Auxiliary controlled singlet-oxygen ene reactions of cyclohexenes

The photooxygenation of homochiral cyclohexene ketals, which are easily available from 2-cyclohexenone and l-tartrates, affords hydroperoxides and after reduction the corresponding allylic alcohols in good yields and high regioselectivities. This can be rationalized by electronic repulsions in a perepoxide intermediate and provides evidence for unfavorable 1,3 diaxial interactions with a dioxolane oxygen atom. Only low stereoselectivities were observed, due to the flexibility of the cyclohexene ring. However, the diastereomers could be separated and after cleavage of the auxiliary, 4-hydroxy-2-cyclohexen-1-one was isolated in enantiomerically pure form, which can serve as a building block for natural product synthesis.     

Direct analysis of biodiesel microemulsions using an inductively coupled plasma mass spectrometry

An analytical procedure for direct introduction of biodiesel samples into an inductively coupled plasma mass spectrometer (ICP-MS) by using microemulsion for sample preparation was developed here. Cadmium, Co, Cu, Mn, Ni, Pb, Ti, and Zn were determined in biodiesel microemulsified samples prepared from different oleaginous sources (African palm, castor beans, palm, soybeans and an unknown oleaginous). Microemulsions were prepared using 0.25 mL Triton X-100, 0.25 mL 20% v v^− 1 HNO₃, 0.50 mL biodiesel sample and 4.0 mL n-propanol. Argon-oxygen mixture was added to the plasma as auxiliary gas for correcting matrix effects caused by the high carbon load due to biodiesel microemulsions. The oxygen gas flow rate was set in 37.5 mL min^− 1. The accuracy of the developed procedure was evaluated by applying addition-recovery experiments for biodiesel samples from different sources. Recoveries varied from 76.5 to 116.2% for all analytes but Zn in castor beans biodiesel sample (65.0 to 76.2%). Recoveries lower than 86.6% were obtained for palm biodiesel sample, probably due to matrix effects. Detection limits calculated by using oxygen in the composition of the auxiliary gas added to the plasma were higher than those calculated without using it, probably due to the highest formation of oxides. Despite oxides formation, best analytical performance was reached by using oxygen as auxiliary gas and by proper correction of transport interferences. The developed procedure based on microemulsion formation was suitable for direct introduction of biodiesel samples in ICP-MS.     

Dark solitonic excitations and collisions from a fourth-order dispersive nonlinear Schrödinger model for the alpha helical protein

Recent protein observations motivate the dark-soliton study to explain the energy transfer in the proteins. In this paper we will investigate a fourth-order dispersive nonlinear Schrödinger equation, which governs the Davydov solitons in the alpha helical protein with higher-order effects. Painlevé analysis is performed to prove the equation is integrable. Through the introduction of an auxiliary function, bilinear forms and dark N-soliton solutions are constructed with the Hirota method and symbolic computation. Asymptotic analysis on the two-soliton solutions indicates that the soliton collisions are elastic. Decrease of the coefficient of higher-order effects can increase the soliton velocities. Graphical analysis on the two-soliton solutions indicates that the head-on collision between the two solitons, overtaking collision between the two solitons and collision between a moving soliton and a stationary one are all elastic. Collisions among the three solitons are all pairwise elastic.     

Improvement in estimating the population mean in simple random sampling using information on auxiliary attribute

This paper proposes some estimators for the population mean by adapting the estimator in Singh et al. (2008) [5] to the ratio estimators presented in Kadilar and Cingi 2006 [2]. We obtain mean square error (MSE) equation for all proposed estimators, and show that all proposed estimators are always more efficient than ratio estimator in Naik and Gupta (1996) [3], and Singh et al. (2008) [5]. The results have been illustrated numerically by taking some empirical population considered in the literature.     

一类新的广义集值变分包含问题解的辅助序列迭代算法

本文提出并研究了Banach空间中的一类新的广义集值变分包含问题：0∈N（ω，y）＋A（z，v），由集值m-增生映射的预解算子建立了广义集值变分包含与不动点问题的等价性，并利用Nadler定理和辅助序列建立了一些迭代算法，证明了解的存在性和算法的全局收敛性．     

A pseudo-empirical log-likelihood estimator using scrambled responses

In this paper, we propose an empirical log-likelihood estimator for estimating the population mean of a sensitive variable in the presence of an auxiliary variable. A new concept of conditional mean squared error of the empirical likelihood estimator is introduced. The proposed method is valid for simple random and without replacement sampling (SRSWOR) and could easily be extended for complex survey designs. The relative efficiency of the proposed pseudo-empirical log-likelihood estimator with respect to the usual, and to a recent estimator due to Diana and Perri (2009b), has been investigated through a simulation study.     

Distribution estimation with smoothed auxiliary information

Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution.In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information,for example,a symmetric distribution of this variable.A smoothing technique is employed to handle the non-differentiable function.Hence,a distribution can be estimated based on smoothed auxiliary information.Asymptotic properties of the distribution estimator are derived and analyzed.The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information.Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.     

A non-standard auxiliary integrating sphere and correction method for the realization of diffuse reflectance

To realize spectral diffuse reflectance scale in 0/d geometric condition at National Institute of Metrology in China (NIM), a facility based on a non-standard auxiliary integrating sphere method with special structure has been built up and a correction method for the influence on the thickness of PTFE (polytetrafluoroethylene) coating at the port of auxiliary integrating sphere is mainly discussed. The uncertainty of spectral diffuse reflectance in NIM is approximately 0.25% (k = 2) in 380–800 nm. This facility has been used to establish China diffuse reflectance scales in the VIS–NIR part of the spectrum. This system and correction method presented in this paper can be easily implemented on most commercial spectrophotometers with a lower cost.     

Ratio methods to the mean estimation with known quantiles

We address the problem of estimating the finite population mean in survey sampling, by exploiting any available auxiliary information in order to increase the precision of classical estimators. The idea is to use any population quantiles of the available auxiliary variables which are known in many real situation from census, administrative files, etc. This is achieved using these known quantities in the construction of the estimators, by modifying the usual ratio estimation methods and afterwards defining a general class of exponentiation ratio estimators. The advantages of the proposed estimators are demonstrated using theoretical asymptotic tools and through a simulation study.     

Dynamical spin susceptibility of the d–p model in the over doping region

Dynamical spin susceptibility χ^s(q,ω) of the d–p model in the over doping region is investigated by using the auxiliary boson technique. It includes higher order terms of the 1/N-expansion within the random phase approximation (RPA) of the local vertex, where frequency dependence of the quasi-particle interaction is taken into account. The incommensurate spin fluctuation is obtained due to the nesting effect in the low energy region (ωω^*), whereas the commensurate one in the high energy region (ωω^*), the characteristic energy ω^* is estimated to be about 30 meV. Both of the spin–lattice relaxation rate 1/T₁ and the spin–spin relaxation rate 1/T_g monotonically increase as T decreases, while the spin Knight shift K is almost independent of T.