可拓数据挖掘研究进展

可拓学研究用形式化模型解决矛盾问题的理论与方法,可拓数据挖掘是可拓学和数据挖掘结合的产物,它探讨利用可拓学方法和数据挖掘技术,去挖掘数据库中与可拓变换有关的知识,包括可拓分类知识、传导知识等可拓知识.随着经济全球化的推进,环境的多变促使了信息和知识的更新周期缩短,创新和解决矛盾问题越来越成为各行各业的重要工作.因此,如何挖掘可拓知识就成为数据挖掘研究的重要任务.研究表明,可拓数据挖掘将具有广阔的应用前景.将介绍可拓数据挖掘的集合论基础、基本知识和目前研究的主要内容,并提出今后需要进一步探讨的问题及其发展前景.     

解决矛盾问题的可拓模型与可拓知识的研究

可拓学是解决矛盾问题的学科,在可拓学的可拓模型原型的基础上,明确了计算机解决矛盾问题的可拓模型,它包括三部分:关联函数、可拓知识和推理算法,其中关联函数和可拓知识对不同的问题需要利用不同的原理,且它们是逐步变化的.在可拓知识中,关联函数的可拓变换需要通过计算证明其值是逐步增加的.这样,矛盾问题在计算机中才能得到解决.本文通过多个实例来说明解决矛盾问题的可拓模型及可拓知识的建立和实现.     

基于可拓集的可拓分类知识获取研究

以可拓集理论为依据,给出基于可拓变换的可拓分类知识的定义,并在信息元集和评价信息元集的基础上,探讨可拓分类知识的获取方法,包括质变域知识的获取、量变域知识的获取和有关拓界的知识的获取.这是可拓数据挖掘的主要内容之一,为从数据库中获取变化的分类知识提供了新的思路.     

管理可拓工程研究

管理可拓工程是可拓工程的一个分支.它把可拓学与管理科学相结合,研究管理过程中矛盾问题的处理.介绍管理可拓工程的研究背景、前期研究工作概况及研究意义,并提出亟待研究的课题,指出目前研究中需要注意的问题.     

可拓学的应用研究、普及与推广(综述)

可拓学研究的核心是如何通过变换处理矛盾问题.介绍了近年在计算机、设计、管理、控制、检测和中医药等领域利用可拓论和可拓方法的应用研究情况,提出今后可拓学普及与推广的方向.     

CPI指数变换对产品销售影响的可拓数据挖掘

目前对数据挖掘的研究主要集中在对静态数据的挖掘,而在实际工作中,经常要处理的矛盾问题,需要通过可拓变换和可拓变换的运算来解决,这就需要用到变换的知识,需要运用动态数据挖掘或可拓数据挖掘来解决问题.运用可拓逻辑和可拓数据挖掘的理论知识,根据国家消费者物价指数的变换对产品销售数据的影响来研究可拓数据挖掘中传导知识的挖掘,为企业的决策者在目前的市场环境下提出更加合理的销售策略提供依据.     

可拓学中关联函数的构造及零界的确定

可拓学的核心是通过可拓变换使矛盾问题转化,而其定量化工具之一是关联函数,针对某些工程计算盲目套用关联函数问题和零界概念的误解,指出了错误所在并予以纠正.     

基于可拓策略生成技术的商品搜索服务改进研究

购买者在使用商品搜索服务时所得搜索结果数量不符合其主观要求是一个典型而普遍的矛盾问题.在分析矛盾问题的基础上,提出以可拓策略生成技术改进商品搜索服务的方法.该方法通过对购买者提出的搜索要求进行发散分析及相关分析,以形成各种可能变换,并依据关联函数寻求问题的解变换,以及利用评价函数对解变换进行优选.给出了关于策略生成的基本算法,并实现于笔记本电脑导购网站平台上.实验及测试结果表明,系统能有效生成矛盾问题的解变换,从而改进了搜索服务的质量.     

可拓数据挖掘在教师科研考核评价中的应用

利用可拓数据挖掘,将可拓分类方法应用到高校教师科研考核评价中.对考核结果进行定"量"和定"性"的分析,将教师的科研情况划分为正质变、负质变、正量变及负量变等类型,并计算其支持度和可信度,为科研管理者衡量策略执行效果提供数量化的参考依据.     

物元可拓集集合性质研究

在可拓集合概念基础上,提出了向量可拓集和区间可拓集概念,研究了物元可拓集合的交、并、求补等集合运算及其性质.     

The Friedrichs Extension of a Pair of Operators

Abstract

An extension of a pair of linear unbounded operators which map from a Banach space X to a Hilbert space Y is constructed and studied. The purpose of the extension is to obtain a pair of jointly closed operators which will be the generating pair of a B-evolution similar to the classical Friedrichs extension of a single operator which generates a holomorphic semigroup. The construction is based on spectral methods.     

Loopless Generation of Linear Extensions of a Poset

Canfield and Williamson gave the first loopless algorithm for generating all linear extensions of a poset. It elegantly generates all signed extensions, resulting in each extension appearing somewhere with each sign, but retains only every other one independent of its sign. It uses an array for the extension. In this paper we give another loopless algorithm for generating all the linear extensions. It generates each extension only once and uses a list for the extensions.     

New methods for generating permutation polynomials over finite fields

We present two methods for generating linearized permutation polynomials over an extension of a finite field Fq. These polynomials are parameterized by an element of the extension field and are permutation polynomials for all nonzero values of the element. For the case of the extension degree being odd and the size of the ground field satisfying , these parameterized linearized permutation polynomials can be used to derive non-parameterized nonlinear permutation polynomials via a recent result of Ding et al.     

Layering strategies for creating exploitable structure in linear and integer programs

The strategy of subdividing optimization problems into layers by splitting variables into multiple copies has proved useful as a method for inducing exploitable structure in a variety of applications, particularly those involving embedded pure and generalized networks. A framework is proposed in this paper which leads to new relaxation and restriction methods for linear and integer programming based on our extension of this strategy. This framework underscores the use of constructions that lead to stronger relaxations and more flexible strategies than previous applications. Our results establish the equivalence of all layered Lagrangeans formed by parameterizing the equal value requirement of copied variables for different choices of the principal layers. It is further shown that these Lagrangeans dominate traditional Lagrangeans based on incorporating non-principal layers into the objective function. In addition a means for exploiting the layered Lagrangeans is provided by generating subgradients based on a simple averaging calculation. Finally, we show how this new layering strategy can be augmented by an integrated relaxation/restriction procedure, and indicate variations that can be employed to particular advantage in a parallel processing environment. Preliminary computational results on fifteen real world zero-one personnel assignment problems, comparing two layering approaches with five procedures previously found best for those problems, are encouraging. One of the layering strategies tested dominated all non-layering procedures in terms of both quality and solution time.This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222 with the Center for Business Decision Analysis and by the US Department of Agriculture Contract 51-3142-4020 with Management Science Software Systems.     

Hermite interpolation and A-stable methods for stiff ordinary differential equations

Hermite interpolation in the form of Newton's divided difference expressions is employed to give a generating function for A-stable difference methods of order 2n. These methods can be used to solve the initial value ordinary differential equation y′=g(y,t), y(a)=η. The extension to higher dimensions is considered, and practical suggestions are given for step size changes and order changes.     

A generalization of the primitive normal basis theorem

The primitive normal basis theorem asks whether every finite field extension has a primitive normal basis of this extension. The proof of this problem has recently been completed by Lenstra and Schoof (1987) [6], and another proof is given by Cohen and Huczynska (2003) [3]. We present a more general result, where the primitive element generating a normal basis is replaced by a primitive element generating the finite Carlitz module. Such generators always exist except for finitely many cases which might not exist.     

A generic view of Dantzig-Wolfe decomposition in mixed integer programming

The Dantzig-Wolfe reformulation principle is presented based on the concept of generating sets. The use of generating sets allows for an easy extension to mixed integer programming. Moreover, it provides a unifying framework for viewing various column generation practices, such as relaxing or tightening the column generation subproblem and introducing stabilization techniques.     

An Embedding Problem with Cyclic Kernel

The problem of embedding a quadratic extension of a number field into an extension with a cyclic 2-group is studied. We prove a reduction theorem showing that, under the compatibility condition, an additional embedding condition consists of the solvability of a problem with cyclic kernel of order 16 (of course, if the degree of the required field is no less than 16). An additional condition of embedding into a field of degree 16 is found; namely, the number generating the given quadratic extension must be a norm in a cyclotomic field containing the primitive eighth roots of unity. For Q, the embedding condition is simpler: all the odd prime divisors of the generating element must be congruent with 1 modulo the order of the extension group. In addition, the quadratic extension must be real. Bibliography: 7 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 144–152.     

On the representations of generating trading strategy for contingent claims in multidimensional diffusion model

In this paper, we find generating trading strategy for discounted security model in multidimensional diffusion model. Also, we observe generating trading strategy in its original model using discounted security model formula.