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991.
Home owners are typically charged differently when they consume power at different periods within a day. Specifically, they are charged more during peak periods. Thus, in this paper, we explore how scheduling algorithms can be designed to minimize the peak energy consumption of a group of homes served by the same substation. We assume that a set of demand/response switches are deployed at a group of homes to control the activities of different appliances such as air conditioners or electric water heaters in these homes. Given a set of appliances, each appliance is associated with its instantaneous power consumption and duration, our objective is to decide when to activate different appliances in order to reduce the peak power consumption. This scheduling problem is shown to be NP-Hard. To tackle this problem, we propose a set of appliance scheduling algorithms under both offline and online settings. For the offline setting, we propose a constant ratio approximation algorithm (with approximation ratio \(\frac{1+\sqrt{5}}{2}+1\)). For the online setting, we adopt a greedy algorithm whose competitive ratio is also bounded. We conduct extensive simulations using real-life appliance energy consumption data trace to evaluate the performance of our algorithms. Extensive evaluations show that our schedulers significantly reduce the peak demand when compared with several existing heuristics. 相似文献
992.
Jinhae?Park Wei?WangEmail author Pingwen?Zhang Zhifei?Zhang 《Calculus of Variations and Partial Differential Equations》2017,56(2):41
In this paper, we investigate the structure and stability of the isotropic-nematic interface in 1-D. In the absence of the anisotropic energy, the uniaxial solution is the only global minimizer. In the presence of the anisotropic energy, the uniaxial solution with the homeotropic anchoring is stable for \(L_2<0\) and unstable for \(L_2>0\). We also present many interesting open questions, some of which are related to De Giorgi conjecture. 相似文献
993.
Jiayu?Li Chuanjing?Zhang Xi?ZhangEmail author 《Calculus of Variations and Partial Differential Equations》2017,56(3):81
In this paper, we study semi-stable Higgs sheaves over compact Kähler manifolds. We prove that there is an admissible approximate Hermitian-Einstein structure on a semi-stable reflexive Higgs sheaf and consequently, the Bogomolov type inequality holds on a semi-stable reflexive Higgs sheaf. 相似文献
994.
In this paper, a new price is given to the online decision maker at the beginning of each day. The trader must decide how many items to purchase according to the current price. We present three variants and an online algorithm based on cost function. The competitive ratio of the online algorithm is given for each variant, which is a performance measure of an online algorithm. More importantly, we show that the online algorithm is optimal. 相似文献
995.
A general framework is constructed for efficiently and stably evaluating the Hadamard finite-part integrals by composite quadrature rules. Firstly, the integrands are assumed to have the Puiseux expansions at the endpoints with arbitrary algebraic and logarithmic singularities. Secondly, the Euler-Maclaurin expansion of a general composite quadrature rule is obtained directly by using the asymptotic expansions of the partial sums of the Hurwitz zeta function and the generalized Stieltjes constant, which shows that the standard numerical integration formula is not convergent for computing the Hadamard finite-part integrals. Thirdly, the standard quadrature formula is recast in two steps. In step one, the singular part of the integrand is integrated analytically and in step two, the regular integral of the remaining part is evaluated using the standard composite quadrature rule. In this stage, a threshold is introduced such that the function evaluations in the vicinity of the singularity are intentionally excluded, where the threshold is determined by analyzing the roundoff errors caused by the singular nature of the integrand. Fourthly, two practical algorithms are designed for evaluating the Hadamard finite-part integrals by applying the Gauss-Legendre and Gauss-Kronrod rules to the proposed framework. Practical error indicator and implementation involved in the Gauss-Legendre rule are addressed. Finally, some typical examples are provided to show that the algorithms can be used to effectively evaluate the Hadamard finite-part integrals over finite or infinite intervals. 相似文献
996.
Using the equivalent block two-by-two real linear systems and relaxing technique, we establish a new block preconditioner for a class of complex symmetric indefinite linear systems. The new preconditioner is much closer to the original block two-by-two coefficient matrix than the Hermitian and skew-Hermitian splitting (HSS) preconditioner. We analyze the spectral properties of the new preconditioned matrix, discuss the eigenvalue distribution and derive an upper bound for the degree of its minimal polynomial. Finally, some numerical examples are provided to show the effectiveness and robustness of our proposed preconditioner. 相似文献
997.
令F是一个域,且|F|n+1,m,n为整数且m,n≥3.Tn(T_m)(F)是F上所有n×n(m×m)上三角矩阵的集合.本文中,刻画了从T_n(F)到T_m(F)的保经典伴随交换的单映射,给出了映射的表达式,对相应的方阵的工作是一个新的补充,所用方法是将其化归为相应的线性保持问题. 相似文献
998.
将经典的Black-Sholes方程转化为一类特殊的线性偏微分方程,并通过对其采用Fourier变换方法求得解析解,最后利用优核的相关性质对所得Black-Sholes方程解析解进行收敛性分析,证明了该解析解的收敛性. 相似文献
999.
马氏链遍历性理论在生物,数值计算,信息理论,自动控制,近代物理和公用事业中的服务系统等众多领域都有着广泛的应用,马氏链的C-强遍历性是马氏链遍历性理论的重要内容.本文给出了马氏链C-强遍历性的一个推广,首先给出了在可列状态空间取值的非齐次马氏链的广义C-强遍历性和广义一致C-强遍历性的概念,然后研究这两种遍历性成立的充分条件. 相似文献
1000.