Hereditary effects of exponentially damped oscillators with past histories

This paper presents hereditary effects of exponentially damped oscillators with past histories. Unlike the classical viscously damped oscillators, the nonviscously damped ones involve damping forces which depend on time-histories of vibrating motions via convolution integrals. As a result, equations of motion of such systems are a set of coupled second-order Volterra integro-differential equations. In this work, initial value problems for the integro-differential equations are revisited. The initial conditions should contain time-histories of vibrating motions. Then, initialization response of exponentially damped oscillators is obtained. It is used to characterize the hereditary effects on the dynamic response. At last, stability of initialization response is proved from the theoretical viewpoint and verified by numerical simulations. This reveals that the hereditary effects gradually recede with increasing of time.     

Finite difference spectral approximation for the time‐space fractional telegraph equation and its parameter estimation

The object of this paper is to present the numerical solution of the time‐space fractional telegraph equation. The proposed method is based on the finite difference scheme in temporal direction and Fourier spectral method in spatial direction. The fast Fourier transform (FFT) technique is applied to practical computation. The stability and convergence analysis are strictly proven, which shows that this method is stable and convergent with (2?α) order accuracy in time and spectral accuracy in space. Moreover, the Levenberg‐Marquardt (L‐M) iterative method is employed for the parameter estimation. Finally, some numerical examples are given to confirm the theoretical analysis.     

Lagrangian duality and saddle points for sparse linear programming

The sparse linear programming(SLP) is a linear programming problem equipped with a sparsity constraint, which is nonconvex, discontinuous and generally NP-hard due to the combinatorial property involved.In this paper, by rewriting the sparsity constraint into a disjunctive form, we present an explicit formula of the Lagrangian dual problem for the SLP, in terms of an unconstrained piecewise-linear convex programming problem which admits a strong duality under bi-dual sparsity consistency. Furthermore, we show a saddle point theorem based on the strong duality and analyze two classes of stationary points for the saddle point problem. At last,we extend these results to SLP with the lower bound zero replaced by a certain negative constant.     

具有转向点的二阶非线性方程Robin问题的奇摄动(英)

本文应用微分不等式的方法，研究了具有转向点的二阶非线性方程Robin问题的奇摄动，根据fy在转向点附近的性态，边值问题的解将呈现冲击层现象和边界层现象，在适当的假设条件下，我们证明了该问题的存在性和不同的渐近性质。     

Nonlinear impulsive system of microbial production in fed-batch culture and its optimal control

In this study the optimal control of fed-batch glycerol fermentation is investigated based on an impulsive dynamical system. Considering the sudden increase of the glycerol and alkali in fed-batch culture of biodissimilation of glycerol to 1,3-propanediol, this paper proposes a nonlinear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. In view of the controllability of volumes of glycerol added to the reactor instantaneously, the paper constructs an optimal control model based on the nonlinear impulsive system and the existence of the optimal control is obtained. The control variables here are the moments and the sizes of jumps in the states at the discrete instants and the objective is to maximize the productivity of 1,3-propanediol over one cycle.     

Superconvergence of finite volume methods for the Stokes equations

A general superconvergence result of finite volume method for the Stokes equations is obtained by using a L² projection post‐processing technique. This superconvergence result can be applied to different finite volume methods and to general quasi‐uniform meshes.© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009     

用修正重标极差法对上证指数长期记忆性的研究

本文以上证指数周收益率为研究对象,分别采用重标极差分析法和修正重标极差分析法,通过计算V统计量的值对其进行长期记忆性的检验。由于不能排除V统计量的值存在超出上侧分位点的可能性,本文进行了双侧检验,并分析了R/S分析法产生偏差的原因。得出上证指数周收益率时间序列并未表现出显著的长期记忆性的结论。     

$\alpha$-可分解4-圈系统

An m-cycle system of order v and index λ, denoted by m-CS（v,λ）, is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS（v,λ） is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m｜λv（v-1）/2,2｜λ（v -1）,m｜αv,α｜λ（v-1）/2. It is shown in this paper that these conditions are also sufficient when m = 4.     

A weak Galerkin finite element method for the stokes equations

This paper introduces a weak Galerkin (WG) finite element method for the Stokes equations in the primal velocity-pressure formulation. This WG method is equipped with stable finite elements consisting of usual polynomials of degree k≥1 for the velocity and polynomials of degree k?1 for the pressure, both are discontinuous. The velocity element is enhanced by polynomials of degree k?1 on the interface of the finite element partition. All the finite element functions are discontinuous for which the usual gradient and divergence operators are implemented as distributions in properly-defined spaces. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. It must be emphasized that the WG finite element method is designed on finite element partitions consisting of arbitrary shape of polygons or polyhedra which are shape regular.     

一类非线性微分方程周期解及全局稳定性

本文研究下面一类非线性微分方程dsdt=1 -s- x1 s0 δQ2 ( m1 s0 sk1 s0 s-k)dx1 dt =x1 Q( m1 s0 sk1 s0 s-k) -x1 -x2m2 x1 /Qk2 x1 /Qdx2dt =x2Qm2 x1 /Qk2 x1 /Q -x2　　如果条件m2 x 2 (k1 δ s0 δ-Qλ2 -x 2 ) 2 >m1 δk1 (k2 Q2 λ2 ) 2成立时 ,系统在Ω内存在周期解 ;如果条件m2 x 2 (k1 δ s0 δ -Qλ2 -x 2 ) 2 相似文献