带五次项的非线性Schrǒdinger方程的显式精确解析解

用两种不同的假设求出了一类带五次项的非线性Schrǒdinger 方程的显式精确行波解,这些解包括两种类型的孤波解、奇异行波解和三角函数型周期波解.     

多重量子阱光致发光及表面本征态数值分析

建立了量子阱的物理模型．通过变分法和数值逼近法分析了多重量子阱光致发光现象及能量本征值和本征函数．采用的量子线多孔硅（PS）量子阱在分析光致发光特性上是比较显著的．能量修正中，无论在弱场中或强场中，变分法优于微扰法．对于光致发光的强度分析，量子阱的重数逐渐增多，更接近于实验值。     

用Bethe Ansatz方法求解本征值

通过对SU(n)Hubbard可积模型的研究，求出该模型的能量本征值．用可积模型中的坐标Bethe Ansatz的方法，首先由薛定谔方程求得能量的本征方程，设定波函数的具体形式，求出本征能量，SU(n)Hubbard可积模型的本征能量可通过Bethe Ansatz的方法求得。     

利用(g′/g~2)展开法求解KdV-Burgers方程和KdV-Burgers-Kuramoto方程

根据(g′/g~2)展开法求得KdV-Burgers方程和KdV-Burgers-Kuramoto方程的精确解,在不同的条件下,得出双曲函数通解、三角函数通解以及有理函数通解.双曲函数通解中的常数项取特殊值时,得出孤立波解.(g′/g~2)展开法求解KdV-Burgers方程和KdV-Burgers-Kuramoto方程,比(g′/g)展开等方法,具有简便、易于计算的特点,是求解非线性方程的较好选择.     

J/ψ粒子夸克势的解析计算

利用一种带相位因子的场方程,给出了J/ψ粒子夸克势的解析表达式,并与文献中给出的KMS和erf两种夸克势作了比较.     

Volterra积分方程的Haar小波解

给出了一种有效求解第一型Volterra积分方程的方法.以有理Haar小波作为逼近函数,利用小波配置方法,将第一型Volterra积分方程的近似求解问题转化为线性方程组求解.进而,得到原方程的近似解.数值算例表明了该方法的可行性和精确性.     

大尺寸抛物线形超声变幅杆频率的瑞利修正

利用瑞利能量法对大尺寸抛物线形超声变幅杆的共振频率进行修正,得到了修正频率表达式.通过数值计算得出大尺寸抛物线形超声变幅杆频率修正结果,并利用有限元软件对一组大尺寸抛物线形变幅杆进行模态分析.将修正结果与一维的理论值进行对比分析,可得修正后的频率值更接近于有限元模拟仿真值.     

Helmholtz问题的径向基无网格配置法的研究

通过引入一种新的径向基函数构造了求解Helmholtz方程配置型的无网格方法,证明了数值解的存在惟一性,并且将该方法用于二维Helmholtz问题的数值检验.与有限元法及其他径向基函数配置法相比较,该方法计算精度高,更加实用有效.     

完整系统Tzénoff方程的Mei对称性对应的新守恒量

研究了完整力学系统Tzénoff 方程Mei对称性所对应的一种新守恒量.给出了这种守恒量的函数表达式并导出了产生这种守恒量的判据方程.利用该方法比以往更易找到守恒量,最后举例说明了新结果的应用.     

双极流体动力学模型初边值问题解的整体存在性

研究了1/4平面上的一维等熵双极流体动力学模型,这个模型是增加了电子场及由摩擦产生的阻尼的动量方程的Euler-Pisson系统,这类双极模型是目前研究较少的一类模型.通过引入合适的新的变量,将此方程转化为常见的阻尼波动方程,并在此基础上利用古典能量估计方法计算.应用分部积分以及边界估计的方法,证明了具有非零边界条件的...     

基于哈密顿原理轴向运动纱线的振动特性研究

为获得任意载荷作用下轴向行进纱线任意点的横向位移参数,建立了轴向运动纱线在哈密顿体系下无量纲动力学微分方程。通过应用最小变分原理得到运动纱线的对偶方程,用分离变量法计算轴向运动纱线系统的各阶特征值和特征函数;基于线性辛特征值得到非奇异模态函数,推导出了模态函数的辛共轭正交归一关系;根据特征值及其分岔规律,分析纱线横向运动的稳定性,并利用非奇异模态函数分析纱线自由振动和受迫振动的位移响应;依据纱线横向振动的近似解,分析运动纱线在不同运行状态下的动力学行为。结果表明,纱线运动速度对响应周期、不同质点的响应幅值以及构形有较大影响,前2项构形经叠加即可求得纱线位移。     

一类Schrodinger算子逆谱问题的惟一性

考虑边值条件中含谱参数的一类Schrodinger算子逆谱的惟一性问题．由Sturm-Liouville问题逆谱理论中的惟一性定理及整函数的性质证明了基于一定条件下,特征值（包括重数）和一个相关的参数γ能惟一确定势函数．     

用近似同伦对称法求解阻尼KdV方程

应用近似同伦对称方法对阻尼KdV方程进行约化并求得近似解.为阻尼KdV方程选取一个同伦模型,其近似解可以用级数形式表示;再应用近似对称法,可以将其方程约化为若干个3阶ODE方程.近似同伦对称方法适用于一类强扰动非线性微分方程.     

新的五类整图

一个图是整的是指它的邻接矩阵的特征多项式的特征值全是整数的图.为了进一步得到更多的整图,从Tang和Hou的文章＂The integral graphs with index 3 and exactly two main eigenval-ues,Linear Algebra Appl.2010,433,984-933＂中得到的5个阶数较小的整图,运用推广的方法构造了阶数与正整数m,n有关的五类新图.通过计算得到新图的特征多项式,进而得到了这五类图是整图的充分必要条件,最终得到了五类新的整图.     

Misapplication of the Clausius–Clapeyron equation for estimating heats of adsorption in foods

It has been pointed out that the Clausius–Clapeyron equation which is currently used to measure isosteric heat of adsorption in reality measures the latent heat of evaporation. The usual Clausius–Clapeyron plot that decays rapidly to low values at low Aws has been compared with a suggested alternative equation derived directly from an expanded form of Caurie's unimolecular adsorption equation. The plot of the proposed equation is higher than that of the Clausius–Clapeyron equation, and it has the shape of an inverse sigmoid isotherm. Two discontinuities in the proposed plots are stated to demarcate three energy levels corresponding to three states of bound water recognised to exist along sigmoid food isotherm plots.     

Modeling water uptake in a cereal grain during soaking

A diffusion equation to describe the isothermal absorption of liquid water in a spherical solid that undergoes uniform swelling was derived. The resulting partial differential equation was solved using a finite difference method, taking into consideration water content dependence of the diffusion coefficient. The developed model was applied to simulate the water uptake of brown rice for the soaking temperatures of 25, 45, 55 and 65 °C. The estimated “differential” diffusion coefficients were a strongly increasing function of moisture content for all temperatures tested, approaching to the self-diffusion coefficients of water for brown rice moisture contents near to the saturation values. The “integral” diffusion coefficient corresponding to range of moisture content resulting from soaking conditions were calculated and correlated according to Arrhenius equation with an activation energy of 32.5 kJ/mol.     

三种不同通风道对浅圆仓通风效果的模拟研究

基于多孔介质流动和热湿耦合传递理论,推导得到了浅圆仓的粮堆内部动量方程、能量方程和水分守恒方程,通过数值求解法解决仓储粮堆的自然对流、热量传递和水分传递之间的问题。采用Fortran编程的方法,针对浅圆仓的十字型通风道、环型通风道、组合型(十字型加环型)通风道的通风效果进行了数值模拟分析。结果表明:组合型通风道相比其它两种通风道仓内气流分布更加均匀,降温保水效果最好,更有利于粮食的安全储存和节能降耗。为浅圆仓通风道的选择和设计提供了理论指导和依据。     

Invited review: Corrected milk: Reconsideration of common equations and milk energy estimates

Corrected milk equations were developed in attempts to bring milk weights to a standardized basis for comparison by expressing the weight and composition of milk as corrected to the energy content of milk of a specific composition. Expressed as milk weights familiar on farm and in commerce, this approach integrates energy contributions of the dissimilar components to make the mass units more comparable. Such values are applied in evaluating feed efficiency, lactation performance, and global milk production, as functional units for lifecycle assessments, and in translation of research results. Corrected milk equations are derived from equations relating milk gross energy to milk composition. First, a milk energy equation is used to calculate the energy value of the milk composition to correct to (e.g., 0.695 Mcal/kg for milk with 3.5% fat, 3.05% true protein, and 4.85% lactose). That energy value is divided into the energy equation to give the corrected milk equation. Confusion has arisen, as different equations purport to correct to the same milk composition; their differences are based on uses of different energy equations or divisors. Accuracy of corrected milk equations depends on the accuracy of the energy equations used to create them. Energy equations have evolved over time as different milk component analyses have become more available. Inclusion of multiple milk components more accurately predicts milk energy content than does fat content alone. Omission of components from an equation requires the assumption that their content in milk is constant or highly correlated with an included component. Neither of these assumptions is true. Milk energy equations evaluated on a small data set of measured milk values have demonstrated that equations that incorporate protein, fat, and lactose contents multiplied by the gross energy of each component more closely predict milk energy than equations containing fewer components or regression-derived equations. This provides a tentative recommendation for using energy equations that include the 3 main milk components and their gross energy multipliers for predicting milk energy and deriving corrected milk equations. Accuracy of energy equations is affected by the accuracy of gross energy values of individual components and variability of milk composition. Lactose has consistent reported gross energy values. In contrast, gross energy of milk fat and protein vary as their compositional profiles change. Future refinements could assess accuracy of milk fat and protein gross energy and whether that appreciably improves milk energy predictions. Fat gross energy has potential to be calculated using the milk fatty acid profile, although the influence on gross energy may be small. For research, direct reporting of milk energy values, rather than corrected milk, provides the most explicit, least manipulated form of the data. However, provision of corrected milk values in addition to information on components can serve to translate the energy information to a form familiar to and widely used in the field. When reporting corrected milk data, the corrected milk equation, citation for the energy equation used, and composition and energy contents of the corrected milk must be described to make clear what the values represent.     

A general method for predicting the water activity of simple and multi-component mixtures of solutes and non-solutes

Caurie's (1985) equation for predicting the water activity ( a ^W) of binary solutions has been revised by replacing molal concentration units and activity coefficient with equivalent expressions for weight concentration (g/kg H₂O). Results obtained using the revised equation, which now applies to both solutes and non-solutes, agree closely with measured literature values. The equation reveals that the relationship between the weight concentration of solute/non-solute binary solution or dispersion and the corresponding a _W exhibits a minimum for carbohydrates and proteins. Electrolytes exhibit no such minimum and are the most effective in depressing a _W while proteins are the least effective. The substitution of the new binary equation into the Ross (1975) equation results in an equation for a mixture identical with the recently corrected Ross one (Caurie, 1985), except that the correction factor in the new equation is expressed in g/kg H₂O making it applicable to simple and multi-component mixtures of both solutes and non-solutes. The new equation has been applied to literature data from various sources and has been found to agree very closely with measured values.