关于概率论中的分段函数问题

分段函数在概率论中有着广泛的应用.通过对几个概率问题的研究,探讨针对分段函数如何合理分段或分区域进行积分问题,体现分段函数在概率论中的重要性.     

一维p-Laplacian方程奇异边值问题的正解

本文讨论了一维p-Laplacian方程奇异边值问题的正解的存在性,其中函数f(t,x)可能在t=0,1都有奇点     

Banach空间中非线性Φ-伪压缩映象不动点的迭代逼近

本文研究了非线性拟西Φ-伪压缩映象与Φ-伪压缩映象的不动点的迭代逼近问题.研究结果表明:在任意实的Banac h空间E中,拟Φ-伪压缩映象与Φ-伪压缩映象T(T不必连续)的具误差的Ishikawa与Mann迭代序列强收敛于T的唯一不动点.所得结果不但改进和推广了最近一些文献的相关结果,而且也改进了定理的证明方法.     

一类Banach空间中的分析性质及反例

本文对具有Schauder基的无穷维Banach空间上的映射定义偏导数,并讨论f的可徽性与偏导数存在并连续的关系;同时,本文还时论象所在空间为具有Schauder基的空间时,映射f与坐标映射f_i在可微性、连续性方面的关系.     

一维 p-Laplacian方程的两点奇异边值问题正解的存在性

该文讨论了如下一维 p-Laplacian 方程-(|u'(t)|^p-2u'(t))'=a(t)f(u(t)), t∈(0,1) u(0)=u(1)=0 的两点奇异边值问题正解的存在性,其中f可能在t=0,1都有奇点.     

Banach空间中非线性$\Phi$-伪压缩映象不动点的迭代逼近

本文研究了非线性拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象的不动点的迭代逼近问题.研究结果表明: 在任意实的Banach空间$E$中,拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象$T$~($T$不必连续)的具误差的Ishikawa与Mann迭代序列强收敛于$T$的唯一不动点.所得结果不但改进和推广了最近一些文献的相关结果,而且也改进了定理的证明方法.     

Dynamic Evolution of Outer Radiation Belt Electrons due to Whistler-Mode Chorus

Following our preceding work, we perform a further study on dynamic evolution of energetic electrons in the outer radiation belt L=4.5 due to a band of whistler-mode chorus frequency distributed over a standard Gaussian spectrum. We solve the 2D bounce-averaged Fokker-Planek equation by allowing incorporation of cross diffusion rates. Numerical results show that whistler-mode chorus can be effective in acceleration of electrons at large pitch angles, and enhance the phase space density for energies of about 1 MeV by a factor of 10^2 or above in about one day, consistent with observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm. Moreover, neglecting cross diffusion often leads to overestimates of the phase space density evolution at large pitch angle by a factor of 5-10 after one day, with larger errors at smaller pitch angle, suggesting that cross diffusion also plays an important role in wave-particle interaction.     

Response of the Earth＇s Magnetosphere and Ionosphere to Solar Wind Driver and Ionosphere Load： Results of Global MHD Simulations

Three-dimensional global magnetohydrodynamic simulations of the solar wind-magnetosphere-ionosphere system are carried out to explore the dependence of the magnetospheric reconnection voltage, the ionospheric transpolar potential, and the field aligned currents （FACs） on the solar wind driver and ionosphere load for the cases with pure southward interplanetary magnetic field （IMF）. It is shown that the reconnection voltage and the transpolar potential increase monotonically with decreasing Pedersen conductance （∑ p ）, increasing southward IMF strength （Bs） and solar wind speed （Vsw）. Moreover, both regions 1 and 2 FACs increase when Bs and vsw increase, whereas the two currents behave differently in response to ∑p. As ∑p increases, the region 1 FAC increases monotonically, but region 2 FAC shows a non-monotonic response to the increase of ∑p ： it first increases in the range of （0,5） Siemens and then decreases for ∑p 〉 5 Siemens.     

铜(II)-锰(II)四核配合物的合成、晶体结构和磁性

(中国地质大学地质实验室, 北京100083) 报道了一个草酰胺桥连的四核Cu(II)Mn(II)配合物[Mn(CuL)3][Mn(H2O)6][N(CN)2]2(ClO4)2 4H2O (L为1,4,8,11-四氮杂环十四烷-2,3-二酮) (C34H74Cl2Cu3Mn2N18O24, Mr = 1490.51)的合成、晶体结构和磁性。配合物属于单斜晶系, 空间群为C2/c, 晶胞参数如下:a = 22.295(5), b = 12.852(3), c = 20.109(4) , = 90.47(3), V = 5762(2) 3, Dc = 1.718 g/m3, Z = 4, F(000) = 3068, m = 1.701mm-1, R = 0.0915, wR = 0.1810 (based on F2)。3个中性Cu(II)大环配合物通过6个氧原子与Mn(II)配位, MnO键长范围为2.190(6)~2.208(5) 拧Mn(CuL)3]2+通过高氯酸根离子连接起来形成一个二维层。高氯酸根的氧原子与CuII键长范围为2.902~2.996 , 为弱相互作用。[Mn(H2O)6]2+, N(CN)2-和H2O位于层间, 并通过氢键连成三维网络结构。磁性研究表明CuII-MnII离子间通过草酰胺传递反铁磁相互作用, 用基于各向同性的Hamiltonian算符 = 2JMnCuMn(Cu1 + Cu2 + Cu3)进行磁性拟合得到磁耦合常数JCuMn =-17 cm-1。