键合成反键分子轨道的原子轨函符合对称性条件

键合成反键分子轨道的两个原子轨函对键轴的对称性是一致的,且它们的重叠积分S和β积分均不为零,故它们符合对称性条件。有两种不同类型的异号原子轨函重叠,反键型和非键型。只有后者不符合对称性条件。不要把反键分子轨函中节面上的φ_(MO)=0误认为是S=0或β=0。

条件分布对称性的一个一致性检验及渐近正态性（英文）

本文研究了条件分布对称性检验的问题.借助能量距离的概念与思路,提出了条件能量距离的概念.基于条件能量距离构造出一个新的条件分布对称性的检验统计量,该统计量具有带随机核的U-统计量的形式.利用带随机核U-统计量理论证明得到该检验统计量的一致性及在原假设下的渐近正态性的结果.

边界元法中对称面条件处理的场点映射法

本文充分利用了格林函数本身的对称性和互易性,建立了更完善、更有效的对称面条件处理的场点映射法.它用对称面把物体分成基本体和非基本体,通过作场点 p 关于对表面的映射,来正确反映非基本体的影响,计算仅需离散基本体的原有物体表面(不包含对称面).与其他方法相比,本方法不受无限域的影响,不会带来附加的奇异性和新的棱边角点;仅与场点有关而与单元特性无关,因此,完全适合在高阶边界元中使用.

国内外豆粕市场之间的价格传递--基于VECM-ADCC-VARMA-GARCH模型的分析

豆粕价格波动对豆粕的生产和营销、上游大豆生产和下游畜禽水产饲养均具有重要影响。为弥补豆粕价格传递建模分析方面的缺陷,构建VECM-ADCC-VARMA-GARCH模型,考察国内外豆粕市场价格之间的均值溢出、波动溢出以及非对称时变条件相关性。结果发现,国内外豆粕市场价格之间存在长期均衡关系,豆粕价格均值和波动均存在从国际市场向国内市场的单向溢出效应,国内外豆粕市场之间存在非对称性时变条件相关性;虽然整个样本期间国内、国际2个市场之间的非对称性时变条件相关性并无明显的升降趋势,但前期负的冲击比同样大小正的冲击会带来当期更大的时变条件相关性。研究结论对于豆粕市场参与者同时利用国内外两个市场进行有效的资产配置以及构建风风险管理策略具有重要启示意义。

Synthesis and Surface Activity of Heterogemini Imidazolium Surfactants

A series of heterogemini imidazolium surfactants with two-methylene spacer groups （[Cm- 2-Cnim]Br2, m, n=8, 10, 12, 14, 16; m≠n） have been synthesized and characterized by 1H NMR and ESI-MS spectroscopy. The effects of various reaction parameters, including stoichiometry, reaction temperature and time, were investigated. In addition, the surface activity study about heterogemini imidazolium surfactants was carried out and the influences of dissymmetric degree on the surface properties were also discussed.

Multi-solution of Semilinear Elliptic Equation on R^N

In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.

Approximate Generalized Conditional Symmetries for Perturbed Evolution Equations

The concept of approximate generalized conditional symmetry （AGCS） for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples.

Conditional Symmetries and Solutions to a Class of Nonlinear Diffusion-Convection Equations

The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained.

Variable Separation and Exact Separable Solutions for Equations of Type uxt=A（u,ux）uxx＋B（u,ux）

The generalized conditional symmetry is developed to study the variable separation for equations of type uxt = A（u,ux）uxx ＋ B（u, ux）. Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their exact separable solutions are constructed.

Current Reversal Due to Coupling Between Asymmetrical Driving Force and Ratchet Potential

Transport of a Brownian particle moving in a periodic potential is investigated in the presence of an asymmetric unbiased external force. The asymmetry of the external force and the asymmetry of the potentlal are the two ways of inducing a net current. It is found that the competition of the spatial asymmetry of potential with the temporal asymmetry of the external force leads to the phenomena like current reversal The competition between the two opposite driving factors is a necessary but not a sufficient condition for current reversals.

Symmetry Reductions of a Lax Pair for(2+1)-Dimensional Differential Sawada-Kotera Equation

Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the （2＋1 ）-dimensional differential Sawada Kotera （SK） equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair＇s compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.

Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations

Lie symmetry reduction of some truly ＂variable coefficient＂ wave equations which are singled out from a class of （1 ＋ 1）-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed.

Hamilton系统的对称辛广义加性Runge-Kutta方法

Sandu和Günther[SIAM J.Numer.Anal.53(2015)17--42]对形如y=N∑k=1 f[k](y)的微分方程提出广义加性Runge-Kutta(GARK)方法.本文利用双色有根树导出GARK方法的阶条件,给出辛条件和对称性条件,并构造了三个二阶对称辛GARK(SSGARK)方法和两个四阶SSGARK方法.对三个经典测试问题的数值实验结果显示,与文献中几个非对称或非辛的ARK/GARK方法相比,新的SSGARK方法能更有效地保持Hamilton量.

A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids

A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.

Interface stress around a nanosized spherical inhomogeneity under asymmetric dynamic loads

In the design and optimization of nanocomposites,the surface/interface stress arising at the inhomogeneity-matrix boundary plays an important role in determining the strength of structures.In this paper,the effect of surface/interface stress on the dynamic stress around a spherical inhomogeneity subjected to asymmetric dynamic loads is investigated.The surface/interface stress effects are taken into account by introducing Gurtin-Murdoch surface/interface elasticity model.The analytical solutions to displacement potentials are expressed by spherical wave function and associated Legendre function.The dynamic stress concentration factors around the spherical nano-inhomogeneity are illustrated and analyzed.The effects of the incident wave number,and the material properties of the interface and inhomogeneity on the dynamic stress around the inhomogeneity are examined.

Reflection and Transmission Coefficients of the Symmetric Barrier-Type Shifted Deng–Fan Potential

By applying continuity and boundary conditions, the reflection and transmission coefficients of one- dimensional time-independent Schr6dinger equation with a symmetric barrier-type shifted Deng-Fan potential are ob- tained and discussed. The numerical and graphical results are very sufficient, accurate and consistent with the conser- vation of probability.

Comparison of Synchronization Ability of Four Types of Regular Coupled Networks

We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.

Nerve pulse propagation in biological membranes： Solitons and other invariant solutions

We investigate a generalized form of the Boussinesq equation, relevant for nerve pulse propagation in biological membranes. The generalized conditional symmetry （GCS） method is applied in order to obtain the conditions that enable the equation to admit a special class of second-order GCSs. For the case of quadratic nonlinearities, we outline a new class of invariant solutions.

The random walking method for the steady linear convection-diffusion equation with axisymmetric disc boundary

In this article,the random walking method is used to solve the steady linear convection-diffusion equation(CDE)with disc boundary condition.The integral solution corresponding to the random walking method is deduced and the relationship between the diffusion coefficient of CDE and the intensity of the random diffusion motion is obtained.The random number generator for arbitrary axisymmetric disc boundary is deduced through the polynomial fitting and inverse transform sampling method.The proposed method is tested through two numerical cases.The results show that the random walking method can solve the steady linear CDE effectively.The influence of the parameters on the results is also studied.It is found that the error of the solution can be decreased by increasing the particle releasing rate and the total walking time.