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91.
We propose a definition of lower closed transitive relations and prove the existence of minimal elements for such a relation. This result is shown to contain probably a large part of existing versions of Ekeland’s variational principle (EVP). We introduce the notion of a weak τ-function p as a generalized distance and use it together with the above result on minimal elements to establish enhanced EVP for various settings, under relaxed lower semicontinuity assumptions. These principles conclude the existence not only of p-strict minimizers of p-perturbations of the considered vector function, but also p-sharp and p-strong minimizers. Our results are proved to be stronger than the classical EVP and many generalizations in the literature, even in the usual one-dimensional case, by numerous corollaries and examples. We include equivalent formulations of our enhanced EVP as well.  相似文献   
92.
This paper addresses the problem of reachable set bounding for linear discrete-time systems that are subject to state delay and bounded disturbances. Based on the Lyapunov method, a sufficient condition for the existence of ellipsoid-based bounds of reachable sets of a linear uncertain discrete system is derived in terms of matrix inequalities. Here, a new idea is to minimize the projection distances of the ellipsoids on each axis with different exponential convergence rates, instead of minimization of their radius with a single exponential rate. A smaller bound can thus be obtained from the intersection of these ellipsoids. A numerical example is given to illustrate the effectiveness of the proposed approach.  相似文献   
93.
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained by decomposing the objective function into convex and concave parts and replacing the concave part by an affine underestimate. It is shown that the best affine underestimate can be expressed in terms of the center and the radius of the smallest sphere containing the feasible set. The concave term is obtained either by a constant diagonal shift associated with the smallest eigenvalue of the objective function Hessian, or by a diagonal shift obtained by solving a semidefinite programming problem. Numerical results show that the proposed algorithm is competitive with state-of-the-art graph partitioning codes.  相似文献   
94.
Phan Van Thien 《代数通讯》2013,41(10):3704-3715
We will give a formula to compute the regularity index of s + 2 fat points not lying on a linear (s ? 1)-space in ? n , s ≤ n (Theorem 3.4). Our result generalizes a formula to compute the regularity index of fat points in general position in ? n ([3 Catalisano , M. V. , Trung , N. V. , Valla , G. ( 1993 ). A sharp bound for the regularity index of fat points in general position . Proc. Amer. Math. Soc. 118 : 717724 .[Crossref], [Web of Science ®] [Google Scholar]], Corollary 8). Our result also shows that the Segre bound is attained by s + 2 points not lying on a linear (s ? 1)-space.  相似文献   
95.
Convex underestimators of a polynomial on a box. Given a non convex polynomial ${f\in \mathbb{R}[{\rm x}]}$ and a box ${{\rm B}\subset \mathbb{R}^n}$ , we construct a sequence of convex polynomials ${(f_{dk})\subset \mathbb{R}[{\rm x}]}$ , which converges in a strong sense to the “best” (convex and degree-d) polynomial underestimator ${f^{*}_{d}}$ of f. Indeed, ${f^{*}_{d}}$ minimizes the L 1-norm ${\Vert f-g\Vert_1}$ on B, over all convex degree-d polynomial underestimators g of f. On a sample of problems with non convex f, we then compare the lower bounds obtained by minimizing the convex underestimator of f computed as above and computed via the popular α BB method and some of its other refinements. In most of all examples we obtain significantly better results even with the smallest value of k.  相似文献   
96.
We propose higher-order radial sets and corresponding derivatives of a set-valued map and prove calculus rules for sums and compositions, which are followed by direct applications in discussing optimality conditions for several particular optimization problems. Our main results are both necessary and sufficient higher-order conditions for weak efficiency in a general set-valued vector optimization problem without any convexity assumptions. Many examples are provided to explain advantages of our results over a number of existing ones in the literature.  相似文献   
97.
In this study, ZnO nanorods (NRs) and nanocombs (NCs) are synthesized by simple galvanostatic electrochemical deposition technique, without prepared any ZnO seed-layer or catalyst. The effect of the different morphologies on the UV sensing characteristics has been studied under ambient conditions. The photoluminescence (PL) spectra and time-dependent photoresponse of the ZnO nanostructures exhibited good optical properties. At room temperature, NCs showed superior response with 9% change of its resistance, few seconds response time and fully recovery. Inversely, in high temperature ZnO NRs indicated better response than NCs with the variation of 25% of its resistance. The dependence photoresponse on temperature demonstrated clearly how surface-defects affect on UV response of ZnO nanostructures. Our approach is to provide a simple and cost-effective way to fabricate UV detectors.  相似文献   
98.
99.
Through accumulation, mercury contamination in aquatic systems still poses serious health risks despite the strict regulations on drinking water and industrial discharge. One effective strategy against this is adsorptive removal, in which a suitably functionalized porous material is added to water treatment protocols. Thiol (SH) group-grafted structures perform commendably; however, insufficient attention is paid to the cost, scalability, and reusability or how the arrangement of sulfur atoms could affect the HgII binding strength. We used an inexpensive and scalable porous covalent organic polymer (COP-130) to systematically introduce thiol functional groups with precise chain lengths and sulfur content. Thiol-functionalized COP-130 demonstrates enhanced wettability and excellent HgII uptake of up to 936 mg g−1, with fast kinetics and exceptionally high selectivity. These Hg adsorbents are easily regenerated with HCl and can be used at least six times without loss of capacity even after treatment with strong acid, a rare performance in the domain of Hg-removal research.  相似文献   
100.
The European Physical Journal C - Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible...  相似文献   
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