Homoclinic Orbits of a Quadratic Isochronous System by the Perturbation-incremental Method

In this paper, the perturbation-incremental method is presented for the analysis of a quadratic isochronous system. This method combines the remarkable characteristics of the perturbation method and the incremental method. The first step is the perturbation method. Assume that the parameter $\lambda$ is small, i.e. $\lambda\approx0$, the initial expression of the homoclinic orbit is obtained. The second step is the parameter incremental method. By extending the solution corresponding to small parameters to large parameters, we can get the analytical-expressions of homoclinic orbits.     

一个特殊的二项系数

利用发生函数和矩阵方法,研究了一个特殊的二项式系数[n λ n-k]和它所构成的矩阵.得到以[n λ n-k]为矩阵元素的Pascal型矩阵的指数分解和乘积分解公式.同时,考察了与二项式型多项式相伴的函数矩阵Pn,λ[x]及其性质.     

响应曲面法提取水松总黄酮的工艺研究

采用响应曲面法,优化了提取水松总黄酮的提取工艺条件为:微波时间3.8min,乙醇浓度69%,固液比1∶31,在此条件下,水松总黄酮的产率为1.88%。     

一种修正的HS共轭梯度法及全局收敛性

<正>1引言考虑无约束极小化问题:(?),(1)其中f(x)连续可微,其梯度函数用g(x)表示.共轭梯度法求解(1)的常用迭代格式为:x_(k+1)=x_k+α_kd_k,(2)(?)(3)其中g_k=▽f(x_k),α_k≥0是由某种线搜索得到的步长因子;d_k为搜索方向,β_k为标量,β_k的不同选择产生了不同的共轭梯度法.著名的β_k公式有:     

Finite groups with the set of the number of subgroups of possible order containing exactly two elements

Let G be a finite group, and n(G) be the set of the number of subgroups of possible order of G. We investigate the structure of G satisfying that n(G)?=?{1, m} for any positive integer m?>?1. At first, we prove that the nilpotent length of G is less than 2. Secondly, we investigate nilpotent groups with m?=?p?+?1 or p ²?+?p?+?1 (p is a prime), and we get the classification of such kinds of groups. At last, we investigate non-nilpotent groups with m?=?p?+?1 and get the classification of the groups under consideration.     

A Posteriori Error Estimates of Mixed Methods for Parabolic Optimal Control Problems

In this article, we shall give a brief review on the fully discrete mixed finite element method for general optimal control problems governed by parabolic equations. The state and the co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control is approximated by piecewise constant elements. Furthermore, we derive a posteriori error estimates for the finite element approximation solutions of optimal control problems. Some numerical examples are given to demonstrate our theoretical results.     

Foam films as instrumentation in the study of amphiphile self-assembly

A survey on recent experimental investigations of microscopic foam films containing self-assembled amphiphilic structures is presented. A specific advantage of the microscopic film techniques is that the fine control of system parameters allows the estimation of the consecutive changes of film properties for low surfactant content and extremely small concentration changes. This gives a unique possibility to reach amphiphile quantities when initial onset of self-assembly is to be observed. The film characteristics are investigated via microinterferometric method, which operates with the measuring cell of Scheludko-Exerowa. The experimental set is additionally improved by including video-recording and consecutive image analysis. The results show the following: (1) Unstable black patterns (dots and spots) are observed; they have very short lifetimes and the films, which contain them rupture quickly. (2) Several of the kinetic characteristics of the films display a sharp change within a narrow surfactant concentration range. The experiments are interpreted on the basis of the assumption that a series of smaller self-assembled aggregates (premicelles) with various geometries exist at the interfaces and inside the thin film. The proposed theoretical scheme puts forward a mechanism connecting the formation of unstable black patterns (dots and spots) with the reorganization and destruction of the existing surfactant assemblies both in the bulk of the film and on the interfaces. The results suggest that the observed unstable black formations may serve as indicators for the presence of surfactant structures in amphiphilic solutions and the microscopic foam-film techniques has a serious potential as a prospective instrumentation in the study of amphiphilic self-assemblies.     

A simple sol–gel hydrothermal method for the synthesis of defective TiO2 nanocrystals with excellent visible-light photocatalytic activity

Research on Chemical Intermediates - Defective TiO2 nanocrystals (D-TiO2) were synthesized by a simple, mild and green sol–gel hydrothermal method. The as-prepared sample possesses a high...     

Effects of ultrasound on Microcystis aeruginosa cell destruction and release of intracellular organic matter

Harmful algal blooms negatively impact ecosystems and threaten drinking water sources. One potential method to effectively counteract algal blooms is ultrasonication. However, ultrasonication can easily lead to the release of intracellular organic matter (IOM). The purpose of this study was to investigate the relationship between the destruction of algal cells and IOM release at different ultrasound frequencies. Microcystis aeruginosa cells were ultrasonicated at 20 kHz with an intensity of 0.038 W/mL, 740 kHz with an intensity of 0.113 W/mL, and 1120 kHz with an intensity of 0.108 W/mL. The IOM release was detected by fluorescence spectroscopy in addition to the more commonly used haemocytometry and optical density. After ultrasonication for 15 min, the removal rate of algal cells reached 10.5% at 20 kHz, 9.46% at 740 kHz, and 35.4% at 1120 kHz. The 20 kHz and 740 kHz ultrasound caused local damage to algal cells and then disrupted them, whereas the 1120 kHz ultrasound directly disrupted most algal cells. The extracellular organic matter (EOM), which was increased by ultrasonication, mainly consisted of protein-like compounds, chlorophyll, and a small amount of humic-like substances. Gas vacuoles had been destructed before the cells were broken, as indicated by the decrease of cell size and the wrinkles on the cell surface. Moreover, the removal of algae cells while upholding integrity is more conducive to the safety of the water environment.