Correlations of13C chemical shifts and geometry modifications

The effect of geometry modifications of¹³C chemical shifts has been investigated in a small subset of molecules using both LO-INDO and Gaussian 70 (4–31) calculations. The Gaussian calculations, while known to give poor absolute shifts, compare well to the reparameterized semi-empirical INDO determinations in calculated shift changes. In virtually all cases the signs of the shift changes were found to be opposite to that of the changes in the calculated electronic energy.     

LaC_3~n(n=-1,0,+1)分子簇的理论研究(英文)

用密度泛函方法研究了ＬａＣ３ｎ（ｎ＝－１，０，＋１）分子簇的结构和稳定性，对这个四原子体系，提出了５种可能构型，其中３种具有Ｃ２ｖ对称性，２种为Ｃ∞ｖ对称性．在Ｃ２ｖ对称性结构中，其中１个为Ｌａ接在弯曲的Ｃ３链上，第２个是Ｌａ通过２个键与Ｃ３环相链，第３个是Ｌａ通过１个键与Ｃ３环相连；在Ｃ∞ｖ对称性中，第１个Ｌａ接在Ｃ３链的一端，而在第２个构型中，Ｌａ被插入在Ｃ３链中．结果表明，环状结构当Ｌａ接在弯曲的Ｃ３链上的是局域极小值并且最稳定     

固定波长同步荧光光谱参数的理论计算

基于荧光激发光谱和发射光谱对波长呈高斯分布的设定,本文推导出固定波长同步荧光光谱峰峰值位置、相对强度和半峰宽度等3个主要光谱参数的理论计算式。所提出的计算式应用于若干荧光物质光谱参数的计算,并和实测值、文献计算值作了对照。结果表明,和文献计算方法相比,本法与所研究物质的实际光谱参数较为接近,可为固定波长同步荧光光谱参数的理论计算提供一有效方法。     

Medium-size Gaussian basis sets for hydrogen through argon

Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the² P states of Li and Na, and the³ P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size.     

Bootstrap,wild bootstrap,and asymptotic normality

Summary We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 Stochastische Mathematische Modelle     

The discrete Gaussian chain with 1/r n interactions: Exact results

We show that the discrete Gaussian chain with interactionV(r) = 1/(r ²–1/4) is self-dual. At the dual temperaturek _B T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent. We also consider interactionsV(r)–1/r ⁿ and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark.     

湍流大气中高斯光束焦移的数值模拟研究

采用数值模拟方法对聚焦高斯光束在湍流大气中传输的焦移进行了研究.结果表明:湍流大气中高斯光束的焦点不再位于真空焦点位置,而是向发射点移动,且前移的幅度随湍流强度的增大而增大,这与理论预计结果一致.引用焦深概念描述光束在焦点附近的准直特性,结果显示:在弱起伏和中等强度起伏情况下,光束的焦深随着湍流强度的增大而增大,焦点附近光束准直度提高;在中等和强起伏情况下,光束在焦点附近高度准直.     

水体透射光谱结合主成分分析(PCA )改进化学需氧量(COD)含量估算研究

化学需氧量（Chemical Oxygen Demand,COD）是水体有机污染的一项重要指标,化学需氧量越高,表示水污染程度越严重。 为了解决传统的COD测量方法耗时较长,不利于快速、实时地获取水体中COD的信息等问题。本文提出了基于透射光谱测量结合主成分分析(Principal Component Analysis, PCA)改进水体COD含量估算模型。具体的,采集100组COD水体光谱信息,分别使用3种不同的高光谱数据预处理方法对光谱数据进行预处理,分析不同预处理方法对模型精度的影响,并基于不同的预处理方法分别建立高斯过程回归模型(Gaussian Process Regression, GPR)和BP神经网络模型,分析不同预处理方法对模型精度的影响;并对各模型结合PCA数据降维方法进行模型的改进,通过比较模型的精度选择最优模型进行水体COD含量的检测。结果显示,相比于原始光谱数据建立的GPR模型和BP神经网络模型,数据预处理后的模型精度明显提升;且结合PCA对预处理后的数据进一步降维处理后,模型精度得到了进一步的提升。其中,基于标准正态变量变换特征结合PCA改进BP神经网络模型基于PCA改进的BP神经网络模型R^2高达0.9940,均方根误差RMSE为0.022540。证明了基于PCA改进的BP神经网络数据降维方法对预处理后的光谱数据进行降维处理,有利于去除光谱中的冗余信息,提取特征信息,可以实现高光谱检测方法可以实现COD含量估算模型的优化,从而为传统COD测量方法存在的问题提出了一种新的解决思路。     

高斯型空间光孤子相互作用的数值研究

 通过数值模拟的方法,对高斯孤子在对数型饱和非线性介质中的相互作用进行了研究,考查了两光束间的相对振幅和相对相位对其相互作用的影响。结果表明：高斯孤子之间的相互作用敏感地依赖于两光束间的相对振幅和相对相位。在不同的振幅差异范围内,光束间的主要作用交替地表现为相互排斥和相互吸引,并由于高斯孤子的不稳定性,导致了光束在碰撞后以一种尺寸周期性变化的呼吸模式传输。随着相对相位的增大,两光束间始终持续地表现出强烈的排斥作用,直到相对相位增加到一个2π周期之后。而且碰撞之后,光束也都以呼吸模式进行传输,其分离的角度越大,呼吸就越明显。     

A Gaussian distribution model of anisotropic magnetorheological elastomers

A Gaussian distribution model was developed to examine the field-induced performance of anisotropic magnetorheological elastomers. The developed model was based on the assumption that the iron particles in magnetorheological elastomers aggregate into a large number of parallel body-centered tetragonal structure columns whose length obeys the Gaussian distribution. By using multi-pole approximation with local field effect and taking into account the nonlinearity and saturation of particle magnetization, the field-induced shear modulus was calculated as a function of distribution and dimension of the particle structures, the external magnetic field and the dynamic shear strain. Compared with other modes as well as the published experimental results, this model shows a remarkable improvement in accurately predicting the behavior of the magnetorheological elastomers.