Solutions and Conditional Lie-Backlund Symmetries of Quasi-linear Diffusion-Reaction Equations

New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.

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.

Cauchy Problems for KdV-type Equations and Higher-Order Conditional Symmetries

We develop the generalized conditional symmetry （GCS） approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations. We characterize these equations that admit certain higherorder GCSs and show the main reduction procedure by some examples. The obtained reductions cannot be derived within the framework of the standard Lie approach.

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.

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.

Noether-Type Symmetries and Associated Conservation Laws of Some Systems of Nonlinear PDEs

The algorithm for constructing conservation laws of Euler Lagvange type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.

STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS

We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.

非线性扩散方程的条件Lie-Backlund对称和符号不变量

考虑了径向对称非线性扩散方程的条件Lie-Bcklund对称和符号不变量.允许二阶条件Lie-Bcklund对称和一阶Hamilton-Jacobi型符号不变量的方程被确定给出,并由对称约化得到了方程的不变解.

非齐次非线性扩散方程的三阶条件Lie-Backlund对称和微分约束

运用线性决定方程方法研究了非齐次非线性扩散方程.给出了允许三阶条件Lie-B?cklund对称和微分约束的非齐次非线性扩散方程,通过基于不变曲面条件和方程相容性的对称约化,得到所得方程的精确解.

Neumann Boundary Conditions Inhibiting SSB in Coleman-Weinberg Mechanism

In this work we show that homogeneous Neumann boundary conditions inhibit the Coleman-Weinberg mechanism for spontaneous symmetry breaking in the scalar electrodynamics if the length of the finite region is small enough （a = e2Mφ-1, where M, is the mass of the scalar field generated by the Coleman-Weinberg mechanism）.

具Dirichlet边界条件积分方程组的对称性研究

考虑如下具Dirichlet边值条件的积分方程组:■其中,R_(+)^(n)为n维欧式空间的上半部分,Gi(x,y)是R_(+)^(n)中满足Dirichlet边值条件的格林函数,fi(u)(i=1,2,…,m)是实值函数。本文假设积分方程组在R_(+)^(n)上存在满足一定可积性的正解ui,利用积分形式的移动平面法,证明了正解ui关于某条轴径向对称。

Energy Conditions and Conservation Laws in LRS Bianchi Type Ⅰ Spacetimes via Noether Symmetries

In this paper, we have completely classified the locally rotationally symmetric(LRS) Bianchi Type Ⅰ spacetimes via Noether symmetries(NS). The usual Lagrangian corresponding to LRS Bianchi Type Ⅰ metric is used to find the set of determining equations. To achieve a complete classification, these determining equations are generally integrated to find the components of NS vector field and the metric coefficients. During this procedure, several cases arise which give different Noether algebras of dimension 5,..., 9, 11, and 17. A comparison is established between the obtained NS and the Killing and homothetic vectors. Corresponding to all NS generators, the conservation laws are stated by using Noether's theorem. The metrics which we have obtained as a result of our classification are shown to be anisotropic or perfect fluids which satisfy certain energy conditions.

土壤湿润条件下基于光谱对称度的盐渍土盐分含量预测

近年来光谱技术以其经济、高效的优势在土壤盐渍化监测研究中得到重视,但是由于土壤水分对反射光谱影响很大,土壤湿润条件下监测精度难以满足农业生产需求。通过对盐土土柱室内模拟蒸发过程中的反射光谱和水分、盐分变化的连续监测,利用多元逐步回归方法,建立了1 370～1 610nm光谱对称度与土壤表层含盐量、含水量之间的线性关系模型,r为0.863;用该模型反演表层土壤含盐量,实测值与预测值之间线性关系的r为0.656(n=54),RMSE为2.059g·kg-1。利用光谱对称度可以实现土壤湿润条件下土壤盐分含量预测。

蒙古冷涡影响下的北京降雹天气特征分析

蒙古冷涡是诱生北京地区冰雹天气的一种主要天气系统,通过对近8年几例冰雹天气过程的分析,得出在蒙古冷涡影响下,北京地区产生的冰雹天气与其他天气类型相比,具有分布范围广、局域性强的特点。对蒙古冷涡影响下的天气形势进行详细分析,可以进一步将其分为两类,一类是蒙古冷涡后部强冷空气与前部暖湿气流交绥,地面强冷锋造成的对流天气;另一类是主冷锋后,蒙古冷涡后部不断南下的冷空气,与增温、增湿的地面低涡或切变线系统而形成不稳定大气层结造成的对流天气。同时该两类天气也有许多共同特征。如对流层低层的能量锋,大气的斜压性和层结的条件对称不稳定激发了能量锋前蕴酿已久的湿有效能量得到了有效的释放,导致对流不稳定天气的发展。对流层中层干冷空气的侵入,正的差动假相当位温平流加剧了大气层结的不稳定,强的风垂直切变更促使对流上升运动的发展。尽管这两类冰雹的各项特征的强弱程度不同,所产生的冰雹天气强弱也有差别,但都表现了有利于冰雹天气发生和发展的动力、热力特点。与其它个例比较,可以综合提出蒙古冷涡影响下冰雹天气的预报着眼点,为北京地区强对流天气潜势预报和临近预报提供理论依据。

对一次台风暴雨的位涡与湿位涡诊断分析

利用中尺度模式WRF对台风卡努模拟所输出的高分辨率资料,借助等熵位涡及湿位涡的方法进行诊断分析,揭示台风暴雨过程中的中尺度系统演变特征以及探讨台风暴雨发展与维持的机制。结果表明:等熵面位涡图的分析清楚地揭示了台风低压及周边环境的位涡演变特征。暴雨区落在低层等熵面位涡高值中心的东北侧,或者在高层等熵面位涡高值中心右侧最大位涡梯度处;等位温面向正位涡异常中心收拢,高层的高位涡值下传,高位涡的干冷空气加强了低层的扰动,引起低层暖空气的抬升,这些条件促使对流不稳定能量与潜热能的释放,有利于暴雨增幅;条件性对称不稳定与对流不稳定是此次台风暴雨发展与维持的重要机制,暴雨区内中尺度系统的发展符合倾斜涡度发展理论。

非对称信息条件下企业税收筹划的博弈分析

信息是企业进行税收筹划活动的前提和依据。企业所获得的信息精度越高,信息的价值越大,所进行的税收筹划也就越有实用性,越有可能成功。在现实条件下,企业进行的税收筹划是在非对称信息条件下进行的。因此,在税收筹划的实践中,企业应根据税收筹划的不同领域制定多套筹划备选方案,筹划的方案越多,筹划的实际效果就越佳,获得成功的概率也就越大。

“049”川渝暴雨的Q矢量与湿位涡分析

采用NCEP/NCAR再分析资料对"049"暴雨过程的准地转Q矢量及湿位涡进行诊断分析,揭示了暴雨期准地转Q矢量散度场、涡度场以及锋生函数的分布特征以及与暴雨之间的时空配置关系,指出了Q矢量散度与垂直运动有很好的配置关系,低层Q矢量辐合有利于上升运动的发展和维持,Q矢量对此次暴雨过程具有一定作用;暴雨区对流层中低层的对流不稳定与条件性对称不稳定对此次暴雨过程起了关键作用,而且很可能是中尺度对流系统发生发展的重要条件之一。

两个相似路径台风深入内陆所致暴雨对比分析

使用中国气象局热带气旋年鉴、FY-2云顶亮温资料、常规观测资料及NCEP/NCAR再分析资料,对两个路径相似北上深入内陆,发生变性并直击黑龙江省的1215号超强台风“Bolaven(布拉万)”和1913号超强台风“玲玲(Lingling)”特征和降水差异进行对比分析。结果表明:(1)两次台风暴雨过程均与中尺度锋生有关。较强冷空气侵入促使“布拉万”西北侧锋区强烈锋生,深厚的上升运动形成中尺度对流区,降水强度大,使其变性快,移动慢。(2)“玲玲”北上到相同纬度时具有更大的强度,更深厚的湿层和低层更大的比湿,但由于仅有扩散南下的弱冷空气侵入台风环流,使其变性慢,移动快,台风中心北侧锋生作用弱,降水强度和范围均较小。(3)对流结构和降水强度有较大差异,“布拉万”云系东侧减弱消散,西侧和北侧与冷空气相互作用触发对流;“玲玲”云系结构基本维持不变,中尺度对流云团出现在台风中心及中心北部。(4)“布拉万”过程,大气具有强对流不稳定性,暴雨区域内对流活跃,强降水持续时间长。“玲玲”北上时,仅在低层有弱对流不稳定,对流较弱,强降水持续时间较短。暴雨区低层对流不稳定、中层湿对称不稳定,有利于强降水的维持和发展。

一个新的具有超级多稳态的五维忆阻超混沌系统

为了描述更加复杂的非线性动力学特性并且得到更适合工程应用的混沌信号,使用一个磁控忆阻器去替换改进的四维Lü混沌系统中的耦合参数,得到了一个新的五维忆阻超混沌系统。采用相图、分岔图、Lyapunov指数谱等常规的非线性分析手段研究新系统丰富的动力学特性。在新系统的基础上,通过引入一个绝对值函数使系统达到新的极性平衡,构建了一个新的条件对称的忆阻超混沌系统。结果表明:新的忆阻系统可以表现出依赖于忆阻器初始状态的超级多稳态特性、持续的混沌或超混沌动力学以及偏移增量控制行为;特别地,当改变系统参数并取适当的初始状态时,可以观察到独特的共存超级多稳态现象;新的条件对称忆阻系统可产生无限多对具有相反极性且吸引子结构相似的共存吸引子。利用Multisim进行电路仿真,验证了系统的存在性和可实现性,从而使超混沌系统能更好地应用在保密通信等实际工程领域。

Boussinesq方程的非古典对称和相容性

研究了一类任意阶的非线性偏微分方程的非古典对称的决定方程,比较了非古典对称和古典对称求解方法的不同,在求解非线性古典对称的过程中,引用了一个简单的偏微分方程,运用向量场和其延拓以及不变表面条件和初始方程的相容性两种方法求出了相同的非古典对称的决定方程,由此,得出了利用不变表面条件和初始方程的相容性也可以求得非线性偏微分方程的非古典对称的重要结论.以Boussinesq方程为例,证明了该结论的可行性.