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Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces
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作者 Akachukwu Offia Ugochukwu Osisiogu +4 位作者 Theresa Efor Friday Oyakhire Monday Ekhator Friday Nkume Sunday Aloke 《Open Journal of Optimization》 2023年第3期99-108,共10页
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su... In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces. 展开更多
关键词 Real Banach Spaces Pseudo-Convex Functions Pseudo-Monotone Maps Sub-Differentials lower semi-continuous Functions and Approximate Mean Value Inequality
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Equilibria of the Abstract Economy under Almost Lower Semi-continuous Assumption 被引量:1
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作者 张玉成 陈福川 《Northeastern Mathematical Journal》 CSCD 2003年第1期26-32,共7页
The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken th... The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved. 展开更多
关键词 almost lower semi-continuity ε-approximate selection EQUILIBRIUM
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Upper semi-continuity of attractors for multivalued semi-flow under random perturbation
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作者 李挺 刘曾荣 《Journal of Shanghai University(English Edition)》 CAS 2006年第4期288-292,共5页
In this paper the upper semi-continuity of global attractors for multivalued semi-flows under random perturbation was studied. First, the existence of random attractors for multivalued random semi-flows was considered... In this paper the upper semi-continuity of global attractors for multivalued semi-flows under random perturbation was studied. First, the existence of random attractors for multivalued random semi-flows was considered, then it was proved that the global attractors for multivalue semi-flows are the upper semi-continuity under random perturbation. This result can be used in the numerical approximation of multivalued semi-flows and non-autonomous perturbation of multivalued semi-flows. 展开更多
关键词 random attractor upper semi-continuity absorbing set.
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Existence and Upper Semi-Continuity of Random Attractors for Nonclassical Diffusion Equation with Multiplicative Noise on Rn
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作者 Fadlallah Mustafa Mosa Abdelmajid Ali Dafallah +2 位作者 Qiaozhen Ma Eshag Mohamed Ahmed Mohamed Y. A. Bakhet 《Journal of Applied Mathematics and Physics》 2022年第12期3898-3919,共22页
This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1... This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1</sup>(R<sup>n</sup>). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise. 展开更多
关键词 Random Attractors Nonclassical Diffusion Equations Asymptotic Compactness upper semi-Continuity
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低丰度致密砂岩天然气分布特征及充注过程半定量评价——以鄂尔多斯盆地定北地区上古生界为例 被引量:1
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作者 张小菊 邓虎成 +6 位作者 伏美燕 王付斌 段博瀚 徐争启 雍洋 李泓运 卢涛 《天然气工业》 EI CAS CSCD 北大核心 2024年第3期119-130,共12页
鄂尔多斯盆地致密砂岩气藏为天然气运移路径上的滞留气藏,气藏充注程度低、丰度低、产气量低、气水关系复杂,天然气是否有效充注、充注程度如何均不明确。为此,以鄂尔多斯盆地定北地区上古生界致密砂岩气藏为例,基于岩心、测井、地震、... 鄂尔多斯盆地致密砂岩气藏为天然气运移路径上的滞留气藏,气藏充注程度低、丰度低、产气量低、气水关系复杂,天然气是否有效充注、充注程度如何均不明确。为此,以鄂尔多斯盆地定北地区上古生界致密砂岩气藏为例,基于岩心、测井、地震、生产动态等资料,厘清了天然气分布特征,并综合烃源岩、砂体以及断裂分布空间组合关系,确定了天然气充注方式,再根据充注点、充注动力和阻力,确定了优势充注路径,最后开展了不同充注路径下的气水分布评价。研究结果表明:(1)上古生界致密砂岩气层主要为下二叠统太原组2段第2层(太2-2层)、第3层(太2-3层)与中二叠统下石盒子组1段,同时存在气层、气水同层以及水层,气水关系复杂,气井产量差异大,存在局部高产气井;(2)致密砂岩气藏天然气充注点可分为源储邻近充注点、近源充注点以及远源充注点3类,天然气充注方式可分为砂体源内充注、砂体叠置纵横扩散充注、储集体内断裂沟通跨砂体充注以及复合充注4类;(3)建立了天然气充注路径评价参数充注动力(P_(M))和充注阻力(P_(D)),P_(M)越小,充注动力越强,P_(D)越小,充注阻力越小,P_(M)大且P_(D)小,则充注动力损失小,从充注点到井点的充注动力最强、阻力最小,为天然气优势充注路径;(4)确定了4大类11小类气水分布类型和4类充注方式下气水分布规律,其中研究区西部源内充注、近源充注、断砂有利配置充注均可形成较高丰度的天然气富集,东西部远源充注和断砂较有利配置充注可形成较低丰度的天然气富集。结论认为,该研究成果不仅可以为该区目的层寻找充注程度更高的天然气富集区提供依据,也能够在低丰度气藏区的天然气充注优势区进行有效评价,较传统方法更加精细,更适合单个气藏的精细评价。 展开更多
关键词 鄂尔多斯盆地 定北地区 上古生界 太原组 下石盒子组 低丰度气藏 天然气充注 半定量评价
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随机反应扩散方程的随机吸引子的高阶稳定性
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作者 李志 赵文强 《广西师范大学学报(自然科学版)》 CAS 北大核心 2024年第3期151-158,共8页
本文研究带加性白噪声的随机反应扩散方程的随机吸引子关于噪声强度的稳定性。首先,在非线性函数满足更一般条件下,在初始空间L^(2)(R^(N))中获得随机微分方程的解收敛到确定方程的解,从而得到随机吸引子的上半连续性;然后,利用非线性... 本文研究带加性白噪声的随机反应扩散方程的随机吸引子关于噪声强度的稳定性。首先,在非线性函数满足更一般条件下,在初始空间L^(2)(R^(N))中获得随机微分方程的解收敛到确定方程的解,从而得到随机吸引子的上半连续性;然后,利用非线性分解和差分估计,证明L^(p)(R^(N))(p>2)空间中解的收敛性和随机吸引子的上半连续性,其中p是非线性函数的增长指数。 展开更多
关键词 随机反应扩散方程 随机吸引子 上半连续性 加性噪声 稳定性
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绿色闭环供应链网络解的存在性研究
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作者 徐嘉磊 林志 《科技和产业》 2024年第11期20-27,共8页
利用变分不等式相关知识对绿色闭环供应链网络均衡条件进行研究,构建各个决策者的可行策略的集值映射,将绿色闭环供应链网络均衡问题转化为广义Nash均衡问题,结合集值映射的连续性、凸性与紧性,利用不动点定理研究绿色闭环供应链网络解... 利用变分不等式相关知识对绿色闭环供应链网络均衡条件进行研究,构建各个决策者的可行策略的集值映射,将绿色闭环供应链网络均衡问题转化为广义Nash均衡问题,结合集值映射的连续性、凸性与紧性,利用不动点定理研究绿色闭环供应链网络解的存在性与均衡条件。基于研究结论,提出绿色闭环供应链网络各层决策者对应的变分不等式以及多准则网络均衡条件和绿色闭环供应链网络解的存在性定理。 展开更多
关键词 绿色闭环供应链 广义Nash均衡 集值映射 上半连续 下半连续 拟凹性
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SOME RESULTS ON CONTINUOUS TYPE CONDITIONAL INPUT-OUTPUT EQUATION-FIXED POINT AND SURJECTIVITY METHODS 被引量:1
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作者 刘颖范 陈晓红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第3期358-366,共9页
Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvabili... Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvability,continuity and surjectivity,and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result,the main theorems are obtained,which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprises consuming operator. 展开更多
关键词 input-output equation SOLVABILITY continuity SURJECTIVITY fixed point upper semi-continuous upper hemi-continuous nonlinear analysis
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The Hyperspace of the Regions Below of Continuous Maps from the Converging Sequence 被引量:4
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作者 杨忠强 范玲玲 《Northeastern Mathematical Journal》 CSCD 2006年第1期46-54,共9页
Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC(S) and ↓C(S) to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all conti... Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC(S) and ↓C(S) to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0(S) = {↓f∈↓C(S) : f(0) = 0}. ↓USC(S) endowed with the Vietoris topology is a topological space. A pair of topological spaces (X, Y) means that X is a topological space and Y is its subspace. Two pairs of topological spaces (X, Y) and (A, B) are called pair-homeomorphic (≈) if there exists a homeomorphism h : X→A from X onto A such that h(Y) = B. It is proved that, (↓USC(S),↓C0(S)) ≈(Q, s) and (↓USC(S),↓C(S)/ ↓C0(S))≈(Q, c0), where Q = [-1,1]^ω is the Hilbert cube and s = (-1,1)^ω,c0= {(xn)∈Q : limn→∞= 0}. But we do not know what (↓USC(S),↓C(S))is. 展开更多
关键词 regions below upper semi-continuity the Hilbert cube pseudo-interior strongly universal the converging sequence
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ON GENERALIZED FEYNMAN-KAC TRANSFORMATION FOR MARKOV PROCESSES ASSOCIATED WITH SEMI-DIRICHLET FORMS
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作者 韩新方 马丽 《Acta Mathematica Scientia》 SCIE CSCD 2016年第6期1683-1698,共16页
Suppose that X is a right process which is associated with a semi-Dirichlet form (ε, D(ε)) on L2(E; m). Let J be the jumping measure of (ε, D(ε)) satisfying J(E x E- d) 〈 ∞. Let u E D(ε)b := D(... Suppose that X is a right process which is associated with a semi-Dirichlet form (ε, D(ε)) on L2(E; m). Let J be the jumping measure of (ε, D(ε)) satisfying J(E x E- d) 〈 ∞. Let u E D(ε)b := D(ε) N L(E; m), we have the following Pukushima's decomposition u(Xt)-u(X0) --- Mut + Nut. Define Pu f(x) = Ex[eNT f(Xt)]. Let Qu(f,g) = ε(f,g)+ε(u, fg) for f, g E D(ε)b. In the first part, under some assumptions we show that (Qu, D(ε)b) is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then (Put〉0is strongly continuous on L2(E;m). If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J(E x E - d) 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf(x) = Ex[eAtf(Xt)] to be strongly continuous. 展开更多
关键词 semi-Dirichlet form generalized Feynman-Kac semigroup strong continuity lower semi-bounded representation of local continuous additive functionalwith zero quadratic variation
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CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS II . LATTICE FLUID MODEL
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作者 胡英 英徐根 +1 位作者 D.T.Wu J.M.Prausnitz 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 1995年第1期14-25,共12页
Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real po... Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real polymer solution containing a solvent and a polydisperse polymer solute occupying a volume at fixed temperature and pressure. In the first step, close-packed pure components including solvent and polymers with different molar masses or different chain lengths are mixed to form a closed-packed polymer solution. In the second step, the close-packed mixture, considered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a volume dependent on temperature and pressure. Revised Freed's model developed previously is adopted for both steps. Besides pure-component parameters, a binary size parameter cr and a binary energy parameter e12 are used. They are all temperature dependent. The discrete-multicomponent approach is adopted to derive expressions for chemical potentials, spinodals and critical points. The continuous distribution function is then used in calculations of moments occurring in those expressions. Computation procedures are established for cloud-point-curve, shadow-curve, spinodal and critical-point calculations using standard distribution or arbitrary distribution on molar mass or on chain length. Illustrative examples are also presented. 展开更多
关键词 continuous thermodynamics polymer SOLUTION polydispersity lattice-fluid model CLOUD-POINT CURVE shadow CURVE SPINODAL upper-critical-solution temperatures lower-critical-solution temperature.
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A topological position of the set of continuous maps in the set of upper semicontinuous maps 被引量:11
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作者 YANG ZhongQiang WU NaDa 《Science China Mathematics》 SCIE 2009年第8期1815-1828,共14页
Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0,1], respec... Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0,1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points, then (↓USCC(X), ↓CC(X)) ≈ (Q, c 0 ∪ (Q Σ)), i.e., there is a homeomorphism h:↓USCC(X) → Q such that h(↓CC(X)) = c 0 ∪ (Q Σ), where Q = [?1,1]ω, Σ = {(x n ) n∈? ∈ Q: sup|x n | < 1} and c 0 = {(x n ) n∈? ∈ Σ: lim n→+∞ x n = 0}. Combining this statement with a result in our previous paper, we have $$ ( \downarrow USCC(X), \downarrow CC(X)) \approx \left\{ \begin{gathered} (Q,c_0 \cup (Q\backslash \Sigma )), if the set of isolanted points is dense in X, \hfill \\ (Q,c_0 ),otherwise, \hfill \\ \end{gathered} \right. $$ if X is an infinite compact metric space. We also prove that, for a metric space X, (↓USCC(X), ↓CC(X)) ≈ (Σ, c 0) if and only if X is non-compact, locally compact, non-discrete and separable. 展开更多
关键词 Hilbert cube strongly universal upper semi-continuous maps continuous maps compact-supported 54B20 54C35 57N20
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一类一阶半正周期边值问题正解的存在性
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作者 杨伟 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2023年第3期298-302,共5页
研究了一类一阶半正周期边值问题{u'(t)=λa(t)[f(u(t))-k],t∈[0,1],u(0)=u(1)正解的存在性,其中,k>0为常数,λ>0为参数。权函数a:[0,1]→R为连续函数,f或是定义在[0,∞)上的非负连续函数,满足f(0)=0且在无穷远处是次线性的... 研究了一类一阶半正周期边值问题{u'(t)=λa(t)[f(u(t))-k],t∈[0,1],u(0)=u(1)正解的存在性,其中,k>0为常数,λ>0为参数。权函数a:[0,1]→R为连续函数,f或是定义在[0,∞)上的非负连续函数,满足f(0)=0且在无穷远处是次线性的,或是定义在(0,∞)上的正连续函数且在0处具有奇异性。运用上下解方法证明了该问题正解的存在性。 展开更多
关键词 半正问题 变号权函数 正解 上下解方法
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非紧条件下广义集值隐向量拟变分不等式问题解的存在性
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作者 吴慧凌 林志 陈小龙 《宝鸡文理学院学报(自然科学版)》 CAS 2023年第1期14-18,共5页
目的研究非紧条件下广义集值隐向量拟变分不等式解的存在性。方法与之前的大部分研究相比,放松了紧的条件,结合集值映射的上半-C-连续性以及C-凸或C-似拟凸性,利用不动点定理进行研究。结果给出了非紧条件下广义集值隐向量拟变分不等式... 目的研究非紧条件下广义集值隐向量拟变分不等式解的存在性。方法与之前的大部分研究相比,放松了紧的条件,结合集值映射的上半-C-连续性以及C-凸或C-似拟凸性,利用不动点定理进行研究。结果给出了非紧条件下广义集值隐向量拟变分不等式问题解的存在性定理,并根据广义集值隐向量拟变分不等式问题与其他向量变分不等式问题的相关性,给出了相应的推论。结论非紧条件下解的存在性结果推广了之前的相关定理。 展开更多
关键词 不动点定理 开下截口 C-似拟凸 上半-C-连续
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Regularization Methods to Approximate Solutions of Variational Inequalities
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作者 Nguyen Van Kinh 《Open Journal of Optimization》 2023年第2期34-60,共27页
In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regul... In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data  satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones. 展开更多
关键词 Ill-Posed Problem Variational Inequality Regularization Method Monotone Operator Hemi-continuous Operator lower semi-continuous Function
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到锥度量空间上的半连续集值映射的连续性 被引量:7
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作者 夏顺友 黄南京 《辽宁工程技术大学学报(自然科学版)》 CAS 北大核心 2012年第2期280-283,共4页
为了获得到锥度量空间的上半连续和下半连续集值映射的连续点所具有的性质,通过构造第二纲集的方法,得到了到锥kR定义的锥度量空间kR的上半连续和下半连续紧值集值映射的连续点构成的集合是定义域中的剩余集.若定义域是Baire空间或完备... 为了获得到锥度量空间的上半连续和下半连续集值映射的连续点所具有的性质,通过构造第二纲集的方法,得到了到锥kR定义的锥度量空间kR的上半连续和下半连续紧值集值映射的连续点构成的集合是定义域中的剩余集.若定义域是Baire空间或完备度量空间,其连续点构成的集合还是稠密的,此时称到锥kR定义的锥度量空间kR的紧值上半连续和下半连续集值映射是通有连续的,也即是说在Baire纲意义下,此时的半连续集值映射在绝大多数点处是连续的,或者说基本上是连续的.该结果对集值分析理论和稳定性问题的研究有一定的理论参考价值和应用指导意义. 展开更多
关键词 集值映射 上半连续 下半连续 通有连续 剩余集 锥度量 锥度量空间 Baire空间
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(∈,∈∨_(q(λ,μ)))-凸模糊集(英文) 被引量:39
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作者 顾慧 廖祖华 《模糊系统与数学》 CSCD 北大核心 2007年第1期92-96,共5页
给出(∈,∈∨q(λ,μ))-凸模糊集的定义,讨论它们的一些基本性质。
关键词 模糊代数 重域 凸模糊集 下半连续
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关于连续型条件投入产出方程的一些结果——不动点与满射性方法 被引量:9
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作者 刘颖范 陈晓红 《应用数学和力学》 EI CSCD 北大核心 2004年第3期323-330,共8页
 基于经典(矩阵型)投入产出分析,引入了一类非线性(连续型)条件Leontief模型、投入产出方程及相关的三个基本问题,即可解性、连续性和满射性,进而非线性分析的一些不动点与满射性方法被用于处理这些问题· 作为结果,得到了三个重...  基于经典(矩阵型)投入产出分析,引入了一类非线性(连续型)条件Leontief模型、投入产出方程及相关的三个基本问题,即可解性、连续性和满射性,进而非线性分析的一些不动点与满射性方法被用于处理这些问题· 作为结果,得到了三个重要定理。 展开更多
关键词 投入产出方程 可解性 连续性 满射性 不动点 上半连续 上h连续 非线性分析
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凸性与度量投影的连续性 被引量:13
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作者 方习年 王建华 《应用数学》 CSCD 北大核心 2001年第1期47-51,共5页
本文研究近强凸、近非常凸 Banach空间中度量投影的连续性 .获得如下结果 :若 A是近强凸 (近非常凸 )空间中的逼近凸集 ,则度量投影 PA是范 -范上半连续的(范 -弱上半连续的 ) .此外 ,我们还利用度量投影的连续性给出 Banach空间为近强... 本文研究近强凸、近非常凸 Banach空间中度量投影的连续性 .获得如下结果 :若 A是近强凸 (近非常凸 )空间中的逼近凸集 ,则度量投影 PA是范 -范上半连续的(范 -弱上半连续的 ) .此外 ,我们还利用度量投影的连续性给出 Banach空间为近强凸、近非常凸的一些充分必要条件 . 展开更多
关键词 度量投影 逼近集 上半连续 近强凸 分离定理 凸性 BANACH空间 连续性
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预不变凸模糊集的一些性质 被引量:7
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作者 张萍 黄虎 王早 《纯粹数学与应用数学》 CSCD 北大核心 2006年第3期355-359,共5页
在下半连续的条件下,给出了一个模糊集是预不变凸模糊集的充分条件,并将模糊凸集上相关性质在模糊不变凸集上作了相应的推广.所给出的条件和证明都是新的.
关键词 不变凸 下半连续 凸模糊集 预不变凸模糊集
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