of hydrogen‐bonded complexes formed between unsaturated hydrocarbons and HX (X?F, Cl) are studied. The properties comprise hydrogen bond distances (R_H), stabilization energies (SE), and frequency shifts (Δν). A 2³ factorial design technique, along with ab initio (HF and MP2) and DFT (B3LYP and PBE1PBE) calculations, has been employed. All three responses are mainly affected by the halogen, and when it is changed from F to Cl, R_H tends to increase, while SE tends to decrease. Surprisingly, the type of substituent is more important than the type of CC bond, for all three responses. Both effects tend to decrease R_H. Significant interaction effects are obtained for the type of CC bond along with the type of substituent, and for the type of substituent along with the type of halogen. Both interaction effects are smaller than the main effects and also tend to decrease R_H. The greatest SE values are obtained with PBE1 functional (BSSE + ZPE corrected values). Again, the next more important effect is due to the type of substituent, and the replacement of H by CH₃ group tends to increase SE. The effect due to the CC bond type is not significant, at all computational levels. The only interaction effect that is significant for SE (corrected) and Δν is between factors 1 (CC bond type) and 2 (substituent), but only at HF and B3LYP levels, and it tends to increase both properties. As the halogen changes from F to Cl, Δν tends to decrease. In contrast, changing the substituent from H to CH₃ leads to greater values of Δν. The effect of CC bond type is not significant at HF level, and when it is changed from double to triple Δν is decreased, at B3LYP and PBE1 levels. A suggestion as to how the results may point toward a better experimental detection of similar (π‐type) complexes is also given. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Comparing methods for design follow‐up: revisiting a metal‐cutting case study

Adding another fraction to an initial fractional factorial design is often required to resolve ambiguities with respect to aliasing of factorial effects from the initial experiment and/or to improve estimation precision. Multiple techniques for design follow‐up exist; the choice of which is often made on the basis of the initial design and its analysis, resources available, experimental objectives, and so on. In this paper, we compare four design follow‐up strategies: foldover, semifoldover, D‐optimal, and Bayesian (MD‐optimal) in the context of a metal‐cutting case study previously utilized to compare fractional factorials of different run sizes. Follow‐up designs are compared for each of a , , and Plackett–Burman initial experiments. Our empirical results suggest that a single follow‐up strategy does not outperform all others in every situation. This case study serves to illustrate design augmentation possibilities for practitioners and provides some basis for the selection of a follow‐up experiment. Copyright © 2013 John Wiley & Sons, Ltd.     

中高能重离子碰撞中的阵发混沌

在量子分子动力学模型计算多重碎裂基础上,应用阶乘矩方法分析了多重碎裂.对¹⁹⁷An(200MeV/u)+¹⁹⁷An碰撞系统进行了计算.发现多重分布有阵发混沌存在.并对临界现象做了初步讨论.     

Large deviations for integer centered poisson approximation

Large deviations in a centered Poisson approximation are examined. For lattice distributions, the centered Poisson approximation is more universal than the normal and standard Poisson laws. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 9–23, January–March, 1999. Translated by V. Čekanavičius     

400GeV/c pp碰撞赝快度分布涨落的分形分析

利用改进的多重分形矩分析了400GeV/c pp碰撞多重产生的分形行为.计算了广义维数D_q(q=2—5),并与由标度阶乘矩方法得到的结果作了比较.结果表明观察到了多重分形特征.对Fujio Takagi提出的分形分析方法作了探讨.     

400GeV/c pp碰撞连续阶数阶乘矩和多重分形分析

对华家照提出的F_q矩的矩阶数连续化方案进行了检验,发现它不能用于真实数据的分析,对此作了改进,使它能用于真实的实验数据的分析,对400GeV/c pp碰撞产生的带电粒子赝快度分布实验数据的分析结果表明,阶乘矩的矩阶数连续崐化方法是可行的,说明在400GeV/c pp碰撞多重产生过程中可能存在多重分形行为.     

Stanley's zrank conjecture on skew partitions

We present an affirmative answer to Stanley's zrank conjecture, namely, the zrank and the rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs are determined by the number of zero entries. We also give a characterization of the rank in terms of the Giambelli-type matrices of the corresponding skew Schur functions. Our approach also applies to the factorial Cauchy matrices and the inverse binomial coefficient matrices.

     

Central Factorial Numbers and Values of Bernoulli and Euler Polynomials at Rationals

The nth order derivatives of tan x and sec x may be represented by polynomials P _n (u) and Q _n (u) in u = tan x, which are known as the derivative polynomials for the tangent and secant and have occurred in diverse contexts. In this paper, explicit representations of P _n (u) and Q _n (u) are derived in terms of the central factorial numbers of the second kind, and the values of the Bernoulli and Euler polynomials at rationals are expressed by means of these polynomials.     

Optimization and modeling of synthesis parameters of neodymium(III) bromide by dry method using full factorial design analysis

The synthesis of neodymium(III) bromide (NdBr₃) by sintering brominating of neodymium oxide (Nd₂O₃) with ammonium bromide (NH₄Br) was investigated. The influence of various synthesis parameters (temperature, contact time and stoichiometry) on the reaction yield was studied and optimized. The main interaction effects of the synthesis parameters on the reaction yield were also determined by a full 2³ factorial designs with six replicates at the center point.This study showed that the optimum conditions for the synthesis of NdBr₃ are following: contact time t = 60 min, stoichiometry in moles Nd₂O₃:NH₄Br = 1:24 and temperature T = 400 °C. The reaction yield for these parameters was equal to 97.80%. The first order model was obtained to predict the reaction yield as a function of these three parameters. It was shown that all parameters have a significant positive influence on reaction yield. In addition it was pointed out also that the interaction effects between them are significant.