全国第九届可拓工程年会征文启事暨可拓工程讲习班通知

全国第九届可拓工程年会定于 2 0 0 2年 8月 9日— 1 2日在大连海事大学召开 .同时 ,2 0 0 2年可拓工程讲习班将于 2 0 0 2年 8月 6日— 1 2日在大连海事大学举办 .现就会议征文及讲习班的有关问题通知如下 :一、征文内容1 .理论研究 :1 )物元理论和事元理论 ;2 )可拓数学 ;3 )可拓逻辑 ;4)可拓学的哲学基础 ;5 )可拓学研究方向的探讨 ;6 )可拓学与数学、系统科学、信息科学和思维科学的关系探讨 .2 .应用研究 :在专业领域中 ,如在计算机与人工智能、控制与检测、管理与决策等领域中的可拓工程理论与方法 ,利用可拓论和可拓方法解决某个实际…     

可拓学的研究、应用与发展

"可拓学"是中国人创立的新学科,在众多专家学者的不懈努力下,历经30余年的潜心研究,建立了可拓论体系和可拓创新方法体系,并已在众多领域的矛盾问题智能化处理方面得到成功应用,形成可拓工程.文章总结综述"可拓学"理论与方法研究、应用与普及推广概况,展望"可拓学"的发展前景.     

随机事件与随机变量概率分布的拓展研究

给出了随机事元的拓展概率以及随机事元可拓集的概念.运用可拓集合、可拓变换与可拓推理等可拓学的理论与方法,对随机事件发生的概率与随机变量概率分布的变化作了初步的拓展研究.     

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.     

可拓建筑形态设计变换数据库初探

可拓建筑形态设计变换数据库是可拓学、数据挖掘的理论和方法在建筑形态设计方面的应用.尝试探讨面向建筑形态设计的可拓变换数据库,论述其概念、类型、实例和作用.以理论概述和实例解析的方法,构建了有效的建筑形态设计数据表达方式,提出了建筑形态数据挖掘工作的前提和基础,为可拓建筑形态设计数据挖掘研究拓展了理论基础.     

电动汽车充换电站选址规划的可拓评价研究

为对未来电动汽车的充换电站的选址规划决策提供科学依据和理论支持,建立电动汽车充换电站选址决策的评价指标体系.运用可拓学理论和方法,构建了基于可拓方法的电动汽车充换电站选址合理性的可拓评价模型,基于熵权法确定评价指标权重.最后通过一个仿真算例验证所提模型的正确性和有效性.     

航空备件可拓聚类分析

应用可拓学的基本理论与方法 ,分析了航空备件的数值特征 ,建立了航空备件的物元模型 ;应用可拓原理对传统的聚类分析方法做了拓展 ,并据此对航空备件集合进行了划分 ,为航空备件的分类管理提供了一种崭新的方法 .     

可拓预测方法

针对以时间为自变量的预测对象—变动性事物的变化原因,通过可拓学中物元的可拓性分析,运用物元方法进行形式化描述,进而给出变动性事物的可拓预测方法.并对预测结果的误差给出评价与修正的方法,建立起对预测对象的定性分析与定量计算有机结合的预测模型,形成了一种集科学性、直观性、准确性、普适性于一身的新型预测方法.     

可拓学在产品制造模式优化中的应用

对可拓学在产品制造模式优化中的应用进行了研究.首先,对可拓学的核心——“物元分析”和“可拓方法”进行了综述,对各种产品制造模式及其定制点进行了分析和比较.在此基础上,把可拓学的物元分析方法中的“发散树”、“相关网”与“蕴含系”等运用到产品制造模式优化中,化不相容问题为相容问题,达到既能满足客户的多样化和个性化需求,又能降低产品成本和价格、缩短交货期的目的.文章还详细地论述了运用可拓学对产品制造模式进行优化的具体方法和步骤,最后以摆线针轮减速机中的若干零件为例进行了具体的计算和实施,使其定制点往后移,优化了它们的制造模式.     

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.     

作物品种对“地区×年份”效应的稳定性分析

本文用回归系数法与变异系数法分析作物品种多年多点区域试验中品种对“地区×年份”效应的稳定性，用品种在各“地区×年份”下的交互作用值来确定品种适宜种植的地区与年份组合，并选用湖北省部分棉花品种作了实例分析。     

Folding procedure for Newton-Okounkov polytopes of Schubert varieties

The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and gives a systematic method of constructing toric degenerations of projective varieties. In the case of Schubert varieties, their Newton-Okounkov polytopes are deeply connected with representation theory. Indeed, Littelmann’s string polytopes and Nakashima-Zelevinsky’s polyhedral realizations are obtained as Newton-Okounkov polytopes of Schubert varieties. In this paper, we apply the folding procedure to a Newton-Okounkov polytope of a Schubert variety, which relates Newton-Okounkov polytopes of Schubert varieties of different types. As an application, we obtain a new interpretation of Kashiwara’s similarity of crystal bases.     

The Hodge theory of algebraic maps

We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new Hodge-theoretic results on the cohomology of projective varieties which extend naturally the classical theory and provide new applications.     

Equations for secant varieties of Veronese and other varieties

New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry. Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations. An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration of our methods. Our new equations and results about them are put into a larger context by introducing vector bundle techniques for finding equations of secant varieties in general. We include a few homogeneous examples of this method.     

Lectures on Wonderful Varieties

These notes are an introduction to wonderful varieties. We discuss some general results on their geometry, their role in the theory of spherical varieties, several aspects of the combinatorics arising from these varieties, and some examples.     

A tropical toolkit

We give an introduction to Tropical Geometry and prove some results in tropical intersection theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of degenerations of varieties using projective not-necessarily-normal toric varieties. The second part is a foundational account of tropical intersection theory with proofs of some new theorems relating it to classical intersection theory.     

PLÜCKER RELATIONS AND SPHERICAL VARIETIES: APPLICATION TO MODEL VARIETIES

A general framework for the reduction of the equations defining classes of spherical varieties to (possibly infinite-dimensional) grassmannians is proposed. This is applied to model varieties of types A, B and C; in particular, a standard monomial theory for these varieties is presented.     

Twisted loop groups and their affine flag varieties

We develop a theory of affine flag varieties and of their Schubert varieties for reductive groups over a Laurent power series local field k((t)) with k a perfect field. This can be viewed as a generalization of the theory of affine flag varieties for loop groups to a “twisted case”; a consequence of our results is that our construction also includes the flag varieties for Kac–Moody Lie algebras of affine type. We also give a coherence conjecture on the dimensions of the spaces of global sections of the natural ample line bundles on the partial flag varieties attached to a fixed group over k((t)) and some applications to local models of Shimura varieties.     

Managing the spread of alfalfa stem nematodes (Ditylenchus dipsaci): The relationship between crop rotation periods and pest reemergence

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (ASN) (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against ASNs and control strategies largely rely on crop rotation to nonhost crops or by planting resistant varieties of alfalfa. In this paper, we present a basic host‐parasite model that describes the spread of the ASN on alfalfa crops. With this discrete time model, we are able to portray a relationship between the length of crop rotation periods and the time at which the density of nematode‐infested plants becomes larger than that of nematode‐free ones in the postrotation alfalfa. The numerical results obtained are consistent with farming practice observations, suggesting that the model could play a role in the evaluation of management strategies.     

Toric P-difference varieties

In this paper, we introduce the concept of P-difference varieties and study the properties of toric P-difference varieties. Toric P-difference varieties are analogues of toric varieties in difference algebraic geometry. The category of affine toric P-difference varieties with toric morphisms is shown to be antiequivalent to the category of affine P [x]-semimodules with P [x]-semimodule morphisms. Moreover, there is a one-to-one correspondence between the irreducible invariant P-difference subvarieties of an affine toric P-difference variety and the faces of the corresponding affine P [x]-semimodule. We also define abstract toric P-difference varieties by gluing affine toric P-difference varieties. The irreducible invariant P-difference subvariety-face correspondence is generalized to abstract toric P-difference varieties. By virtue of this correspondence, a divisor theory for abstract toric P-difference varieties is developed.