Z-半连续格

作为连续格和半连续格的公共推广,引入了广义理想子系统Z、Z-半连续格及强Z-连续格的概念,讨论了它们的基本性质和Z-半连续格的函数空间的结构,给出了强Z-连续格到方体的嵌入,证明了当子系统Z满足一定条件时,Z-半连续格范畴SCLZ是笛卡儿闭的。     

基于模糊中值滤波的椒盐噪声去除方法

研究基于模糊中值滤波的椒盐噪声去除方法。通过比较图像各像素点的灰度值,定义基于图像梯度信息的各点被判别为噪声点的模糊隶属函数。利用此模糊隶属函数对中值滤波方法进行加权,得到了一种加权中值滤波器,可实现边缘处椒盐噪声的有效滤除。讨论这种模糊加权方法与其它先进滤波方法的结合途径,指出了其推广应用价值。最后利用数值实验验证本文方法的有效性,结果表明,相比于自适应中值滤波方法,本文方法得到的滤波图像在峰值信噪比及结构相似度方面均有明显提高。     

一个基于模糊偏好的选择函数

研究了一个基于模糊偏好关系的模糊选择函数。首先对文献中基于普通关系的最好元集所确定的选择函数进行了回顾,并给出了进一步结果。然后,讨论了该选择函数的模糊化形式,给出了基于模糊偏好的选择集确定模糊选择函数的充要条件,同时研究了该选择函数的合理性性质。     

Uniqueness theorems for an impulsive Sturm-Liouville boundary value problem

In this study, an impulsive boundary value problem, generated by Sturm-Liouville differential equation with the eigenvalue parameter contained in one boundary condition is considered. It is shown that the coefficients of the problem are uniquely determined either by the Weyl function or by two given spectra.     

涉及分担函数的亚纯函数族的正规定则

本文得到一个涉及分担函数的亚纯函数族的正规定则：设F是区域D内的一族亚纯函数,k,l是正整数,ψ（z）季0为区域D内全纯函数,且其零点重数至多为l,如果对F中的任意函数,ff≠0,且f的所有极点重数都至少是l＋1,如果F中的任意函数f与g满足f^（k）与g^（k）在D内分担ψ（z）,那么F在D内正规．     

Non-real Zeros of Derivatives of Real Entire Functions and the Pólya-Wiman Conjectures

A function f is in the class $ V_2p $ iff $ f(z) = e^{-az^{2p+2}}g(z) $ where a S 0 and g is a constant multiple of a real entire function of genus h 2 p + 1 with only real zeros. The class $ U_2p $ is defined as follows: $ U_0 = V_0 $ , $ U_{2p} = V_{2p}-V_{2p-2} $ . Functions in the class $ U_{2p}^{*} $ are represented as $ g(z) = c(z)f(z) $ where $ f\in U_{2p} $ and c is a real polynomial with no real zeros. Every real entire function g , of finite order with at most finitely many non-real zeros satisfies $ g\in U_{2p}^{*} $ for a unique p . We show the exact number of non-real zeros of f" , for $ f\in U_{2p} $ , in terms of the number of non-real zeros of f' and a geometrical condition on the components of Im Q ( z ) > 0, where $ \displaystyle Q(z) = z-({f(z)}/{f'(z)}) $ . Further, for a subclass of $ f\in U_{2p} $ , we show necessary and sufficient conditions for f" to have exactly 2 p non-real zeros. For a subclass of $ U_{2p}^{*} $ we show that if f' has only real zeros, then f" has exactly 2 p non-real zeros. For $ f\in U_{2p}^{*} $ we show that 2 p is a lower bound for the number of non-real zeros of $ f^{(k)} $ for k S 2.     

Monsters in Hardy and Bergman Spaces

A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary. In this paper, the Hardy spaces H p and the Bergman spaces B p (1 h p < X ) on the unit disk are considered, and it is shown that there are no Luh-monsters in them. Nevertheless, it is proved that T -monsters (as introduced by the authors in an earlier work) can be found in each of these spaces for any finite order linear differential operator T .     

Theoretical analysis of structure, thermodynamic properties, and optical properties of Ge-doped amorphous SiO2

Different stable geometric configurations of Ge doped amorphous SiO₂ (a-SiO₂) system, originating from one, two, or three Si atoms in various places of the a-SiO₂ substituted by Ge atoms randomly have been investigated using interatomic potentials in this work. The most stable structures have been identified and corresponding evolutional rules obtained. The structural growth pattern for Ge-doped a-SiO₂ system is that Ge atoms tend to spread far away from each other and keep away from the center. Furthermore, the thermodynamic properties including speci?c heat, Debye temperature, vibrational entropy, and so on are calculated from the structure with 16 Si atoms of the constructed a-SiO₂ cell replaced by Ge atoms and with the biggest Ge-Ge distance. It can be seen that entropy of Ge doped system with larger specific heat is higher than that of the pure system with smaller specific heat. At last, optical properties including optical absorption spectrum and electron energy loss function of nGe-doped a-SiO₂ (n=0-3, 8) system is also obtained.     

基于三片曲面反射镜的离轴投影成像系统

采用调制传递函数和波前像差分析方法,设计了基于偶次非球面反射镜和Zernike自由曲面反射镜构成的放大倍数为80,相对孔径为2.8的三个离轴投影成像系统.其中第一片反射镜M1表面为凹面用于减小第二片反射镜的尺寸及获得高的对比度,而第二片反射镜M2和第三片反射镜M3表面为凸面用于校正系统像差及获得更短的投影距离.经软件设计与分析,三系统中基于三片Zernike自由曲面反射镜的成像系统光学性能最好,调制传递函数实现60lp/mm时60%以上,畸变小于2.0%.与其它文献相比,基于三片Zernike自由曲面反射镜系统可以更好地消除像差,缩短系统厚度,增大系统的可视角与相对孔径.     

股票价格指数、消费指数与CHIBOR的关联性研究

本文研究表明,CHIBOR 7日拆放利率分别与股票价格指数、消费物价指数呈协整关系和显著正相关关系,且股票价格指数、消费物价指数为CHIBOR的Granger成因,从而反映了股市的财富效应增加了银行间资金的需求成本的上升。同时CHIBOR与消费物价指数呈互为因果关系,且消费物价指数对CHIBOR的脉冲响应时间较长,从而增加了货币市场管理难度.