Some notes on 2-D graphical representation of DNA sequence

Some 2-D and 3-D graphical representations of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences. In this paper, we presented a novel graphical representation of DNA sequences by taking four special vectors in 2-D Cartesian coordinate system to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a directed walk. It is shown that the new graphical representation of DNA sequences has lower or nondegeneracy.     

Permanence of species in nonautonomous discrete Lotka–Volterra competitive system with delays and feedback controls

A nonautonomous N-species discrete Lotka–Volterra competitive system of difference equations with delays and feedback controls is considered. New sufficient conditions are obtained for the permanence of this discrete system. The results indicate that one can choose suitable controls to make the species coexistence in the long run. Moreover, we give some examples to illustrate the feasibility of our result which can be well suited for computational purposes.     

拓扑化学行为及其对镧系元素和锕系元素的QSPR应用

提出拓扑化学行为概念,把对化合物性质最具影响力的因素归纳为拓扑生长力和拓扑阻滞力。根据该原理,利用价电子轨道能量对价电子距离矩阵进行修正。研究表明OET(轨道能量拓扑指数)对镧系元素和锕系元素的物理化学性质具有良好的应用，尤其是对尚未借助QSPR(定量结构性质关系)手段进行研究的光谱性质。LOO CV(留一法交叉检验)的结果验证了模型的良好稳定性和预测能力,采用的检验参数有：PRESS/SSY，SEP_CV，R_CV，S_PRESS 和PSE，其中PRESS/SSY比值介于0.000 6和0.114 8之间。与文献进行比较,本文方法所得结果与之接近或更好。研究显示正是基于拓扑化学行为才有本文方法良好和较广的应用。     

Determination of trace elements in residual oil by high-resolution inductively coupled plasma mass spectrometry

An analytical method using high-resolution inductively coupled plasma mass spectrometry (HR-ICP-MS) for rapid simultaneous determination of 20 elements, including Na, Mg, Al, Ca, Ti, V, Mn, Fe, Co, Ni, Cu, Zn, Ga, As, Mo, Cd, Sn, Sb, Ba, and Pb elements, in residual oil was described. The sample was dissolved in HNO₃ by microwave digestion, and then the above 20 elements in the solution were analyzed directly by HR-ICP-MS. Most of the spectral interferences could be avoided by measuring in the high-resolution mode. The matrix effect caused by the sample-digesting solution and corrected by Sc, Rh, and Bi as the internal standard elements was studied in detail. The optimum condition of the determination was also tested and discussed. The result showed that the detection limits of the method were in the range of 0.014 to 11.6 μg L⁻¹; the relative standard deviation was less than 3.8% and recoveries in the samples were in the range of 88.4% to 108.0%. This method can be used to determine the trace elements in residual oil with the features of accurate, rapid, and convenient determination.     

Homoclinic orbits for second order self-adjoint difference equations

In this paper we discuss how to use variational methods to study the existence of nontrivial homoclinic orbits of the following nonlinear difference equations

     

托卡马克等离子体不同运行模式下的电子回旋波电流驱动

在给定等离子体密度分布下，从电子、离子的能量方程出发，根据不同运行模式下等离子体的热传导率不同，分别求出了中心负剪切模式，常规剪切H模式和L模式下的等离子体温度分布，然后通过求解波迹方程与相对论情况下的Fokker-Planck方程，分别计算了这些模式下的电子回旋波电流驱动和波功率沉积.得到在中心负剪切下，驱动电流最大，驱动效率最高，功率沉积和电流分布区间跨度大；在常规剪切H模式下，驱动电流较小，分布区间跨度比较窄，驱动效率相对较低；在常规剪切L模式，驱动电流效率最低，分布区间跨度也非常集中. 关键词： 托卡马克 电子回旋波电流驱动 中心负剪切 常规剪切     

Homoclinic orbits and subharmonics for nonlinear second order difference equations

We show the existence of a nontrivial homoclinic orbit and subharmonic solutions for a class of second order difference equations by applying the “Mountain Pass” theorem relying on Ekeland’s variational principle and the diagonal method, and the homoclinic orbit as the limit of the subharmonics. A completely new way is provided for dealing with the existence of solutions for difference equations.     

一类二元离散神经网络模型的渐近性

本文考虑的是一类具有分段常数非线性时滞差分系统,该系统可作为二元人工神经网络模型的离散形式,本文得到了系统解的渐近性的一些结果。     

Some properties of a class of symmetric functions

The Schur-convexity and Schur-geometric-convexity of a class of symmetric functions are investigated. As consequences some new proofs of the well-known Ky Fan's inequality and Shapiro's inequality are presented, respectively. We also give another proof of a problem posted by S. Gabler in [S. Gabler, Aufgabe 830, Elem. Math. 3 (1980) 124-125]. Some interesting matrix and geometric inequalities are established to show the applications of our results.     

POSITIVE SOLUTIONS OF NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS

In this paper we apply a cone theoretic fixed-point theorem proved by Kras-nosel'skii to obtain sufficient conditions for the existence of positive solutions to some boundary value problems for a class of functional difference equations. We consider the case that the nonlinear term satisfies asymptotically linear growth.