带对称齐次核的级数算子的范数刻画及其应用

对带对称齐次核K(m,n)的级数算子T:T{an}=Σ_(n=1)~∞ K(m,n)an,{an}∈lω(n),l={{an)| an≥0,Σ_(n=1)~∞ω(n)an<+∞},本文研究了T的范数刻画,并讨论其应用.     

Thermalcapillary Convection in NaBi（WO4）2 Melt

Surface-tension drive flow in NaBi(WO4)2 melt is visualized by means of the already proved method of high temperature in situ optical observation.The transition phenomena of the melt from steady spatial to oscillatory behaviour in melt are observed.The oscillatory thermocapillary convection is accompanied by synchronous temperature oscillations with the frequency 10Hz.The onset temperature of thermocapillary convection varies with the change of meniscus curvature of the melt free surface,which probably due to the liquid pressure at the surface associated with the curvature of meniscus.The oscillatory frequency is proportional to the temperature.Finally another kind of oscillatory thermocapillary convection with the frequency about 5Hz dominating in the undercooled melt is also observed.     

n-球面上的Cesàro算子的带权强性求和

设1(n-1)/p-n/2，f∈L^p(Ω_n)，σ^δ_N(f)(x)表示f(x)在n-球面Ω_n上的Cesàro平均.本文证明了(?)a_k≤A（A是绝对常数），这个结果加强了现有的结论.     

涉及多个函数的Hardy型积分不等式

利用权系数方法和Fubini定理,研究涉及多个函数的Hardy型积分不等式,得到若干新的结果．     

辽宁抚顺和新疆吉木萨尔煤精的显微组成和拉曼光谱对比研究

煤精又称煤玉,是一种资源稀缺且价格昂贵的煤种,可作为工艺美术雕琢材料。采集了辽宁抚顺和新疆吉木萨尔这两个地区的6件煤精样品,测试分析了其煤岩煤质(显微组成、腐植体最大反射率、工业分析、元素分析)和拉曼光谱特征。研究结果表明6件煤精样品中显微组分均以腐植组为主,稳定组次之,惰质组含量最低,腐植体最大反射率(R_{o, max})介于0.41%～0.55%;抚顺煤精的稳定组以沥青质体和孢子体为主,而吉木萨尔煤精的稳定组则以角质体为主;这两个地区煤精的拉曼光谱特征差异显著,拉曼结构参数显著受控于煤岩煤质;煤精的拉曼光谱参数D₁峰与G峰的强度比(I_D1/I_G)、面积比(A_D1/A_G)均随稳定组含量增加而显著增大,随腐植组和惰质组含量的增加而明显减小;吉木萨尔煤精的I_D1/I_G和A_D1/A_G值均显著...     

齐次核的半离散Hilbert型不等式取最佳常数因子的条件及应用

利用实分析技巧和权系数方法,讨论了具有齐次核的半离散Hilbert型不等式■及取最佳常数因子的条件,最后讨论其在算子理论中的应用。     

In Situ Observation of Cell-to-Dendrite Transition

The cell-to-dendrite transition of succinonitrile melt suspended on a loop-shaped Pt heater is observed in real time by a differential interference microscope coupled with Schlieren technique. The transition is divided into two parts： a dendrite coalition process and a subsequent dendrite elimination process. Firstly the dendrites from the same cell are united into a single dendrite. Secondly the competitive growth of dendrites from different cells leads to the elimination of dendrites. The two processes can be understood when involving crystallographic orientation. In addition, the tip velocity and primary spacing of a cell/dendrite are also measured. It turns out that the primary spacing has a significant jump, whereas the growth velocity has no abrupt change during the cell-to-dendrite transition.     

一类具有准齐次核的涉及多个函数的Hilbert型积分不等式

引入准齐次多元函数新概念,研究了具有准齐次核的涉及多个函数的Hilbert型积分不等式,并讨论了最佳常数问题.     

齐次核的Hilbert型级数不等式取最佳常数因子的充要条件

利用实分析技巧及权函数方法,解决了具有齐次核的Hilbert型级数不等式取最佳常数因子的充要条件,并讨论其在算子理论中的应用.     

球面上的变阶分数次积分

定义了球面ｎ上的函数的变阶分数次积分和变阶Ｌｉｐｓｃｈｉｔｚ类． 设且若则的阶积分属于