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31.
32.
In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
33.
M. V. Dolgopolik 《Optimization》2017,66(10):1577-1622
In this article, we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be both smooth and exact unlike the standard (i.e. non-parametric) exact penalty functions that are always nonsmooth. We obtain several necessary and/or sufficient conditions for the exactness of parametric penalty functions, and for the zero duality gap property to hold true for these functions. We also prove some convergence results for the method of parametric penalty functions, and derive necessary and sufficient conditions for a parametric penalty function to not have any stationary points outside the set of feasible points of the constrained optimization problem under consideration. In the second part of the paper, we apply the general theory of exact parametric penalty functions to a class of parametric penalty functions introduced by Huyer and Neumaier, and to smoothing approximations of nonsmooth exact penalty functions. The general approach adopted in this article allowed us to unify and significantly sharpen many existing results on parametric penalty functions. 相似文献
34.
We consider random subgraphs of a fixed graph with large minimum degree. We fix a positive integer k and let Gk be the random subgraph where each independently chooses k random neighbors, making kn edges in all. When the minimum degree then Gk is k‐connected w.h.p. for ; Hamiltonian for k sufficiently large. When , then Gk has a cycle of length for . By w.h.p. we mean that the probability of non‐occurrence can be bounded by a function (or ) where . © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 143–157, 2017 相似文献
35.
The Hamilton–Waterloo problem asks for a 2‐factorization of (for v odd) or minus a 1‐factor (for v even) into ‐factors and ‐factors. We completely solve the Hamilton–Waterloo problem in the case of C3‐factors and ‐factors for . 相似文献
36.
Vicenţiu D. Rădulescu Gelson C. G. dos Santos Leandro S. Tavares 《Mathematische Nachrichten》2023,296(6):2555-2574
This paper is concerned with the existence and multiplicity of solutions for a class of problems involving the Φ-Laplacian operator with general assumptions on the nonlinearities, which include both semipositone cases and critical concave convex problems. The research is based on the subsupersolution technique combined with a truncation argument and an application of the Mountain Pass Theorem. The results in this paper improve and complement some recent contributions to this field. 相似文献
37.
In this paper, we present a unified finite volume method preserving discrete maximum principle (DMP) for the conjugate heat transfer problems with general interface conditions. We prove the existence of the numerical solution and the DMP-preserving property. Numerical experiments show that the nonlinear iteration numbers of the scheme in [24] increase rapidly when the interfacial coefficients decrease to zero. In contrast, the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero, which reveals that the unified scheme is more robust than the scheme in [24]. The accuracy and DMP-preserving property of the scheme are also veried in the numerical experiments. 相似文献
38.
Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two- and three-dimensions are
developed and analyzed. Different from a few sixth-order compact finite difference
schemes in the literature, the finite difference and weight coefficients of the new
methods have analytic simple expressions. One of the new ideas is to use a weighted
combination of the source term at staggered grid points which is important for grid
points near the boundary and avoids partial derivatives of the source term. Furthermore, the new compact schemes are exact for 2D and 3D Poisson equations if the
solution is a polynomial less than or equal to 6. The coefficient matrices of the new
schemes are $M$-matrices for Helmholtz equations with wave number $K≤0,$ which
guarantee the discrete maximum principle and lead to the convergence of the new
sixth-order compact schemes. Numerical examples in both 2D and 3D are presented
to verify the effectiveness of the proposed schemes. 相似文献
39.
课程体系是人才培养的载体。为了更好地培养拔尖创新人才,南京大学化学国家级实验教学示范中心依据化学学科的特点和发展趋势,以科学内容的内在联系和研究规律为主线构建了“化学实验基础?化学合成与表征+化学原理与测量?化学功能分子实验+化学生物学综合实验+基于项目的研究实验”实验课程新体系,按照一流课程建设要求(高阶性、创新性和挑战度)对实验教学内容进行了优化,并建立起与之相适应的实验教学平台。新课程体系综合考虑了化学一级学科的整体性和关联学科的交叉性,在南京大学化学化工学院“拔尖计划”和“强基计划”学生中实施,教学效果显著。 相似文献
40.
弹性力学的混合方程和Hamilton正则方程 总被引:1,自引:0,他引:1
本文指出,在弹性力学基本方程中,按变量分类的位移方程,应力方程以外的第三种混合方程,以及按运算子分类的微分方程、变分原理以外的第三种Hamilton方程,它们正好是对应的。本文讨论了静力的和动力的情况以及它们可能的应用。 相似文献