Modeling uncertainty in multi-criteria decision analysis

his paper provides a review of multiple criteria decision analysis (MCDA) for cases where attribute evaluations are uncertain. The main aim is to identify different tools which can be used to represent uncertain evaluations, and to broadly survey the available decision models that can be used to support uncertain decision making. The review includes models using probabilities or probability-like quantities; explicit risk measures such as quantiles and variances; fuzzy numbers, and scenarios. The practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed.     

基于功能不可加系统的系统优化

为了揭示系统的某一功能达到最优与其所有子系统为实现系统这一功能而提供的功能之间的关系,基于系统功能具有可加和不可加的特性,探讨了功能不可加系统的功能优化方法,以子系统功能的实现度为决策变量,以系统功能发挥最大效用为目标函数,以实现功能所需的资源为约束条件,建立了功能不可加系统优化的规划模型,最后辅以算例,并通过EXCEL Solver求解进行了分析.     

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 .     

Applied thermodynamics of the real gas with respect to the thermodynamic zeros of the entropy and internal energy

Gibbs's work on the thermodynamic properties of substances [1] presented a complete thermodynamic theory. The formulations of the entropy S and internal energy U as extensive quantities allow the zeros of the real gas to be given: S=0 at absolute zero (Nernst, Planck) and U=0 at the critical point. Consequently, every thermodynamic function is unique and absolutely specified. Interdependences among quantities such as temperature, vapor pressure, chemical potential, volume, entropy, internal energy, and heat capacity are likewise unique and numerically well defined. This is shown for the saturated fluid, water, in the region between absolute zero and the critical point. As a consequence of the calculation of the chemical potential, it follows that the free particle flow in an inhomogeneous system is essentially governed by the difference in chemical potential, and not through the difference in pressure, this effect being of importance for meteorology and oceanography.