活動類別：“Workshop on Order, Topology and Logic”系列學(xué)術(shù)報告

活動時間：9:00

活動日期：2018-4-14

地點：長安校區(qū) 數(shù)學(xué)與信息科學(xué)學(xué)院學(xué)術(shù)報告廳

主辦單位：數(shù)學(xué)與信息科學(xué)學(xué)院

講座題目1：Regularity vs. constructive complete (co) distributivity

講座時間：9:00-10:00

講座日期：2018-4-14

報告人：賴洪亮教授

講座內(nèi)容簡介：

It is well known that a relation ? between sets is regular if and only if K? is completely distributive (cd), where K? is the complete lattice consisting of fixed points of the Kan adjunction induced by ?. For a small quantaloid Q, we investigate the Q-enriched version of this classical result, i.e., the regularity of Q-distributors versus the constructive complete distributivity (ccd) of Q-categories, and prove that “the dual of K? is (ccd) ?? is regular ?K? is (ccd)” for any Q-distributor ?. Although the converse implications do not hold in general, in the case that Q is a commutative integral quantale, we show that these three statements are equivalent for any ? if and only if Q is a Girard quantale.

講座人簡介：

賴洪亮，四川大學(xué)數(shù)學(xué)學(xué)院教授。主要從事序、拓撲和范疇論相關(guān)領(lǐng)域的研究。主持國家自然科學(xué)基金3項，主要工作發(fā)表在Topology and its Applications, Theory and Applications of Categories, Journal of Pure and Applied Algebra, Fuzzy Sets and Systems等雜志上。

講座題目2：On fuzzy differentiability of fuzzy-number-valued functions

講座時間：10:00-11:00

講座日期：2018-4-14

報告人：邱東 教授

講座內(nèi)容簡介：

The importance of the derivative of a function in the study of analysis is well-known. For fuzzy functions, the Hukuhara difference and its generalized differences are used to define the differentiability. These generalized derivatives are motivated by their usefulness in a very quickly developing area at the intersection of set-valued analysis and fuzzy sets, namely, the area of fuzzy analysis and fuzzy differential equations. But in many applications they appear to have own imperfections and to be very restrictive.

In this talk, on the one hand, I will give an improved characterization for the g-derivative which is the most general of those existing generalized H-derivatives. On the other hand, I will define the differentiability from a totally new point of view. I also show connections to the ideas of generalized H-derivatives. Finally, some potential applications will be discussed.

講座人簡介：

邱東，教授，博士生導(dǎo)師，重慶郵電大學(xué)文峰高端省部級后備人才項目獲得者，重慶郵電大學(xué)模糊數(shù)學(xué)與人工智能創(chuàng)新團隊負責(zé)人。2009年博士畢業(yè)于電子科技大學(xué)應(yīng)用數(shù)學(xué)專業(yè)。主要從事不確定性的數(shù)學(xué)理論及其在自然語言處理中的應(yīng)用研究，研究工作主要集中在模糊分析理論和自然語言的語義分析研究。在FSS、INS、JMAA等國際學(xué)術(shù)期刊發(fā)表論文50余篇，其中SCI檢索40余篇。主持和參與國家和省部級項目10余項。

講座題目3：模糊系統(tǒng)的互模擬理論

講座時間：11:00-12:00

講座日期：2018-4-14

報告人：吳恒洋 博士

講座內(nèi)容簡介：

遷移系統(tǒng)是描述系統(tǒng)行為的重要數(shù)學(xué)模型?；ツM是系統(tǒng)行為比較的科學(xué)方法和狀態(tài)空間約簡技術(shù)，也是并發(fā)系統(tǒng)和模態(tài)邏輯模型論的核心概念之一，它在并發(fā)系統(tǒng)的規(guī)范與驗證中扮演重要角色。本報告重點闡述模糊遷移系統(tǒng)互模擬的基礎(chǔ)理論。主要內(nèi)容包括：（1）互模擬的背景介紹；（2）狀態(tài)互模擬的概念、算法、余代數(shù)、以及邏輯刻畫；（3）分布互模擬；（4）基于狀態(tài)/分布的行為距離的概念、算法、以及邏輯刻畫；（5）可進一步研究的問題。

講座人簡介：

吳恒洋，華東師范大學(xué)計算機科學(xué)與軟件工程學(xué)院副教授。主要研究領(lǐng)域是形式化方法，包括形式語義學(xué)、Domain理論等。近年來，主要研究興趣是模糊系統(tǒng)的互模擬理論。相關(guān)工作發(fā)表在IEEE Transitions on Fuzzy Systems, Information Sciences, Fuzzy Sets and Systems, Frontiers of Computer Science以及計算機學(xué)報等雜志上。

講座題目4：On some open problems in domain theory

講座時間：14:30-15:30

講座日期：2018-4-14

報告人：奚小勇 博士

講座內(nèi)容簡介：

In this talk, we will talk about some open problems in domain theory, which is the intersection between mathematics (especially topology) and theoretical computer science. Some problems are hard, some are relatively easy ones.

講座人簡介：

奚小勇，江蘇師范大學(xué)副教授，四川大學(xué)博士。主要從事拓撲學(xué)與Domain理論的研究，發(fā)表論文20多篇，完全或部分解決了Domain理論領(lǐng)域內(nèi)若干公開問題，如Amadio-Curien問題，Ho-Zhao問題等

講座題目5：Diagonals between distance distributions

講座時間：15:30-16:30

講座日期：2018-4-14

報告人：申力立 博士

講座內(nèi)容簡介：

The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the quantaloid of diagonals between distance distributions, which is expected to establish the categorical foundation of probabilistic partial metric spaces. Observing that the quantale of distance distributions w.r.t. an arbitrary continuous t-norm is non-divisible, we precisely characterize diagonals between distance distributions, and prove that one-step functions are the only distance distributions on which the set of diagonals coincides with the generated down set.

講座人簡介：

申力立，2014年6月畢業(yè)于四川大學(xué)數(shù)學(xué)學(xué)院，獲博士學(xué)位。2014年7月至2016年4月在加拿大約克大學(xué)從事博士后研究。現(xiàn)為四川大學(xué)數(shù)學(xué)學(xué)院副教授，主要研究方向為范疇論及其應(yīng)用。個人主頁：http://math.mickeylili.com/

講座題目6：Weak algebraic information systems and a new equivalent category of DOM of domains

講座時間：16:30-17:30

講座日期：2018-4-14

報告人：何青玉 博士

講座內(nèi)容簡介：

In this topic, concepts of generalized algebraic information system (in short, GA-inf) and weak algebraic information system (in short, wA-inf) are introduced. Relationships among several algebraicities of information systems are explored. Main results are:

(1) A dcpo D is an algebraic domain iff D is represented by an algebraic information system (in short, A-inf), and iff D is represented by a GA-inf;

(2) every A-inf is a GA-inf and a wA-inf;

(3) every C-inf S(D, B) induced by a domain with a basis B is a wA-inf;

(4) the category WAINF of wA-infs and approximable mappings is equivalent to the category DOM of domains and Scott continuous functions.

講座人簡介：

何青玉，揚州大學(xué)數(shù)學(xué)科學(xué)學(xué)院講師。主要從事Domain理論與一般拓撲學(xué)的研究，主要工作發(fā)表在Topology and its Applications, Algebra Universalis, Order等雜志上。主持國家自然科學(xué)基金2項，江蘇省自然科學(xué)基金1項。

講座題目7：Some research progress on (L,M)-fuzzy convergence theory

講座時間：9:15-10:15

講座日期：2018-4-15

報告人：龐斌 博士

講座內(nèi)容簡介：

With the development of fuzzy topology, various types of fuzzy convergence structures have been investigated in different frameworks of fuzzy topological spaces. In this talk, we mainly focus on three types of fuzzy convergence structures in the framework of (L,M)-fuzzy topological spaces, including stratified (L,M)-fuzzy Q-convergence structures, enriched (L,M)-fuzzy convergence structures and stratified (L,M)-ordered convergence structures. Generally, we call them (L,M)-fuzzy convergence structures. Concretely, we will study their Cartesian-closedness and their categorical relations with stratified (L,M)-fuzzy topological spaces.

講座人簡介：

龐斌，北京理工大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院副研究員。2015年6月，在北京理工大學(xué)獲得博士學(xué)位。2015年7月至 2017年8月在哈爾濱工業(yè)大學(xué)從事博士后研究。主要研究方向為模糊拓撲學(xué)與模糊凸空間理論。主持1項國家自然科學(xué)基金，1項博士后基金和1項廣東省自然科學(xué)基金。主要工作發(fā)表在Fuzzy Sets and Systems, IEEE Transactions on Fuzzy Systems, Journal of Intelligent and Fuzzy Systems, Iranian Journal of Fuzzy Systems等雜志上。

講座題目8：Aggregation Functions: Uninorms

講座時間：10:15-11:15

講座日期：2018-4-15

報告人：蘇勇 博士

講座內(nèi)容簡介：

This report is a brief survey on uninorms as a mixed aggregation functions. Firstly, research backgrounds concerning uninroms are presented. Then, present research situations on the characterizations of several most studied classes of uninorms are given. Finally, present research situations on equations involving uninorms, including distributivity equations, migrativity equations and modularity equations are stated.

講座人簡介：

蘇勇，江南大學(xué)理學(xué)院副教授。主要從事模糊系統(tǒng)算子與函數(shù)方程的研究。主要工作發(fā)表在IEEE Transactions on Fuzzy Systems, Fuzzy Sets and Systems, Information Sciences, International Journal of Approximate Reasoning等雜志上。