Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures

In this paper, we extend the basic distance measure in picture fuzzy sets to the new measures called generalized picture distance measures and picture association measures. Some properties of these measures are examined. An application to clustering problem is given to illustrate applicability of the proposed works.     

图犹豫模糊Power Heronian平均算子及其在多属性决策中应用

针对需要同时考虑属性关联性及整体均衡性多属性决策问题,联合图犹豫模糊集对于不确定信息的表达优势,提出一种基于图犹豫模糊Power Heronian平均算子的多属性决策方法。首先,给出图犹豫模糊数的得分函数、精确函数及距离公式;在此基础上,提出图犹豫模糊Power Heronian平均算子和图犹豫模糊Power加权Heronian平均算子;最后,将所提算子应用于多属性决策问题中,验证所提算子的有效性和可行性。     

Optimizing color picture tubes by high-cost nonlinear programming

In this paper we discuss the application of optimization techniques for the design of several parts of the color picture tube, the key component of television sets and computer monitors. These projects have been carried out for Philips Display Components in Eindhoven. Philips developed several computer simulation models of picture tube parts. Designers use these models to simulate the physical behavior of a particular part design. Depending on the amount of detail in the model, the running time of a typical simulation ranges from one up to 10 hours. Tube designers are confronted with the problem of finding settings for a large number of design parameters that are optimal with respect to several simulated tube characteristics. This problem can be modeled as a so-called high-cost nonlinear programming problem. This paper reports on the successful application of our four-step compact model approach to solve this problem. The presented results are based on four projects in which we optimized picture tube parts. Among the realized benefits for Philips are a design improvement of 30% and a time-to-market reduction of 50–60%.     

Actions of Picture Groups on CAT(0) Cubical Complexes

A class of groups, called picture groups, is defined. Richard Thompsons groups F, T, and V are all picture groups. Each picture group is shown to act properly and isometrically on a CAT(0) cubical complex. In particular, all picture groups are a-T-menable.Mathematics Subject Classifications (2000). 20F65, 43A15.     

一种测距定位仪的数学模型

将观测定距的一般性问题归结为对于已知平面矩形的测距问题.将实物成像的标示点屏幕坐标作为已知观测数据,给出了物距的简明计算方法.     

Blow-up for doubly degenerate nonlinear parabolic equations

In this paper, we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem of some doubly degenerate nonlinear parabolic equations. The project is supported by the Natural Science Foundation of Fujian Province of China (No. Z0511048)     

Picture模糊幂几何Heronian平均算子及其在多属性决策中的应用

针对决策信息为Picture模糊数的多属性决策问题,将经典范畴内的几何Heronian平均算子和幂几何算子结合,提出了Picture模糊幂几何Heronian平均(PFPGHM)算子与Picture模糊加权幂几何Heronian平均(PFWPGHM)算子。该类算子不仅能体现待集结数据间的关联性,而且还能反映决策过程中信息的整体性,降低了与整体信息偏差较大的待集结数据对决策结果的影响。推导其数学表达式,证明相关性质。提出了基于PFWPGHM算子的多属性决策方法,通过决策实例分析了参数p和q对决策结果的影响,并对比分析新方法与现存的决策方法,进而表明所研究方法的可行性与优点。     

Notes应用程序中角色组合的最少策略

在Ｎｏｔｅｓ 应用程序设计过程中,角色的分配合一直是一个容易被忽略的问题．本文将此问题提炼为一个数学模型,并用图论中已有的顶点染色法解决,得出了较为合理的算法和结果．     

On the Cauchy problem for non-effectively hyperbolic operators,the Gevrey 5 well-posedness

In this paper, we prove that for non-effectively hyperbolic operators with smooth double characteristics exhibiting a Jordan block of size 4 on the double manifold, the Cauchy problem is well-posed in the Gevrey 5 class, beyond the generic Gevrey class 2 (see, e.g., [5]). Moreover, we show that this value is optimal, due to certain geometric constraints on the Hamiltonian flow of the principal symbol. These results, together with results already proved, give a complete picture of the well-posedness of the Cauchy problem around hyperbolic double characteristics.     

Liquid Flow in Partially Saturated Porous Media

We consider a picture for the filtration of a liquid in a partiallysaturated porous medium, leading to a two-phase one-dimensionalfree boundary problem of the following type: The liquid pressuresatisfies an elliptic equation in the saturated region and anon-linear parabolic equation in the unsaturated region, whilepressure and velocity are continuous across the interface. This scheme reduces to the study of the non-linear parabolicfree boundary problem in the unsaturated phase with cauchy dataprescribed on the free boundary, for such a problem existence,uniqueness and continuous dependence theorems are proved.