The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay

In this paper, we consider an autonomous predator-prey Lotka-Volterra system in which individuals in the population may belong to one of two classes: the immatures and the matures, the age to maturity is represented by a time delay. By using eigenvalue analysis, principal term analyze method, reduction to absurdity, and iterative method, we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point. Moreover, a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained. Meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures.     

An interior trust region algorithm for solving linearly constrained nonlinear optimization

In this paper, an interior point algorithm based on trust region techniques is proposed for solving nonlinear optimization problems with linear equality constraints and nonnegative variables. Unlike those existing interior-point trust region methods, this proposed method does not require that a general quadratic subproblem with a trust region bound be solved at each iteration. Instead, a system of linear equations is solved to get a search direction, and then a linesearch of Armijo type is performed in this direction to obtain a new iteration point. From a computational point of view, this approach may in general reduce a computational effort, and thus improve the computational efficiency. Under suitable conditions, it is proven that any accumulation of the sequence generated by the algorithm satisfies the first-order optimality condition.     

动态模糊随机信息处理的数学方法

本文系统地概述了我们近年来提出的动态模糊随机信息处理的数学方法,内容包括模糊随机变量、模糊随机过程和模糊随机微分方程的基本解法等方面的基本概念、基本定义和某些重要的定理,以及动态系统的模糊随机响应与可靠性分析的方法等。这些方法是为我们研究工程实际问题的需要逐步发展起来的,对于处理某些类型的问题简便实用。     

Structure–electrical property study of anisotropic polyaniline films

The relationships of the structure and electrical properties of anisotropic HCl‐doped polyaniline (PANI) films cast from N,N′‐dimethylpropylene urea (DMPU) solutions and stretched to different draw ratios were studied. The anisotropic structure of the stretched PANI films was examined by X‐ray diffraction, near‐infrared wave‐guide coupling, and polarized infrared measurements. The PANI emeraldine base (EB) films cast from DMPU solutions had a single‐phase noncrystalline structure, and stretching of the films did not cause crystallization to occur. The transition moment angles of two weakly absorbing infrared bands were determined, and the Hermans' orientation functions for the PANI EB films were calculated. The PANI films were then doped with HCl, and the electrical properties were determined by impedance spectroscopy. With a specially designed test fixture, the in‐plane and through‐plane impedance was obtained. The conductivity along the stretch direction increased with orientation. The in‐plane conductivity was significantly higher than the through‐plane conductivity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 823–841, 2003     

Two long-standing problems in Tsallis’ statistics

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis’ statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis’ statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis’ statistics, because its corollary is in contradiction with the zeroth law of thermodynamics.     

A comparative study of quantitative structure-activity relationship methods based on gallic acid derivatives

By using hologram quantitative structure-activity relationship (HQSAR) and comparative molecular field analysis (CoMFA) methods, the relationships between the structures of 49 gallic acid derivatives and their analgesic activity have been investigated to yield statistically reliable models with considerable predictive power. The best HQSAR model was generated using atoms, bond and connectivity as fragment distinction parameters and fragment size 5-7 from a hologram length of 307 with 3 components. High conventional r2 (r2 = 0.825) and cross-validation r2 (r2(cv) = 0.726) values were obtained. CoMFA analyses varying lattice size and location, grid spacing, probe charges and using, Tripos standard and Indicator force field were performed. The best model was developed with 4 components using sp3-hybridized carbon atom with +1.0 charge as probe, grid spacing (2 A), lattice offset (1.0, 3.0, -2.5). The CoMFA model showed a conventional correlation coefficient r2 of 0.889 and across-validation r2(cv) equals to 0.633. The robustness and predictive ability of the HQSAR and CoMFA models have been validated by means of an external test set. The results indicate that both models possess high statistical quality in the prediction of analgesic potency of novel gallic acid analogs.     

Chiral separation of 1,1'-bi-2-naphthol and its analogue on molecular imprinting monolithic columns by HPLC

Two molecular imprinting polymer (MIP) monolithic columns with (S)-(-)-1,1'-bi-2-naphthol and (R)-(+)-5,5',6,6',7,7',8,8'-octahydro-1,1'-bi-2-naphthol as the templating molecules, respectively, have been prepared by in situ polymerization using 4-vinylpyridine and ethylene dimethacrylate as functional monomer and cross-linker, respectively. The columns with good flow-through properties were obtained by changing the molar ratio of the functional monomer and the template molecule. The effects of mobile-phase composition on separation of enantiomers were systematically investigated. The results indicate that hydrophobic interaction in aqueous solution and hydrogen-bonding interaction in ACN between the enantiomers and polymers could play important roles in the retention and resolution. The effects of chromatographic conditions, such as flow rate, column temperature, sample loading, on the enantioseparation were also studied. Further, these two MIP columns show a cross-reactivity.     

Probing metabolic alterations in breast cancer in response to molecular inhibitors with Raman spectroscopy and validated with mass spectrometry

Rapid and accurate response to targeted therapies is critical to differentiate tumors that are resistant to treatment early in the regimen. In this work, we demonstrate a rapid, noninvasive, and label-free approach to evaluate treatment response to molecular inhibitors in breast cancer (BC) cells with Raman spectroscopy (RS). Metabolic reprogramming in BC was probed with RS and multivariate analysis was applied to classify the cells into responsive or nonresponsive groups as a function of drug dosage, drug type, and cell type. Metabolites identified with RS were then validated with mass spectrometry (MS). We treated triple-negative BC cells with Trametinib, an inhibitor of the extracellular-signal-regulated kinase (ERK) pathway. Changes measured with both RS and MS corresponding to membrane phospholipids, amino acids, lipids and fatty acids indicated that these BC cells were responsive to treatment. Comparatively, minimal metabolic changes were observed post-treatment with Alpelisib, an inhibitor of the mammalian target of rapamycin (mTOR) pathway, indicating treatment resistance. These findings were corroborated with cell viability assay and immunoblotting. We also showed estrogen receptor-positive MCF-7 cells were nonresponsive to Trametinib with minimal metabolic and viability changes. Our findings support that oncometabolites identified with RS will ultimately enable rapid drug screening in patients ensuring patients receive the most effective treatment at the earliest time point.

Rapid and accurate response to targeted therapies is critical to differentiate tumors that are resistant to treatment early in the regimen.