Rational general solutions of higher order algebraic odes

This paper generalizes the method of Ngô and Winkler (2010, 2011) for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation (AODE) to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.     

EXISTENCE AND UNIQUENESS AND STABILITY OF SOLUTIONS FOR STOCHASTIC IMPULSIVE SYSTEMS

This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stability of solutions for stochastic impulsive systems are established. Furthermore, the results are specialized to the case of linear stochastic impulsive systems. Finally, some examples are given to illustrate the applications of our theory.     

浅谈声乐教育中的心理因素

本文认为,心理在声乐教学中的地位非常重要,在声乐教育中应该注意对学生心理情感的培养.     

Interpretation of the architectural design methods

文章结合笔者近年来的工作实践,从建筑设计因素入手,分析和阐述了建筑设计的几种方法,并提出了自己的一些看法.     

[Zn（en）2]3[V10O28]·6H2O的合成、结构及表征

利用水热技术合成了以V₁₀O₂₈型同多钒酸盐为基本建筑单元、过渡金属锌化合物修饰的新型多金属氧酸盐,通过元素分析和TG分析,确定其化学式为:[Zn（en）₂]₃[V₁₀O₂₈]·6H₂O（1）,利用IR和X-射线单晶衍射对合成配合物进行了结构表征.化合物1为Monoclinic晶系,P2（1）/c空间群,晶胞参数为:a=12.9266（6）,b=11.7875（5）,c=16.6458（7）,α=90,β=109.3860（10）,γ=90,V=2392.56（18）,R₁=0.0497,wR₂=0.1227.     

问题型物理习题的解答及其策略

问题型物理习题是指生疏性物理习题,它是问题的一种特殊类型.根据物理问题的定义,提出了问题型物理习题解答的四个特点和认知心理活动模式;分析和阐述了问题型物理习题解答策略中的五个步骤:习题提出,习题分析,习题求解,习题验讨,习题应用;着重讨论了求解阶段的两种模式:尝试错误式和直觉顿悟式.     

具有时滞和常数收获率种群模型的稳定性

在生态系统中,种群的稳定性一直是研究的重点内容之一,在已有结果的基础上,考虑了一个同时具有时滞和常数收获率的捕食-被捕食模型,通过对特征方程的研究,给出了正平衡点稳定的充分条件.利用Matlab软件给出了种群模型的数值模拟结果,描述出了相平面的相轨线和种群数量随时间变化的曲线,进而更加直观地预测种群的发展趋势.