具有Size结构的捕食种群系统的最优收获策略

分析了一类捕食者种群带有Size结构的捕食-被捕食系统的最优收获问题. 利用不动点定理证明了状态系统及其共轭系统非负解的存在唯一性、解对控制变量的连续依赖性. 应用切锥法锥技巧导出了最优性条件, 借助Ekeland变分原理讨论了最优收获策略的存在唯一性, 推广了年龄结构种群模型中的相应结论.     

一种估计精度限制下的加速退化试验最优设计

讨论了一类步进应力的加速退化试验,在试验假定下,以退化失效分布平均寿命的极大似然估计与其真值的接近程度为标准得到一个精度限制．然后根据试验的过程得到了试验成本函数的一般表达形式．在估计精度的限制之下,最小化成本函数,以此得出试验的最优设计模型．最后,给出了一个数值例子,展示了优化设计的过程．     

Maximum principle for optimal distributed control of the viscous Dullin-Gottwald-Holm equation

In this paper, the optimal distributed control of the viscous Dullin-Gottwald-Holm equation is investigated. Adopting the Dubovitskii and Milyutin functional analytical approach, we obtain the Pontryagin maximum principle of the system. The necessary optimality condition is established for an optimal control problem in fixed final horizon case. Finally, an illustrative example is also given.     

Optimal timing of interventions in fishery resource and pest management

Assuming that a fish population follows the continuous logistic growth or the discrete Beverton-Holt model, several optimal impulsive harvesting policies for the maximum stock level of the fish at the end of a fishing season are investigated under the condition of fixed intensity and frequency of impulsive harvesting. The optimal impulsive harvesting moments for all cases considered are given analytically and the related numerical simulations are also provided. Furthermore, the methods employed can also be used to investigate the optimal timing of chemical control in pest management. Our results confirm that the optimal timing of pesticide applications such that the density of the pest population is minimal at any time during a planting season or the average of density of the pest population over the planting season is minimal is the beginning of the planting season. In practice, the results can be used to guide the fisherman to manage fisheries and guide farmers to control pests.     

自适应间断Galerkin 有限元的多水平方法

本文讨论在自适应网格上间断Galerkin 有限元离散系统的局部多水平算法. 对于光滑系数和间断系数情形, 利用Schwarz 理论分析了算法的收敛性. 理论和数值试验均说明算法的收敛率与网格层数以及网格尺寸无关. 对强间断系数情形算法是拟最优的, 即收敛率仅与网格层数有关.     

Fractional differential equations of motion in terms of combined Riemann—Liouville derivatives

In this paper,we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system.A combined Riemann-Liouville fractional derivative operator is defined,and a fractional Hamilton principle under this definition is established.The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle.A number of special cases are given,showing the universality of our conclusions.At the end of the paper,an example is given to illustrate the application of the results.     

Base force element method of complementary energy principle for large rotation problems

Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.     

Effects of high order deformations on the strength of planar lattice materials

Lattice materials have been attractive over the last decade for use as load-carrying structures, energy absorbing elements and heat exchanging structures because of their excellent mechanical properties and multifunctional characters. However, the quantitative analysis accounting for high order deformations upon the collapse of lattice materials, which is important for their applications, has not been reported. An analytical investigation of yield surfaces with respect to the high order deformations was carried out for two typical planar lattice materials： triangular and Kagome lattices separately. The analytical results were validated by the finite element method （FEM） simulations. It was found that the effect of high order deformation on the yield strength increases with the relative density. The bending effect of the Kagome lattice is more obvious than that of the triangular one with the same relative density and stress state. The yield strength of the Kagome lattice calculated by neglecting the bending effect overestimates the result by more than 10% when the relative density is higher than about 11.1%, which may not be ignored in engineering applications. The yielding surfaces of the two lattice materials demonstrated in the paper also confirm the analytical results.     

Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions

The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.     

Deployment/retrieval optimization for flexible tethered satellite systems

A methodology for deployment/retrieval optimization of tethered satellite systems is presented. Previous research has focused on the case where the tether is modeled as an inelastic, straight rod for the determination of optimal system trajectories. However, the tether shape and string vibrations can often be very important, particularly when the deployment/retrieval speed changes rapidly, or when external forces such as aerodynamic drag or electrodynamic forces are present. An efficient mathematical model for flexible tethered systems is first derived, which treats the tether as composed of a system of lumped masses connected via inelastic links. A tension control law is presented based on a discretization of the tether length dynamics via Chebyshev polynomials. A scheme that minimizes the second derivative of length over the trajectory based on physically meaningful coefficients is presented. This is utilized in conjunction with evolutionary optimization methods to minimize the rigid body and flexible modes of the system during deployment/retrieval. It is shown that only a very small number of parameters are required to generate accurate trajectories. The results are compared to the case where the tether is modeled as a straight rod.