Scaling Behavior between Heat Capacity and Thermal Expansion in Solids

We experimentally analyze the heat capacity and thermal expansion of reference solids in a wide temperature range from several Kelvin to melting temperature,and establish a universal double-linear relation between the experimental heat capacity C_p and thermal expansion β,which is different from the previous models.The universal behavior between heat capacity and thermal expansion is important to predict the thermodynamic parameters at constant pressure,and is helpful for understanding the nature of thermal properties in solids.     

Growth of NaBi（WO4）2 Dendrite and Mechanism

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.     

In Situ Observation of Skeletal Shape Transition during BaB2O4 Crystal Growth in High-Temperature Solution

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.     

非齐次核的Hilbert型重积分不等式适配参数的等价条件及应用

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。     

Optical and atomic force microscopic study on step bunching in BaB2O4 crystal growth

The formation of macrostep during high-temperature phase of barium meta-borate (α-BaB 2 O 4) single crystal growth has been investigated by both optical in-situ observation system and atomic force microscopy (AFM).The insitu observation results demonstrate that the critical linear size of growing facet exceeding the size that the macrostep generates is significantly anisotropic.The critical linear sizes are around 280 μm and 620 μm for {1010} and {1010} planes,respectively.AFM study illustrates that macrostep train with a height of 150 nm～200 nm is one typical morphological feature of the as-grown crystal surface.The riser of each macrostep consists of several straight and parallel sub-steps,indicating the occurrence of step bunching.Additionally,triangular sub-steps with heights of several nanometers on the treads of the macrosteps are found to be another typical feature of surface morphology,which implies a microscopically competitive bunching of sub-steps between various crystallographic orientations.     

一类具有准齐次核的Hilbert型奇异重积分算子的范数及应用

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.     

一类带齐次核的奇异重积分算子的范数及其应用

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.     

核为G(nλ1xλ2)(λ1λ2 > 0)的半离散Hilbert型不等式成立的等价参数条件及应用*

利用权函数方法和实分析技巧, 在λ₁λ₂ > 0 的条件下,讨论具有非齐次核K(n,x)=G(n^λ₁x^λ₂)的半离散Hilbert型不等式成立的等价参数条件及最佳常数因子问题, 最后讨论其在算子理论中的应用.     

齐型空间上Riesz位势算子的Lipschitz有界性

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 .     

泛函中的两个对偶定理

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．