一些新的数论函数及其均值公式

对于给定的自然数m,我们利用最大公约数和最小公倍数定义数论函数(m,n)和[m,n]/m.本文主要目的是研究这两个新的函数的渐近性质,利用解析方法得到这两个函数的几个渐近公式.     

Least‐squares finite element method on adaptive grid for PDEs with shocks

We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

回归系数的混合估计与最小二乘估计的一个新的相对效率

本文对具有附加信息的线性回归模型中的混合估计与最小二乘估计给出了一种新的相对效率,研究了新的相对效率与其它几种相对效率的关系,得出了新的相对效率的上、下界.     

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

偏最小二乘法分光光度同时测定复方扑热息痛片中各组分含量

本文介绍了偏最小二乘法(PLS)用于多组分分光光度分析的基本原理和算法.研究了复方扑热患痛片中扑热息痛、阿司匹林和咖啡因的PLS测定方法,各组分的平均回收率分别为99.88±0.33％、99.99±0.14％和99.92±1.24％(置信度95％).     

Simulation of aerated lagoon using artificial neural networks and multivariate regression techniques

The aim of this study was to develop an empirical model that provides accurate predictions of the biochemical oxygen demand of the output stream from the aerated lagoon at International Paper of Brazil, one of the major pulp and paper plants in Brazil. Predictive models were calculated from functional link neural networks (FLNNs), multiple linear regression, principal components regression, and partial least-squares regression (PLSR). Improvement in FLNN modeling capability was observed when the data were preprocessed using the PLSR technique. PLSR also proved to be a powerful linear regression technique for this problem, which presents operational data limitations.     

Metabolomic-based investigation of Yinlan alleviating hyperlipidemia by inhibiting blood stasis and phlegm turbidity through the PXR-CYP3A4-ABCB1-FXR pathway

Yinlan lipid regulatory capsule (YL) is a composite traditional Chinese medicine (TCM) new drug to alleviate hyperlipidemia, while its therapeutic mechanism in vivo was not clarified with nontargeted metabolomics investigation. An animal model was established in rats fed a high-fat diet, and their body weights, body mass index (BMI) and blood cholesterol levels were measured. Serum, liver and kidney tissue samples were also extracted for PXR-CYP3A4-ABCB1-FXR signaling pathway research using PCR and UHPLC–MS. The obtained plasma samples were analyzed by UHPLC-Q-TOF-MS metabolomic investigation, which revealed PXR-CYP3A4-related metabolites and changes induced by YL. Finally, the key metabolites were chosen as index components, and their levels in the serum, liver, small intestine and bile were used for simultaneous UHPLC–MS-MS determination. The results indicated that YL was effective in rebalancing blood TG and TC levels (compared to controls). With respect to the PXR-CYP3A4-ABCB1 pathway, as a result of YL’s effect, gene expression or activity of the two targets decreased significantly in both the liver and kidney. The same trend was observed in the serum samples mentioned above. Metabolomics screening and data revealed that 44 metabolites can be regarded as biomarkers related to hyperlipidemia, fatty acids synthesis, and body energy consumption, as well as synthesis, transportation and exertion of cholesterol. YL’s treatment focused on 26 of them, primarily bile acids, indicating that the antihyperlipidemic effect of this drug lies in its inhibitory activity of cholesterol metabolism. Subsequent analysis of those in vivo components revealed that significant increases (compared to the model group) occurred in the blood, liver, small intestine and bile in groups that received medium and high doses of YL (while the low dose was relatively unchanged). Those target components exhibit a close relationship with PXR and/or CYP3A4. The use of YL repressed PXR expression and subsequently decreased CYP3A4 activity. As a result, synthesis of related bile acids increased, while cholesterol levels decreased, consequently leading to the attenuation of hyperlipidemia. This study comprehensively investigated the antihyperlipidemia mechanism of YL based on its repression of PXR-CYP3A4 activity and related metabolite yield, establishing an accurate method for evaluating the therapeutic effect of YL.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

Quality evaluation of fingerprints of herbal medicine with chromatographic data

In this study, local least squares (LLS) and principal component analysis (PCA) were applied to deal with the disturbances in a data set of chromatographic fingerprints after necessary data transformations. It has been demonstrated that PCA with standard normal variate (SNV) transformation of data led to meaningful classification of 33 different Erigeron breviscapus herbal samples. The result was also corroborated by variance squares discriminant method. The quality of herbal objects was further evaluated, and the causes of this fact have been explained from a chemical point of view. At the same time, it implied an idea for qualitative evaluation of the herbal objects with a common class pattern of chromatographic fingerprints.