Reflecting Diffusion Processes on Manifolds Carrying Geometric Flow

Let \(L_t:=\Delta _t+Z_t\) for a \(C^{\infty }\)-vector field Z on a differentiable manifold M with boundary \(\partial M\), where \(\Delta _t\) is the Laplacian operator, induced by a time dependent metric \(g_t\) differentiable in \(t\in [0,T_\mathrm {c})\). We first establish the derivative formula for the associated reflecting diffusion semigroup generated by \(L_t\). Then, by using parallel displacement and reflection, we construct the couplings for the reflecting \(L_t\)-diffusion processes, which are applied to gradient estimates and Harnack inequalities of the associated heat semigroup. Finally, as applications of the derivative formula, we present a number of equivalent inequalities for a new curvature lower bound and the convexity of the boundary. These inequalities include the gradient estimates, Harnack inequalities, transportation-cost inequalities and other functional inequalities for diffusion semigroups.     

Decoupled schemes for unsteady MHD equations. I. time discretization

In this article, a time discretization decoupled scheme for two‐dimensional magnetohydrodynamics equations is proposed. The almost unconditional stability and convergence of this scheme are provided. The optimal error estimates for velocity and magnet are provided, and the optimal error estimate for pressure are deduced as well. Finite element spatial discretization and numerical implementation are considered in our article (Zhang and He, Comput Math Appl 69 (2015), 1390–1406). © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 956–973, 2017     

Local and parallel finite element algorithm for stationary incompressible magnetohydrodynamics

This article presents a local and parallel finite element method for the stationary incompressible magnetohydrodynamics problem. The key idea of this algorithm comes from the two‐grid discretization technique. Specifically, we solve the nonlinear system on a global coarse mesh, and then solve a series of linear problems on several subdomains in parallel. Furthermore, local a priori estimates are obtained on a general shape regular grid. The efficiency of the algorithm is also illustrated by some numerical experiments.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1513–1539, 2017     

Existence and limit behavior of prescribed L2‐norm solutions for Schrödinger‐Poisson‐Slater systems in

In this paper, we study constraint minimizers of the following L ²?critical minimization problem: where E (u ) is the Schrödinger‐Poisson‐Slater functional and N denotes the mass of the particles in the Schrödinger‐Poisson‐Slater system. We prove that e (N ) admits minimizers for and, however, no minimizers for N >N ^?, where Q (x ) is the unique positive solution of in . Some results on the existence and nonexistence of minimizers for e (N ^?) are also established. Further, when e (N ^?) does not admit minimizers, the limit behavior of minimizers as N ↗N ^? is also analyzed rigorously.     

Optimizing garbage collection vehicle routing problem with alternative fuel-powered vehicles

Abstract

This paper considers the garbage collection problem in which vehicles with multiple compartments are used to collect the garbage. The vehicles are considered to be Alternative Fuel-powered Vehicles (AFVs). Compared with the traditional fossil fuel powered vehicles, the AFVs have limited fuel tank capacity. In addition, AFVs are allowed to refuel only at the depot. We provide a mathematical formulation and develop two solution approaches to solve the problem. The first approach is based on the saving algorithm, while the second is based on the ant colony system (ACS) metaheuristic. New problem instances have been generated to evaluate the performance of the proposed algorithms.     

一种新的求非线性方程组的数值延拓法

针对迭代过程中的Jacobi奇异问题,本文提出了一种新的数值延拓法.通过构造双参数同伦算子,采用可控条件和适当选取参数的方式克服Jacobi奇异性,并分析了方法的收敛性.最后,通过数值实验对比,验证了方法的可行性和优越性.特别是具有可调控越过Jacobi奇异(点、线、面)的优势,从而也在某种程度上解决了数值延拓法严重依赖于初值的问题.     

一类新的(2n-1)点二重动态逼近细分

利用正弦函数构造了一类新的带有形状参数ω的(2n-1)点二重动态逼近细分格式.从理论上分析了随n值变化时这类细分格式的C~k连续性和支集长度;算法的一个特色是随着细分格式中参数ω的取值不同,相应生成的极限曲线的表现张力也有所不同,而且这一类算法所对应的静态算法涵盖了Chaikin,Hormann,Dyn,Daniel和Hassan的算法.文末附出大量数值实例,在给定相同的初始控制顶点,且极限曲线达到同一连续性的前提下和现有几种算法做了比较,数值实例表明这类算法生成的极限曲线更加饱满,表现力更强.     

iGreen: green scheduling for peak demand minimization

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.