Finite symmetry transformation group of the Konopelchenko-Dubrovsky equation from its Lax pair

Starting from a weak Lax pair,the general Lie point symmetry group of the Konopelchenko-Dubrovsky equation is obtained by using the general direct method.And the corresponding Lie algebra structure is proved to be a Kac-Moody-Virasoro type.Furthermore,a new multi-soliton solution for the Konopelchenko-Dubrovsky equation is also given from this symmetry group and a known solution.     

玻色化方法在超对称可积系统的应用

利用玻色化方法可以避免超对称可积系统中反对易费米场带来的计算困难. 本文以N=1超对称mKdVB系统为例, 利用玻色化方法, 将其转化为只有玻色场的耦合系统. 应用标准的WTC方法, 证明了该耦合系统具有Painlevé性质. 运用Painlevé截断方法, 可以得到玻色化后超对称mKdVB系统的非局域对称. 为了求解与非局域对称相关的Lie第一性原理, 引入新的场将玻色化后系统拓展为更大的系统. 通过引入新的场, 该非局域对称局域化为Lie点对称. 因此, 可以利用Lie点对称约化方法研究拓展后的系统, 得到超对称mKdVB系统的孤子与其他孤波相互作用解.     

利用室温反应系数法计算轿车室内温度变化引起的空调动态负荷

在高温环境下长时间停放后的汽车在空调系统启动后的降温速度和降温辐度，是衡量汽车空调制冷系统性能优劣的主要指标。本文利用室温反应系数法建立了轿车室内温度变化时的汽车空调动态负荷模型。并以福特Ｅｓｃｏｒｔ家用轿车为例进行了实验测试，以实验结果验证了理论模型的可靠性。     

Interactions Between Solitons and Cnoidal Periodic Waves of the(2+1)-Dimensional Konopelchenko–Dubrovsky Equation

The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.     

毁伤目标时间与格斗持续时间的PH表示与特性

本文研究毁伤目标所需时间与格斗持续时间的概率分布．在射击时间间隔服从PH分布的假设下,文章导出了不考虑发现目标因素和考虑该因素二种情况下,毁伤目标时间的PH表示与特性及格斗持续时间的PH表示．最后,文章用二个实例给出了毁伤目标时间概率分布的具体求法．     

受延迟随机损伤系统可修复时间的分布特征与修复概率

研究受延迟随机损伤系统可修复时间的概率特性．即系统初始运行安全期时间长度为一随机变量,受Poisson过程规律的随机冲击并产生随机损伤．用条件随机过程和条件Markov过程为数学工具,求出系统可修复时间的密度函数与特征函数以及可修复概率．     

一种近邻密度估计的Lp模强相合性

本文对一种新的近邻密度估计的相合性继续进行研究。在相当自然的件条下得到了它的L_p模强相合性。并证得这些条件是必要的。     

具有常数迁入率和非线性传染率βI~pS~q的SI模型分析

对一种具有种群动力和非线性传染率的传染病模型进行了研究,建立了具有常数迁入率和非线性传染率βI~pS~q的SI模型.与以往的具有非线性传染率的传染病模型相比,这种模型引入了种群动力,也就是种群的总数不再为常数,因此,该类模型更精确地描述了传染病传播的规律.还讨论了模型的正不变集,运用微分方程稳定性理论分析了模型平衡点的存在性及稳定性,得出了疾病消除平衡点和地方病平衡点的全局渐进稳定的充分条件.进一步的,得出了在某些参数范围内会出现Hopf分支现象,并对上述模型进行了生物学讨论.     

Finite symmetry transformation group of the Konopelchenkoben Dubrovsky equation from its Lax pair

Starting from a weak Lax pair, the general Lie point symmetry group of the Konopelchenko-Dubrovsky equation is obtained by using the general direct method. And the corresponding Lie algebra structure is proved to be a Kac-Moody-Virasoro type. Furthermore, a new multi-soliton solution for the Konopelchenko-Dubrovsky equation is also given from this symmetry group and a known solution.     

Baicklund transformations for the Burgers equation via localization of residual symmetries

We obtain the non-local residual symmetry related to truncated Painlev~ expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie＇s first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also Iocalize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th B~icklund transformation for Burgers equation can be expressed by determinants in a compact way.