Three 1‐phenylindolin‐2‐one derivatives displaying different molecular dipole moments and different crystallographic symmetries

Three 1‐phenylindolin‐2‐one derivatives, namely 1‐phenylindolin‐2‐one, C₁₄H₁₁NO, (I), 5‐bromo‐1‐phenylindolin‐2‐one, C₁₄H₁₀BrNO, (II), and 5‐iodo‐1‐phenylindolin‐2‐one, C₁₄H₁₀INO, (III), have been synthesized and their structures determined. Compounds (I) and (II) crystallized in the centrosymmetric space groups Pbca and P2₁/c, respectively, while compound (III) crystallized in the polar space group Aea2. Density functional theory (DFT) calculations show that the molecular dipole moment gradually decreases in the order (I) > (II) > (III). The relatively smaller dipole moment of (III) and the larger non‐electrostatic intermolecular interactions may be the main reasons for the noncentrosymmetric and polar structure of (III).     

Basis Sets Dependency in Constructing Spectroscopy-Accuracy Ab Initio Global Electric Dipole Moment Functions

Recently, more attention have been paid on the construction of dipole moment functions (DMF) using theoretical methods. However, the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do. In this letter, using Ar...He as an example, we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods. We especially focused on the basis set dependency in this scenario, i.e., the convergence of DMF with the sizes of basis sets, basis set superposition error, and mid-bond functions. We also tested the explicitly correlated method, which converges with smaller basis sets than the conventional methods do. This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.     

NA随机变量阵列的完全矩收敛性

利用NA随机变量的矩不等式和截尾方法,研究了NA随机变量阵列的完全矩收敛性,给出了证明NA随机变量阵列完全矩收敛性的一些充分条件.所得结果推广了已有文献关于NA随机变量的相应结果.     

小样本定数截尾场合下威布尔和对数正态分布的拟合检验

本文给出了小样本定数截尾场合下两参数威布尔分布和对数正态分布的拟合检验方法,该方法还适用于一般的位置-刻度参数族分布,论文还通过实际算例说明方法的可行性。     

Geometrical structure and nonlinear response variations of metal (M = Ni2+, Pd2+, Pt2+) octaphyrin complex derivatives: A DFT study

Nonlinear optical response of designed organometallic complexes of Ni²⁺, Pd²⁺, and Pt²⁺ metal ions with octaphyrin (OP) as ligand were explored by using DFT at CAM-B3LYP/6–311G++(d, p)/LANL2DZ/DEF2SV level of theory. The geometries of these organometallic complexes were studied in terms of effect on molecular framework by metal ion and substituent groups. The optimized geometry of free ligand displays that one of the four pyrrole rings orients out of plane to reduce the steric hindrance. The effect of the substituents on the geometry was found more prominent in the Ni²⁺-OP complexes. The calculations reveal enhancement in the values of dipole moment and hyperpolarizability on introducing electron withdrawing and electron donating groups in ligand framework with maximum enhancement in case of Pt²⁺-OP derivatives. In this study no regular trend was observed for the HOMO and LUMO energies with the second-order hyperpolarizability of M²⁺-OP complexes. However, we have observed that the excited-state properties calculated by using TD-DFT correlate well with the second-order hyperpolarizability values and the dependence was rationalized in terms of two-level model. Thus, from overall calculations we have observed that the designed organometallic complexes display higher polarizability and hyperpolarizability values and can be effective candidates for nonlinear response.     

The p-th moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion

In this paper, we consider a class of impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs in short). By means of the G-Lyapunov function method, some criteria on p-th moment stability and p-th moment asymptotical stability for the trivial solutions of IGSDEs are established. An example is presented to illustrate the efficiency of the obtained results.     

A matrix rational Lanczos method for model reduction in large‐scale first‐ and second‐order dynamical systems

In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given.     

Semiparametric Bayesian inference for mean-covariance regression models

In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.     

Some closed form robust moment‐based estimators for the MEM(1,1)

In this paper, we extend the closed form moment estimator (ordinary MCFE) for the autoregressive conditional duration model given by Lu et al (2016) and propose some closed form robust moment‐based estimators for the multiplicative error model to deal with the additive and innovational outliers. The robustification of the closed form estimator is done by replacing the sample mean and sample autocorrelation with some robust estimators. These estimators are more robust than the quasi‐maximum likelihood estimator (QMLE) often used to estimate this model, and they are easy to implement and do not require the use of any numerical optimization procedure and the choice of initial value. The performance of our proposal in estimating the parameters and forecasting conditional mean μ_t of the MEM(1,1) process is compared with the proposals existing in the literature via Monte Carlo experiments, and the results of these experiments show that our proposal outperforms the ordinary MCFE, QMLE, and least absolute deviation estimator in the presence of outliers in general. Finally, we fit the price durations of IBM stock with the robust closed form estimators and the benchmarks and analyze their performances in estimating model parameters and forecasting the irregularly spaced intraday Value at Risk.     

Artificial Caries Lesion Characteristics after Secondary Demineralization with Theobromine-Containing Protocol

Developing artificial caries lesions with varying characteristics is needed to adequately study caries process in vitro. The objective of this study was to investigate artificial caries lesion characteristics after secondary demineralization protocol containing theobromine and fluoride. Sixty bovine enamel slabs (4 × 3 mm) were demineralized using a Carbopol-containing protocol for 6 days. A baseline area (2 × 3 mm) was protected with acid-resistant nail varnish, after which specimens were exposed for 24 h to a secondary demineralization protocol containing acetic acid plus one of four fluoride/theobromine combinations (n = 15): theobromine (50 or 200 ppm) and fluoride (0 or 1 ppm). Specimens were sectioned and analyzed using transverse microradiography for changes in mineral content, lesion depth, and surface layer mineralization. Data was analyzed using paired t-test and analysis of variance followed by Bonferroni test at 0.05 significance level. After secondary demineralization, fluoride-containing groups had significantly deeper lesions (p = 0.002 and 0.014) compared to the group with 0 ppm fluoride and 50 ppm theobromine. Mineral content and lesion depth were significantly different compared to baseline for all groups. Theobromine did not show an added effect on mineral uptake. Theobromine-containing groups exhibited particularly deep lesions with a more uniform mineral profile in the presence of fluoride.