Conformity and independence with coherent lower previsions

We define the conformity of marginal and conditional models with a joint model within Walley's theory of coherent lower previsions. Loosely speaking, conformity means that the joint can reproduce the marginal and conditional models we started from. By studying conformity with and without additional assumptions of epistemic irrelevance and independence, we establish connections with a number of prominent models in Walley's theory: the marginal extension, the irrelevant natural extension, the independent natural extension and the strong product.     

A survey of the theory of coherent lower previsions

This paper presents a summary of Peter Walley’s theory of coherent lower previsions. We introduce three representations of coherent assessments: coherent lower and upper previsions, closed and convex sets of linear previsions, and sets of desirable gambles. We show also how the notion of coherence can be used to update our beliefs with new information, and a number of possibilities to model the notion of independence with coherent lower previsions. Next, we comment on the connection with other approaches in the literature: de Finetti’s and Williams’ earlier work, Kuznetsov’s and Weischelberger’s work on interval-valued probabilities, Dempster–Shafer theory of evidence and Shafer and Vovk’s game-theoretic approach. Finally, we present a brief survey of some applications and summarize the main strengths and challenges of the theory.     

An aggregation framework based on coherent lower previsions: Application to Zadeh’s paradox and sensor networks

The problem of aggregating two or more sources of information containing knowledge about a common domain is considered. We propose an aggregation framework for the case where the available information is modelled by coherent lower previsions, corresponding to convex sets of probability mass functions. The consistency between aggregated beliefs and sources of information is discussed. A closed formula, which specializes our rule to a particular class of models, is also derived. Two applications consisting in a possible explanation of Zadeh’s paradox and an algorithm for estimation fusion in sensor networks are finally reported.     

Coherence, Homotopy and 2-Theories

2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a Quillen model category structure on the category of 2-theories and 2-theory-morphisms where the weak equivalences are biequivalences of 2-theories. A biequivalence of 2-theories induces a biequivalence of 2-categories of algebras. This model category structure allows one to talk of the homotopy of 2-theories and discuss the universal properties of coherence.     

On lower semicontinuity in BH and 2-quasiconvexification

It is proved that if , with p > 1, if is bounded in , , and if in then provided is 2-quasiconvex and satisfies some appropriate growth and continuity condition. Characterizations of the 2-quasiconvex envelope when admissible test functions belong to BH^p are provided. Received: 10 October 2001 / Accepted: 8 May 2002 / Published online: 17 December 2002     

A note on lower bound of centered L2-discrepancy on combined designs

This note provides a theoretical justification of optimal foldover plans in terms of uniformity. A new lower bound of the centered L ₂-discrepancy values of combined designs is obtained, which can be used as a benchmark for searching optimal foldover plans. Our numerical results show that this lower bound is sharper than existing results when more factors reverse the signs in the initial design.     

On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations

The present paper is concerned with asymptotic behaviours of the solutions to the micropolar fluid motion equations in R². Upper and lower bounds are derived for the L² decay rates of higher order derivatives of solutions to the micropolar fluid flows. The findings are mainly based on the basic estimates of the linearized micropolar fluid motion equations and generalized Gronwall type argument.     

2-Absorbing and Weakly 2-Absorbing Elements in Multiplicative Lattices

In this article we study weakly 2-absorbing elements and 2-absorbing elements in C-lattices. Next we characterize C-lattices in which every nonzero proper element is a (weakly) 2-absorbing element. We also establish a new characterization for principal element domains in terms of 2-absorbing elements.     

2-noncrossing trees and 5-ary trees

Recently, Gu et al. [N.S.S. Gu, N.Y. Li, T. Mansour, 2-Binary trees: Bijections and related issues, Discrete Math. 308 (2008) 1209-1221] introduced 2-binary trees and 2-plane trees which are closely related to ternary trees. In this note, we study the 2-noncrossing tree, a noncrossing tree in which each vertex is colored black or white and there is no ascent (u,v) such that both the vertices u and v are colored black. By using the representation of Panholzer and Prodinger for noncrossing trees, we find a correspondence between the set of 2-noncrossing trees of n edges with a black root and the set of 5-ary trees with n internal vertices.     

随机值Ⅱ-型模糊集及其不确定性知识表示

针对人工智能中的不确定性问题,在研究了Ⅱ-型模糊集理论的基础上,提出了一种随机值Ⅱ-型模糊集概念,给出了正态随机值Ⅱ-型模糊集数学模型及其生成算法,并对正态随机值Ⅱ-型模糊集的参数及形态特征进行解析.实例证明随机值Ⅱ-型模糊集可以用来处理社会和自然科学中诸多不确定性问题.     

二型模糊系统研究与应用

简单介绍模糊系统和二型模糊系统发展,概述二型模糊系统的应用范围、条件和组成,比较详细的介绍了二型模糊集合基础理论,按照二型模糊系统的组成模块描述模糊器,规则库,推理引擎,降型器,精确器的表达式和推导过程,最后还总结了二型模糊系统现阶段存在的不足和可能发展方向。     

Minimal regular 2-graphs and applications

A 2-graph is a hypergraph with edge sizes of at most two. A regular 2-graph is said to be minimal if it does not contain a proper regular factor. Let f2(n) be the maximum value of degrees over all minimal regular 2-graphs of n vertices. In this paper, we provide a structure property of minimal regular 2-graphs, and consequently, prove that f2(n) = n 3-i/3, where 1 ≤ i ≤ 6, i ≡ n (mod 6) and n ≥ 7, which solves a conjecture posed by Fan, Liu, Wu and Wong. As applications in graph theory, we are able to characterize unfactorable regular graphs and provide the best possible factor existence theorem on degree conditions. Moreover, fa(n) and the minimal 2-graphs can be used in the universal switch box designs, which originally motivated this study.     

Commutativity Conditions for Rings and Generalized 2-CN Rings

Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions: (1) if for each x ∈ R\N(R) and each y ∈ R,(xy)k =xkyk for k =m,m + 1,n,n + 1,where m and n are relatively prime positive integers,then R is commutative;(2) if for each x ∈ R\J(R) and each y ∈ R,(xy)k =ykxk for k =m,m+ 1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented.     

均衡二部图中含2k条指定边的k个独立圈及2-因子

得到了对于二部图G=(V_1,V_2;E),当|V_1|=|V_2|=n≥2k+1时的结果:对G中任意2k条独立边e_1,e_1~*,…,e_k,e_k~*,G中一定存在k个独立的4-圈C_1,C_2,…,C_k,使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i).并在此基础上进一步证明了当|V_1|=|V_2|=n≥3k时若对任意两顶点x∈V_1,y∈V_2,都有d(x)+d(y)≥2n-k+1成立,则G有一个2-因子含有k+1个独立圈C_1,C_2,…,C_(k+1)使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i)且|C_i|=4.     

Derivation Algebras and 2-Cocycles of the Algebras of q-Differential Operators

Abstract

In the paper, the deriviation algebras of the associative algebras of the one-variable (resp. multivariable) q-differential operators and of their corresponding Lie algebras are determined. The completeness of the derivation algebras of the algebras of q-differential operators is also discussed. Finally, we calculate H ²(𝒟 _q (n)^?, C) for n ≥ 1, as well as H ²(g l _n (𝒟 _q ), C) under the assumption that q is transcendental over the rational numbers field Q.     

Free 2-step nilpotent Lie algebras and indecomposable representations

Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V)?=?V⊕Λ²(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations of the solvable Lie algebra 𝔤?=??x??L(V), where x acts on V via an arbitrary invertible Jordan block.     

带双势的非线性Schr dinger方程爆破解的L^2集中性质和L^2集中率

本文研究一类带双势的具有临界幂的非线性Schrodinger方程的初值问题.得到该方程爆破解的L2集中性质并在此基础上得到其爆破解为径向对称情形的L2集中速率.