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.     

A new torsion-rotation fitting program for molecules with a sixfold barrier: Application to the microwave spectrum of toluene

A new program is described for fitting rotation-torsion energy levels in molecules like toluene, in which the frame (C₆H₅) has C_2v symmetry and the methyl top has C_3v symmetry, i.e., for molecules where the internal rotation barrier is expanded in cos6nα, where α is the internal rotation angle and n = 1,2,…. The program is based on the theoretical framework developed by Sørensen and Pedersen in their application of the Longuet-Higgins permutation-inversion group G₁₂ to the microwave spectrum of CH₃NO₂. It is specifically designed for sixfold barrier molecules, and allows the user to select almost any symmetry-allowed torsion-rotation term for inclusion in the fitting Hamiltonian. This program leads to a very successful fit of transitions in the microwave spectrum of toluene characterized by J ? 30, K_a ? 12, and by the free-rotor quantum number ∣m∣ ? 3. In these fits we included both published and rather extensive unpublished new measurements, for which fits using other torsion-rotation programs have not been very successful. The fit presented here uses 28 parameters to give an overall standard deviation of 7.4 kHz for 372 line frequencies, and results in a much improved value for the sixfold barrier for toluene, V₆ = 13.832068(3) cal mol⁻¹.     

Analysis of the sensitivity to the electrochemical potential of the width of a metallic nanoconstriction

In relation to a metallic nanowire in the presence of an electrochemical potential, the sensitivity to this potential of the nanowire width is evaluated by defining and calculating a suitable parameter that can be regarded as a normalized gradient, this gradient being the derivative of the above-mentioned width with respect to the electrochemical potential.     

肖特基结的制备与势垒测量

采用磁控溅射方法在Nb07％-SrTiO3基片上制作Au薄膜接触,并在氧气气氛下750℃退火30 min,在室温环境下测量电流电压和电容电压等特性曲线,观测整流特性,根据相应实验数据采用饱和电流法、电容C-2与反偏电压V成线性关系计算肖特基势垒的大小.     

ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.     

Particle tunneling and scattering in a three-dimensional potential with a barrier

The particle tunneling through a 3-D rectangular potential barrier has been studied. The simplest model for multiple internal reflections has been assumed. The explicit expression for all the transmission and reflection probability amplitudes have been derived, as well as the tunneling and reflection phase times.      

Performance of gain-switched all-solid-state quasi-continuous-wave tunable Ti:sapphire laser system

We have made a gain-switched all-solid-state quasi-continuous-wave （QCW） tunable Ti：sapphire laser system, which is pumped by a 532 nm intracavity frequency-doubled Nd：YAG laser. Based on the theory of gain-switching and the study on the influencing factors of the output pulse width, an effective method for obtaining high power and narrow pulse width output is proposed. Through deliberately designing the pump source and the resonator of the Ti：sapphire laser, when the repetition rate is 6 kHz and the length of the cavity is 220 mm, at an incident pump power of 22 W, the tunable Ti：sapphire laser from 700 to 950nm can be achieved. It has a maximum average output power of 5.6W at 800nm and the pulse width of 13.2 ns, giving an optical conversion efficiency of 25.5% from the 532 mn pump laser to the Ti：sapphire laser.     

LD泵浦Nd：YAG激光器纵模特性及频率稳定性实验研究

摘要为了更好地研究LD泵浦Nd：YAG激光器的输出光束质量，利用共焦球面干涉仪设计了一套用于测量和分析该激光器纵模特性的简易装置，对该激光器的纵模进行了实验分析。在室温下测得纵模间隔为1.83GHz，纵模谱线宽度为113.83MHz。同时利用此装置，对该激光器的频率稳定性进行了分析，在120s取样时间内，测得频率稳定度为2.94×10^-4。     

On Some Extremal Properties of Lagrange Interpolatory Polynomials

In this paper, we will show that Lagrange interpolatory polynomials are optimal for solving some approximation theory problems concerning the finding of linear widths.In particular, we will show that

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, where _n is a set of the linear operators with finite rank n+1 defined on −1,1], and where _n+1 denotes the set of polynomials p=∑_i=0ⁿ⁺¹a_ixⁱ of degreen+1 such that a_n+11. The infimum is achieved for Lagrange interpolatory polynomial for nodes .