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在模糊化拓扑空间基础上,放宽了模糊化拓扑结构的公理体系,引入模糊化弱拓扑和模糊化预拓扑的概念,并且讨论了它们构成的范畴和模糊化拓扑空间范畴的关系.结果表明,模糊化拓扑空间范畴既是模糊化弱拓扑空间范畴的双余反射满子范畴,又是模糊化预拓扑空间范畴的双余反射满子范畴. 相似文献
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本文利用模糊滤子的m-收敛概念对模糊拓扑空间的最小Hausdorff拓扑的特征进行了刻画,对模糊网的m-收敛与模糊拓扑空间的m-紧之间的关系以及最小Hausdorff拓扑与m-紧之间的关系进行了研究。 相似文献
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灰拓扑群 总被引:1,自引:1,他引:0
杨志民 《纯粹数学与应用数学》2000,16(3):6-8,14
给出了灰拓扑群的定义及有关定理,在此基础上讨论灰拓扑群与Fuzzy拓扑群、一般拓各之关系,并且研究了灰拓扑群的子群。 相似文献
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从整体角度出发,证明拓扑空间范畴Top分别是拓扑Fuzz范畴TopFuzz与拓扑分子格范畴TML的反射与余反射满子范畴,TopFuzzy是TML的反射与余反射(非满)子范畴。 相似文献
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弱拓扑和强可容许拓扑之间的一个关系 总被引:2,自引:0,他引:2
本文对局部凸空间X及其对偶X′,建立了弱拓扑σ(X,X′)和强拓扑β(X,X′)之间的一个新关系,改进了有关(X,X′)--可容许拓扑全体上的不变性结果。 相似文献
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Locale的弱拓扑表达 总被引:7,自引:0,他引:7
本文引入了弱拓扑空间的概念,证明了locale范畴与弱拓扑空间范畴的关系类似于拓扑空间范畴与locale范畴的关系。locale范畴严格包含于弱拓扑空间范畴并且与Sober的弱拓扑空间范畴等价。 相似文献
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拓扑遍历与拓扑双重遍历 总被引:24,自引:1,他引:23
令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在[2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质. 相似文献
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本文利用Hartle-Hawking的宇宙波函数方法,讨论了Planck时期的宇宙时空拓扑结构,由所得波函数的分析,发现宇宙在Planck时期形成球拓扑与环拓扑的可能性都存在,从而表明形成单连通宇宙与多连通宇宙可能性都存在。 相似文献
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首先考察模糊数空间中Skorokhod度量与紧承下方图度量之间的关系,然后说明了文献[4]中的关于Skorokhod拓扑紧致性的例子是错误的并给出了正确的例子. 相似文献
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讨论抽象基(特别是偏序集带辅助序)上的伪Scott拓扑与伪Scott开滤子集的一些基本性质, 推广了Domain理论中一些熟知的结论,证明了抽象基上的伪Scott拓扑是完全分配格;若在偏序集P上赋予辅助关系<, 则其上伪Scott开滤子之集是连续domain. 相似文献
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Periodic structures exhibit unique dynamic characteristics that make them act as tunable mechanical filters for wave propagation. As a result, waves can propagate along the periodic structures only within specific frequency bands called the ‘pass bands’ and wave propagation is completely blocked within other frequency bands called the ‘stop bands’ or ‘band gaps’. The spectral width of these bands can be optimized using topology optimization. In this paper, topology optimization is used to maximize the fundamental natural frequency of Mindlin plates while enforcing periodicity. A finite element model for Mindlin plates is presented and used along with an optimization algorithm that accounts for the periodicity constraint in order to determine the optimal topologies of plates with various periodic configurations. The obtained results demonstrate the effectiveness of the proposed design optimization approach in generating periodic plates with optimal natural frequency and wide stop bands. The presented approach can be invaluable design tool for many structures in order to control the wave propagation in an attempt to stop/confine the propagation of undesirable disturbances. 相似文献
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Pre—Separation Axioms in Fuzzifying Topology 总被引:1,自引:0,他引:1
K.M.AbdEl-Hakeim F.M.Zeyada 《模糊系统与数学》2003,17(1):28-36
1 IntroductionYing[5,6 ] introduced and elementally developed so called fuzzifying topology with the semanticmethod of continuous valued L ogic.Shen[7] introduced and studied T0 -,T1-,T2 (Hausdorff) -,T3(regularity) -,T4 (normality) -separation axioms in fuzzifying topology.In [3 ]the concepts of thefamily of fuzzifying pre-open sets,fuzzifying pre-neighbourhood structure of a point and fuzzifyingpre-closure are introduced and studied.It is worth to mention that pre-separation axioms are … 相似文献
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This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology. 相似文献
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Agnes Vathy-Fogarassy Agnes Werner-Stark Janos Abonyi 《Journal of Mathematical Modelling and Algorithms》2008,7(4):351-370
In practical data mining tasks, high-dimensional data has to be analyzed. In most of the cases it is very informative to map
and visualize the hidden structure of a complex data set in a low-dimensional space. In this paper a new class of mapping
algorithms is defined. These algorithms combine topology representing networks and different nonlinear mapping algorithms.
While the former methods aim to quantify the data and disclose the real structure of the objects, the nonlinear mapping algorithms
are able to visualize the quantized data in the low-dimensional vector space. In this paper, techniques based on these methods
are gathered and the results of a detailed analysis performed on them are shown. The primary aim of this analysis is to examine
the preservation of distances and neighborhood relations of the objects. Preservation of neighborhood relations was analyzed
both in local and global environments. To evaluate the main properties of the examined methods we show the outcome of the
analysis based both on synthetic and real benchmark examples. 相似文献
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Lotfi Lassoued 《东北数学》1998,(2)
ARemarkontheWeakTopologyandtheDegreeLotfiLassoued(Laboratoired'AnalyseNumériqueUniversitéPierreetMarieCurie4,placeJusieu,7525... 相似文献
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Anton Evgrafov 《Applied Mathematics and Optimization》2005,52(3):263-277
We consider a problem concerning the distribution of a solid material
in a given bounded control volume with the goal to minimize the potential power
of the Stokes flow with given velocities at the boundary through the material-free
part of the domain.We also study the relaxed problem of the optimal distribution of
the porous material with a spatially varying Darcy permeability tensor, where the
governing equations are known as the Darcy–Stokes, or Brinkman, equations. We
show that the introduction of the requirement of zero power dissipation due to the
flow through the porous material into the relaxed problem results in it becoming a
well-posed mathematical problem, which admits optimal solutions that have extreme permeability properties (i.e., assume only
zero or infinite permeability); thus, they are also optimal in the original (non-relaxed) problem. Two numerical techniques
are presented for the solution of the constrained problem. One is based on a sequence of optimal Brinkman flows with increasing
viscosities, from the mathematical point of view nothing but the exterior penalty approach applied to the problem. Another
technique is more special, and is based on the “sizing” approximation of the problem using a mix of two different porous materials
with high and low permeabilities, respectively. This paper thus complements the study of Borrvall and Petersson (Internat.
J. Numer. Methods Fluids, vol. 41, no. 1, pp. 77–107, 2003), where only sizing optimization problems are treated. 相似文献
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文献[8]提出了一类基于分层量化的偏序集结构(以下简称R-偏序集).此结构是sfe[5]的非对称推广,也是拟度量空间(quasi-metric spaces,qms)[3]和广义超度量空间(generalized ultrametric spaces,gums)[4]的一种特殊情形.本文定义了其上的广义Alexande... 相似文献