JONES型电导池测量的LCR电桥等效电路选择

JONES电导池系统的交流阻抗由电极过程的相关阻抗和电极间溶液的电阻两部分组成,可用适当的等效电路模拟。采用LCR电桥测量JONES电导池中溶液的电阻时需要选择合适的等效电路为模型解析测量的交流阻抗。通过等效电路的分析发现,选择串联电路作为LCR电桥的解析等效电路测量JONES型电导池中溶液的电阻时引入的误差比并联电路小。     

微分变换法求解二维非线性Volterra积分微分方程

为了解决二维非线性Volterra积分微分方程的求解问题,本文给出微分变换法.利用该方法将方程中的微分部分和积分部分进行变换,这样简化了原方程,进而得到非线性代数方程组,从而将原问题转换为求解非线性代数方程组的解,使得计算更简便.文中最后数值算例说明了该方法的可行性和有效性.     

关于曲线积分中值定理“中间点”的一个一般性结果

讨论了第一类曲线积分中值定理“中间点”的渐近性质,得到了更具一般性的新结果.     

构造非线性发展方程的无穷序列复合型类孤子新解

为了构造非线性发展方程的无穷序列复合型类孤子新解, 进一步研究了G'(ξ)/G(ξ) 展开法. 首先, 给出一种函数变换, 把常系数二阶齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题. 然后, 利用Riccati方程解的非线性叠加公式, 获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解. 在此基础上, 借助符号计算系统Mathematica, 构造了改进的(2+1)维色散水波系统和(2+1)维色散长波方程的无穷序列复合型类孤子新精确解. 关键词： G'(ξ)/G(ξ)展开法')" href="#">G'(ξ)/G(ξ)展开法 非线性叠加公式 非线性发展方程 复合型类孤子新解     

On the quasi-chemical theory of solutions

The classical canonical partition function for a one-dimensional, two-component system is examined for the case of nearest-neighbor interactions. The quasi-chemical model of solid solutions is found to be a natural consequence of the definition of the partition function when one replaces the normal configurational energy with a configurational free energy. Consequently, the quasi-chemical theory may be viewed as a consequence of the definition of the partition function and not as merely a physically pleasing model.     

Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”.A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.     

高阶非线性薛定谔方程的一个新型孤波解

给出了高阶非线性薛定谔方程的一个新型孤波解, 该解描述了满足一定参数条件时光纤中超短光脉冲的传输, 解的表达式可以表示为亮孤子和暗孤子和的形式. 同时利用分步傅里叶方法在一定微扰条件下对脉冲传输进行了数值模拟.     

以含碘氨基酸类激素为例刍议微量非金属元素在生物体内的作用机制

选取第五周期元素碘,结合多学科的研究方法论对含碘氨基酸类激素在生物体内的合成和分解代谢进行系统性分析。通过解析碘元素本身性质及其各个氧化态之间的转化,探讨碘元素在生物体内的作用机制,揭示自然界对物质代谢的精细调控。这一教学模式探索性地融入无机化学、元素有机化学、分子生物学、生物化学、生物物理学、化学生物学等一系列学科内容,旨在让学生在领悟生命科学内在规律,从而激发其科研及学习热情,并训练学生的类比思维和思辨能力。期对培养21世纪跨学科综合型人才的培养有所助益。     

聚丙烯酰胺水溶液的流变性质

粘性指进现象;聚丙烯酰胺水溶液的流变性质     

Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.