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1.
In this paper, by the theory of geometric inequalities, some new Bonnesen-style isoperimetric inequalities of n-dimensional simplex are proved. In several cases, these inequalities imply characterizations of regular simplex. 相似文献
2.
Helmut Rudolph 《Optimization》2015,64(8):1739-1757
3.
A new photoelastic model for studying fatigue crack closure 总被引:1,自引:0,他引:1
The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in
brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual
effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic
model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth
of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach
of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field
photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant
advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new
insights into the associated mechanisms. 相似文献
4.
A new computational framework is proposed for the form-finding and design of tensegrity structures with or without super-stability. The form-finding of tensegrities is formulated as two unconstrained minimisation problems where their objective functions are defined based on eigenvalues of a modified force density matrix. The Nelder–Mead simplex method is then used to solve the minimisation problems. Furthermore, another efficient method is suggested for the interactive form-finding and design of tensegrities with geometrical and force constraints. Examples of the form-finding of tensegrities are presented and the results obtained are compared and contrasted with those analytical results documented in the literature, to verify the accuracy and efficiency of the developed methods. 相似文献
5.
本文研究如下一种场站设置问题:设S是欧空间E~m中由有限个点A_1,A_2,…,A_n组成的集合.d(A_i,A_j)表示点A_i和A_j之间的距离.令σ(S)=Σ_(1≤i相似文献
7.
讨论了线性规划的单纯形解法,给出了不须加人工变量就可得到一个可行基的算法.通过大量的算例表明此法比传统的单纯形方法具有算法结构简单,计算量小的优点. 相似文献
8.
Rolf Schneider 《Mathematische Nachrichten》2019,292(8):1811-1822
We consider the tessellation induced by a stationary Poisson hyperplane process in d‐dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the k‐faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical k‐face, under the condition of given size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet. 相似文献
9.
In the recent paper [E. C. Balreira, S. Elaydi, and R. Luís, J. Differ. Equ. Appl. 23 (2017), pp. 2037–2071], Balreira, Elaydi and Luís established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luís' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application. 相似文献
10.
本文对变量目标函数系数、变量约束系数向量以及约束右端项向量同时变化进行灵敏度分析。不仅对变化后可能出现的各种情况进行分析处理,尤其在对偶可行性和可行性都不满足时,利用联合算法进行处理,并通过算例加以说明。 相似文献