Internal dynamics of flexible molecules: Cyclohexane

Summary The international motions of a single cyclohexane molecule are studied by molecular dynamics calculations. Classical trajectories are calculated by integrating Newton's equation of motion. The potential functions used are essentially the same as in Allinger's MM2 program which is widely applied for calculations on conformational energies of organic molecules.Geometries and relative energies are reported for all stable low energy conformers and some transition states of cyclohexane. Vibrational frequencies of classical oscillations of individual bonds — computed for ethane as reference system — are close to the experimental values.Two trajectories of the molecular dynamics of cyclohexane were simulated. In the first we were able to follow the process of ring inversion: chair twisted forms inverted chair. The reaction path is analysed in detail and compared with static approaches. The second trajectory shows the correlated reorientation of the possible twisted forms alone. This process is known as pseudorotation.Dedicated to Prof. Dr. Karl Schlögl     

Chaotropic Monovalent Anion‐Induced Rectification Inversion at Nanopipettes Modified by Polyimidazolium Brushes

A nonintuitive observation of monovalent anion‐induced ion current rectification inversion at polyimidazolium brush (PimB)‐modified nanopipettes is presented. The rectification inversion degree is strongly dependent on the concentration and species of monovalent anions. For chaotropic anions (for example, ClO₄^?), the rectification inversion is easily observed at a low concentration (5 mm ), while there is no rectification inversion observed for kosmotropic anions (Cl^?) even at a high concentration (1 m ). Moreover, at the specific concentration (for example, 10 mm ), the variation of rectification ratio on the type of anions is ranged by Hofmeister series (Cl^?≥NO₃^?>BF₄^?>ClO₄^?>PF₆^?>Tf₂N^?). Estimation of the electrokinetic charge density (σ^ek) demonstrates that rectification inversion originates from the charge inversion owing to the over‐adsorption of chaotropic monovalent anion. To qualitatively understand this phenomenon, a concentration‐dependent adsorption mechanism is proposed.     

Ab initio study of the structure and conformations of 2-fluoroethanal in the ground and lowest excited electronic states

The structure of the conformationally flexible 2-fluoroethanal molecule (CH₂FCHO, FE) in the ground (S₀) and lowest excited triplet (T₁) and singlet (S₁) electronic states was investigated by ab initio quantum-chemical methods. The FE molecule in the S₀ state was found to exist as two conformers, viz., as cis (the F—C—C—O angle is 0°) and trans (the F—C—C—O angle is 180°) conformers. On going both to the T₁ and S₁ states, the FE molecule undergoes substantial structural changes, in particular, the CH₂F top is rotated with respect to the core and the carbonyl CCHO fragment becomes nonplanar. The potential energy surfaces for the T₁ and S₁ states are qualitatively similar, viz., six minima in each of the excited states of FE correspond to three pairs of mirror-symmetrical conformers. Based on the potential energy surfaces calculated for the FE molecule in the T₁ and S₁ states, the one-dimensional problems on the torsion and inversion nuclear motions as well as the two-dimensional torsion-inversion problems were solved.     

聚氨酯(PU)/聚乙烯醇(PVA)共混体系的有关性能及其模型研究

本文研究了聚氨酯(PU)-聚乙烯醇(PVA)共混体系的动态力学性质、相逆转现象和透气性能.发现当PVA重量含量为30-50％时,共混体系发生了连续相与分散相的逆转.进一步,通过力学模型描述了该共混体系的模量-组成关系、动态力学温度谱以及透气系数与PVA含量的关系曲线.所有实验数据都落在理论预测的范围内,并分别与改进的Kerner模型和组合Kerner模型相符合.     

Fourier Inversion Formulas in Option Pricing and Insurance

Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (S – K, 0) also arises in excess-of-loss or stop-loss insurance, and we show that Fourier methods may be used to compute them. In this paper, we take the idea of using Parseval’s theorem further: (1) formulas requiring weaker assumptions; (2) relationship with classical inversion theorems for probability distributions; (3) formulas for payoffs which occur in insurance. Numerical examples are provided.      

Density functional and spectroscopic studies of nitrogen inversion in substituted dizocilpines

While developing a synthesis towards tagged dizocilpine (MK‐801) analogues, we observed highly restricted inversion of a nitrogen centre in a number hydroxylamines obtained as key intermediates. These compounds are shown to possess some of the structural elements which are expected to significantly hinder the nitrogen inversion, potentially leading to hydroxylamines with a chiral nitrogen centre. Free energy barriers (ΔG^≠) of the nitrogen inversion were estimated to be ca. 22 kcal mol^?1 at temperatures near 420 K using variable temperature NMR measurements in DMSO‐d₆. Further density functional studies of a number model systems were undertaken in order to better rationalize the measured inversion barriers and follow the role of various structural factors in raising the barrier height of the nitrogen inversion process. Copyright © 2008 John Wiley & Sons, Ltd.     

Radon transforms on affine Grassmannians

We develop an analytic approach to the Radon transform , where is a function on the affine Grassmann manifold of -dimensional planes in , and is a -dimensional plane in the similar manifold k$">. For , we prove that this transform is finite almost everywhere on if and only if , and obtain explicit inversion formulas. We establish correspondence between Radon transforms on affine Grassmann manifolds and similar transforms on standard Grassmann manifolds of linear subspaces of . It is proved that the dual Radon transform can be explicitly inverted for , and interpreted as a direct, ``quasi-orthogonal" Radon transform for another pair of affine Grassmannians. As a consequence we obtain that the Radon transform and the dual Radon transform are injective simultaneously if and only if . The investigation is carried out for locally integrable and continuous functions satisfying natural weak conditions at infinity.

     

Study of gain flatness for multi-channel amplification in single stage EDFA for WDM applications

In this paper, gain flatness is studied for simultaneous 16-ITU-T channel amplifications at C-band (1,532–1,558 nm) in a single stage EDFA for WDM application at different average inversion levels. The inversion levels are varied due to the change of the input signal levels from the targeted operating point and also for dropping few numbers of channels. Specially designed gain flattening filter (GFF) is used in order to get the flat gain with gain variation ±0.5 dB for −20 dBm/ch input signal power (total input signal power is −8.0 dBm) at a fixed average inversion level which is maintained by proper selection of optimum fibre length and pump power. A specific loss spectrum of GFF is obtained by writing a chirped fibre Bragg grating of length 20 mm. Gain variations are studied by changing the total input signal levels from −8.0 dBm to −20.0 dBm and maintained within 20.0 ± 0.5 dB by using automatic gain control (AGC) circuit. About 15 out of 16 channels are dropped and observed ± 0.5 dB gain-variation which is an important parameter in optical network system.     

A review ofL=λW and extensions

A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.     

非对称Abel逆变换研究及其在等离子体辐射功率分析中的应用

一、引言 在实验等离子体物理中,常遇到测量量是待求物理量沿等离子体截面弦的线积分值,为待求量,L为弦长。从测量到的I(x)值,求出i r值的Abel逆变换,在等离子体诊断的数据处理中得到了广泛应用。 在假定等离子体截面为中心对称的前提条件下,人们对Abel逆变换方法做了很多的研