Gauss半群上的M(o)bius反演公式

将经典的M(o)bius反演公式在Gauss半群上作了进一步的推广. 即如果对任何c∈G恒有g(c,x)=Σa(ε)GAaf(ac,x)则有M(o)bius反演公式Σh(ε)Uf(hc,x)=1-NΣb(ε)GBbg(bc,x)其中G为Gauss半群.     

Optimal aeroassisted symmetric transfer between coplanar elliptical orbits

The problem of optimal aeroassisted symmetric transfer between elliptical orbits is concerned.The complete trajectory is assumed as consisting of two impulsive velocity changes at the beginning and the end of an interior atmospheric subarc,where the vehicle is controlled via the lift coefficient and thrust.The corresponding dynamic equations are built and bounded controls are considered.For the purpose of optimization computation,the equations are normalized.In order to minimize the total fuel consumption,the geocentric radius of initial elliptical transfer orbital perigee and controls during atmospheric flight should all be optimized.It is an optimal control problem which involves additional parameter optimization.To solve the problem,a two-level optimization method denoted by "genetic algorithm + Gauss pseudospectral method" is adopted:the genetic algorithm is used for parameter optimization and the Gauss pseudospectral method is used for optimal control problems.The flow chart of simulation is given.On this basis,the issue of more realistic modeling with two finite-thrust subarcs in the nonatmospheric part of the trajectory is simultaneously addressed.The orbital transfer problem is transformed to three continuous optimal control problems,and the constraints at different times are given,which are respectively solved by using the Gauss pseudospectral method.The obtained numerical results indicate that the optimal thrust control is of bangbang type.The minimum-fuel trajectory in the atmosphere consists of aeroglide,aerocruise and aeroglide.They are compared with the results of pure impulsive model,and the conclusions that a significant fuel saving will be achieved by synergetic maneuver are drawn.     

一个改进两点Gauss公式的推导及应用

本文利用代数精度的概念对两点Gauss公式进行改进，获得了改进两点Gauss公式，代数精度提高了2次。同时也进行了一个数值算例验证，得到了满意的数值效果。     

利用时域有限差分法分析和计算介质柱内瞬态场分布

讨论了采用ＦＤＴＤ计算瞬态Ｇａｕｓｓ脉冲在介质柱体内电场分布的方法，得到了一些有价值的结果，特别是对于瞬态场与生物体相互作用的研究很有意义。     

Hilbert值鞅测度的表示定理

研究Ｈｉｌｂｅｒｔ值鞅测度的表示定理，并在一定条件下，证明任一连续的Ｈｉｌｂｅｒｔ值正交鞅测度可以表示为Ｈｉｌｂｅｒｔ值Ｇａｕｓｓ鞅测度经时间变换后所得鞅测度的随机积分．     

调和函数的一个积分恒等式

本文推导出调和函数的一个积分恒等式,并把这个结果推广到方程△_pu=0(P>1)的解的情形.     

考虑多约束的UCAV对地攻击轨迹规划

针对多约束条件下UCAV对地攻击轨迹规划问题,提出了一种基于Radau伪谱法(RPM)的求解策略。首先,分析并建立UCAV三自由度(3-DOF)质点模型,初始和终端位置、速度、姿态、飞行性能、敌方火力或探测威胁、禁飞区、地形等约束条件模型,构建考虑多约束的UCAV对地攻击轨迹规划模型;在分析RPM求解最优控制问题的基本原理及实现方式的基础上,采用RPM将轨迹规划的最优控制问题转化为非线性规划问题;最后,利用SNOPT软件包求解,并进行了数字仿真。仿真结果表明,该方法能以较高的精度和速度生成满足多种复杂约束要求、连续并且真实可行的最优轨迹。     

拟欧氏空间^4R2中的类空曲面

给出2阶实对称矩阵(h=(hij))空间到C的Hopf变换L(h)与平均曲率向量H满足的条件，讨论了拟欧氏空间^4R2中的类空曲面的一些性质，并将Pinl关于Gauss映射的一个结果推广到拟欧氏空间^4R2上．     

Sierpinski镂垫上Gauss模型的普适性

应用实空间重整化群变换的方法，研究了标度系数l=3的Sierpinski镂垫上Gauss模型的相变和临界性质，求出了系统的临界点和临界指数．结果表明，l=2和l=3的Sierpinski镂垫上的Gauss系统属于不同的普适类．说明其普适性除了决定于系统的空间维数外，还与分形维数有关．     

一类新的Dirichlet L-函数倒数的二次加权均值

利用解析方法、三角和估计，特征和估计研究了Dirchlet L-函数倒的二次加权均值，得到了一个较强的均值分布公式．