Dynamic and static nature of activated interactions in transition states as elucidated by quantum theory of atoms-in-molecules dual functional analysis: A case of ligand exchange at the N of sulfonylimino-λ3-bromanes

A method to elucidate the dynamic and static natures of the activated interactions in transition states (TSs) is proposed using quantum theory of atoms-in-molecules (QTAIM) dual functional analysis (QTAIM-DFA). The natures are determined for the ligand exchange at the N of sulfonylimino-λ³-bromanes, RBr-*-N(SO₂CF₃)-*-X′R′ (R, R′ = Me or Ph, X′ = Br′ or I′). Asterisks (*) emphasize the presence of bond critical points within the interactions in question. While data from the optimized structures of TSs correspond to the static nature, those from the perturbed and optimized structures represent the dynamic nature. The nature of the interactions in Br-*-N-*-X′ calculated with QTAIM-DFA, using the perturbed structures generated using the normal coordinates for the imaginary frequencies (NIV), was very similar to that in trigonal bipyramidal adduct formation through charge transfer. The results with NIV were precisely the same as those obtained based on intrinsic reaction coordinate (IRC). The high applicability of QTAIM-DFA is demonstrated when analyzing the activated interactions in TSs.     

Quantification of erythromycin in pharmaceutical formulation by transmission Fourier transform infrared spectroscopy

A simple, cost-effective and environmental friendly analytical method was developed for the quantification of erythromycin in tablet formulation using transmission Fourier Transform Infrared (FT-IR) spectroscopy for routine quality control analysis. There is no need of sample preparation except pellet formation for FT-IR analysis. Use of solvent was totally avoided in this method. Calibration was carried out by using simple Beer’s law in the FT-IR region between 1743 and 1697 cm⁻¹. The excellent coefficient of determination (R² = 0.998) was achieved with 0.0247 and 1.14 root mean square error of prediction (RMSEP) and root mean square error of cross validation (RMSECV), respectively. The results of the study revealed that the transmission FT-IR spectroscopy could be effectively used for rapid determination of active ingredients like erythromycin in pharmaceutical formulations to control the quality of finished products.     

光纤光谱仪绝对光谱辐射定标新技术

在700 nm～900 nm波段范围内,用1 000℃黑体标定光纤光谱仪(200 nm～1 100 nm),获得其在该波段范围内的绝对光谱响应函数.通过测量光纤光谱仪对不同色温下卤钨灯的光谱响应,将700 nm～900 nm波段的响应函数推延至400 nm～700 nm波段范围,最终得到400 nm～900 nm波段内的绝对光谱响应函数.光纤光谱仪对不同色温下卤钨灯的5次测量结果表明:在550 nm～900 nm范围内,所获得的绝对光谱响应合成不确定度小于3.53%.     

高功率准分子激光主振荡功率放大系统光学元件的稳定性

为了分析高功率准分子激光主振荡功率放大(MOPA)系统中各光学元件稳定性对靶面光斑定位精度的影响,建立了分析模型,利用分析结果指导高稳定性镜架设计以满足系统实验需求。根据高功率准分子激光MOPA系统特点,有效地简化了系统光路,建立了系统光路模型;按照系统打靶精度要求,利用三维坐标变换和光线追迹法,计算得到了系统单个光学元件稳定性对靶面光斑定位精度的影响规律;最后,对自行设计的镜架进行了稳定性测量。计算结果表明,反射镜的旋转变化和透镜垂直光轴的平移变化是影响靶面光斑定位精度的主要因素,且主放大光路中反射镜在X方向和Y方向上最大的变化范围分别不能超过0.8和1.6μrad。实际测量结果表明,设计的镜架在X方向和Y方向最大的变化范围分别为0.6和0.81μrad,满足系统实验要求。     

狭义相对论中没有“矛盾方程”

根据洛伦兹变换把两个惯性系的坐标原点的时空坐标从一个坐标系变换到另一坐标系,从相对运动的角度说明洛伦兹变换是自洽的,运动物体上发生的自然过程比起静止物体的过程延缓了,并且两个坐标系中的观察者都认为对方的时钟变慢,是“动钟变慢”而非“动钟变快”,不会导致“矛盾方程”,不能混淆同一事件的变换规律与两个事件的变换结果．     

交错级数敛散性判别法

给出交错级数的几个判别法,它们可直接用以判别交错级数是绝对收敛,条件收敛还是发散.     

ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.     

A NOTE ON GENERALIZED ABSOLUTE SUMMABILITY FACTORS FOR A TRIANGULAR MATRIX

In this paper, a general theorem on | A, δ |k -summability factors of infinite series is proved under different conditions.     

Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation

This paper presents a geometric nonlinear analysis formulation for beams of functionally graded cross-sections by means of a Total Lagrangian formulation. The influence of material gradation on the numerical response is investigated in detail. Two examples are given that illustrate the main features of the formulation, in which the behavior of beams of graded cross-sections is compared with homogeneous material beams. A motivation for this work is the potential development of functionally graded risers for the offshore oil exploration industry.     

Absolute Configuration of Small Molecules by Co‐Crystallization

The most reliable method to determine the absolute configuration of chiral molecules is X‐ray crystallography, but small molecules can be difficult to crystallize. We report rapid co‐crystallization of tetraaryladamantanes with small molecules as different as n‐decane to nicotine to produce crystals for X‐ray analysis and the assignment of absolute configuration when the molecules are chiral. A screen of 52 diverse compounds gave inclusion in co‐crystals for 88 % of all cases and a high‐resolution structure in 77 % of cases. Furthermore, starting from three milligrams of analyte, a combination of NMR spectroscopy and X‐ray crystallography produced a full structure in less than three days using an adamantane crystallization chaperone that encapsulates the analyte at room temperature.