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排序方式: 共有37条查询结果,搜索用时 15 毫秒
1.
引入准齐次函数的概念,研究了具有准齐次核的一类Hilbert型奇异重积分算子的范数问题,并讨论其应用.  相似文献   
2.
设核函数K(u,v)具有对称性和齐次性,对如下定义的奇异重积分算子T:(Tf)(y)=∫R_+~n K(‖x‖α,‖y‖α)f(x)dx,y∈R_+~n,其中‖x‖α=(x_1~α+…+x_n~α)~1/α(α>0),研究了T的范数及其应用.  相似文献   
3.
利用权函数方法和实分析技巧,讨论了一类非齐次核■(λ1λ2>0)的Hilbert型重积分不等式的搭配参数,得到最佳搭配参数的充分必要条件及最佳常数因子的表达式。利用所得结果,讨论了相应的重积分算子的有界性及算子范数。  相似文献   
4.
Hardy-Hilbert积分不等式的全方位推广   总被引:26,自引:0,他引:26  
洪勇 《数学学报》2001,44(4):619-626
本文对 Hardy-Hilbert积分不等式进行了积分重数和多参数方面的全方位推广,同时得到了很多形式优美的全新不等式.  相似文献   
5.
关于Hardy-Hilbert不等式的新推广   总被引:1,自引:0,他引:1  
给出一个涉及n个函数的且带有参数λ的Hardy-Hilbert积分不等式和级数不等式,并证明在λ=1时,其常数因子是最佳的。  相似文献   
6.
The solid-liquid interface motion of NaBi(WO4)2 (NBWO) melt crystal growth is observed in an in situ system, in which the whole processes of interface transition from fiat interface and cellular to dendrite are visualized. The spacing of the dendrite under smaller temperature gradient turns out to be larger than that under larger temperature gradient, which is found to be sensitive to the temperature distribution. The mechanism of dendrite growth of NBWO is studied based on the model of the growth units of anion coordination polyhedra. The { 001} face has two apex links, so it shows higher stability and has high growth rate and forms the arm of dendrite, whereas the {010} face has only one apex link, and thus shows relative slower growth rate and firstly forms the branches.  相似文献   
7.
The transition from a fiat solid-liquid interface to a skeletal shape during BaB2O4 (BBO) single crystal growth in Li2B4O7 flux is observed in real time by an optical high-temperature in-situ observation system. The movement of crystal step is also investigated. The observation results demonstrate that the steps propagate along and parallel to the fiat interface when the crystal size is small. Nevertheless, they will ‘bend' close to the face centre if the crystal size becomes greater. Atomic force microscopy reveals that more deposition places near the face centre give rise to the bending of advancing steps and thus the formation of a vicinal interface structure. Measurements of step velocity show that the velocity keeps nearly constant at different moments for one specific step, whereas the step on a newly formed layer advanced faster than that on a previously formed one when the crystal size is larger than 210μm or so. Thus interracial morphological instability occurs and a skeletal interface is obtained.  相似文献   
8.
朱振和  洪勇  葛培文  俞育德 《中国物理》2004,13(12):1982-1991
The stability of the shapes of the growing crystal face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied. Effects of the interface kinetics and anisotropy of crystallization and dissolution on the stability are also studied. It is proved that the stable shapes of crystal growth face and dissolution face do exist, which are of suitably shaped curves with their upper parts inclined backward properly no matter whether the interface kinetics and the anisotropy are taken into account or not. The stable shapes of the growing crystal faces and dissolution faces are calculated for various cases. The interface kinetics will make the inclination degree of stable crystal growth face reduce and that of stable dissolution face reduce slightly. The anisotropy of crystallization and dissolution may make the inclination degree of stable-growing crystal face smaller or larger, and that of the stable dissolution face varies very slightly.  相似文献   
9.
泛函中的两个对偶定理   总被引:1,自引:0,他引:1  
本文利用*隔离定理,证明了Mazur定理和凸集的最佳逼近元存在性定理的对偶定理.  相似文献   
10.
洪勇 《数学研究》1999,32(4):409-413
定义了齐型空间上的 Riesz位势算子 Iβ ,并研究了它的 L ipschitz有界性等性质 .  相似文献   
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