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41.
In this paper, in terms of the Fréchet normal cone, we establish exact separation results for finitely many disjoint closed sets in an Asplund space, which supplement the extremal principle and some fuzzy separation theorems. As an application, we provide a new optimality condition for a constraint optimization problem in terms of Fréchet subdifferential and Fréchet normal cone. 相似文献
42.
43.
We analyze the detection and classification of singularities of functions , where and . It will be shown how the set ?S can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ?S is a dimensional piecewise smooth manifold with or 3, we will classify smooth and non-smooth components of ?S. This improves previous results given for shearlet systems with a certain band-limited generator, since the estimates we derive are uniform. Moreover, we will show that our bounds are optimal. Along the way, we also obtain novel results on the characterization of wavefront sets in 3 dimensions by compactly supported shearlets. Finally, geometric properties of ?S such as curvature are described in terms of the continuous shearlet transform of f. 相似文献
44.
The idea of combine aggregation and intuitionistic fuzzy information plays essential role in multi criteria decision making (MCDM) process. However, this new branch has attracted researchers that study in different fields recently. In this paper, we study MCDM problems with intuitionistic fuzzy environment. Firstly, we introduce some operations related with Einstein t-norm and t-conorm such as, Einstein sum, product and exponentiation. After that, we define dynamic intuitionistic fuzzy Einstein averaging (DIFWA) operator and dynamic intuitionistic fuzzy Einstein geometric averaging (DIFWG) operator. Their notable property is that collect and aggregate values in different period based on Einstein operations in intuitionistic fuzzy set (IFS)s. In addition, we compare the defined operators with the existing intuitionistic fuzzy dynamic operators and get the corresponding relations. We establish two methods using with DIFWA and DIFWG to solve MCDM problems with intuitionistic fuzzy tools. Finally, an illustrated example is presented to show the applicability of the introduced methods. 相似文献
45.
This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice. 相似文献
46.
Aastha Gupta Aditya Kaushik Manju Sharma 《Numerical Methods for Partial Differential Equations》2023,39(2):1220-1250
We propose a hybrid numerical scheme to discretize a class of singularly perturbed parabolic reaction–diffusion problems with robin-boundary conditions on an equidistributed grid. The hybrid difference scheme is developed by using a modified backward difference scheme in time, a combination of the cubic spline and exponential spline difference scheme in space. The proposed scheme uses a cubic spline difference scheme for the discretization of robin-boundary conditions. For the time discretization of the problem, we use the standard uniform mesh while a layer adapted equidistributed grid is generated for the spatial discretization. By equidistributing a curvature-based monitor function, the spatial adaptive grid is able to capture the presence of parabolic boundary layers without using any prior information about the solution. Parameter uniform error estimates are derived to illustrate an optimal convergence of first-order in time and second-order in space for the proposed discretization. The accuracy of the proposed scheme is confirmed by the numerical experiments that underpin the theoretical analysis. 相似文献
47.
Uniform Convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients 下载免费PDF全文
Haijun Wu & Weiying Zheng 《数学研究通讯:英文版》2023,39(3):437-475
The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients are
considered. Under the conditions that the coefficient is quasi-monotone up to
a constant and the meshes are locally refined by using the newest vertex bisection algorithm, some uniform convergence results are proved for the standard
multigrid V-cycle algorithm with Gauss-Seidel relaxations performed only on
new nodes and their immediate neighbours. The multigrid V-cycle algorithm
uses $\mathcal{O}(N)$ operations per iteration and is optimal. 相似文献
48.
49.
This paper addresses the reachable set bounding for discrete-time switched nonlinear positive systems with mixed time-varying delays and disturbance, which contains switched linear positive systems as a special case. By resorting to a new method that does not involve the common Lyapunov–Krasovskii functional one, explicit criteria to ensure any state trajectory of the system converges exponentially into a prescribed sphere are obtained under average dwell time switching. The results can then be extended to more general time-varying systems. Finally, two numerical examples are used to demonstrate the effectiveness of the obtained results. 相似文献
50.
采用分子动力学模拟的方法研究了Cu50Ni50合金在不同冷却速度下的凝固过程,利用均方位移、径向分布函数和结构可视化等方法分析其微观结构.并对凝固模型进行拉伸模拟,通过应力应变曲线和直观结构变化分析其性能.研究表明:冷却速度对Cu50Ni50合金凝固形成的结构有较大影响,随着冷却速度的升高,凝固形成的结构中晶体含量减少,在较低的冷却速度下,如冷却1×1012K/s时,Cu50Ni50合金凝固形成晶体结构;在较高的冷却速度下,如1×1014K/s时,Cu50Ni50合金凝固形成非晶体结构,且非晶Cu50Ni50合金的抗拉性能要优于晶体Cu50Ni50合金. 相似文献