High accuracy analysis of tensor-product linear pentahedral finite elements for variable coefficient elliptic equations

For a general second-order variable coefficient elliptic boundary value problem in three dimensions,the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements.In addition,the estimate for the W^1,1 -seminorm of the discrete derivative Green’s function is given.Finally,the authors show that the derivatives of the finite element solution u_h and the corresponding interpolantΠ_u are superclose in the pointwise sense of the L^∞-norm.     

Two-scale finite element Green’s function approximations with applications to electrostatic potential computation

<正> In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in three-dimensions.This approach is based on a two-scale finite elementspace defined,respectively,on the whole domain with size H and on some subdomain containing singularpoints with size h (h H).It is shown that this two-scale discretization approach is very efficient.In particular,the two-scale discretization approach is applied to solve Poisson-Boltzmann equationssuccessfully.     

Asymptotic normality of wavelet estimator in heteroscedastic model with <Emphasis Type="Italic">α</Emphasis>-mixing errors

Consider heteroscedastic regression model Y _ni = g(x _ni ) + σ _ni ɛ _ni (1 ≤ i ≤ n), where σ _ni ² = f(u _ni ), the design points (x _ni , u _ni ) are known and nonrandom, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors {ɛ _ni , 1 ≤ i ≤ n} are assumed to have the same distribution as {ξ _i , 1 ≤ i ≤ n}, which is a stationary and α-mixing time series with Eξ _i = 0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g(·) and f(·). Finite sample behavior of the estimators is investigated via simulations, too.     

L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

This paper investigates L~∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods.The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.The authors derive L~∞-estimates for the mixed finite element approximation of nonlinear optimal control problems.Finally,the numerical examples are given.     

ACCURACY ANALYSIS FOR QUASI-CAREY ELEMENT*

In this paper, a new triangular element （Quasi-Carey element） is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is of order O（h^2）, one order higher than its interpolation error when the exact solution belongs to H^3（Ω）. However, the interpolation error and consistency error of Carey element are of order O（h）. It seems that the above special property has never been seen for other triangular elements for the second order problems.     

Least-squares Galerkin procedure for second-order hyperbolic equations

This paper proposes the least-squares Galerkin finite element scheme to solve second-order hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in (L ²(Ω))² × L ²(Ω) norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example testifies the efficiency of the novel scheme.     

Finite volume element method with Lagrangian cubic functions

This paper establishes a new finite volume element scheme for Poisson equation on triangular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uniformly positive definite and convergence rate to be O(h ³) in H ¹-norm. Some numerical experiments confirm the theoretical considerations.     

The limit theorem for dependent random variables with applications to autoregression models

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {X _t } be a linear process defined by X _t = Σ _k=0^∞ψ _k ɛ _t−k , where {ψ _k , k ≥ 0} is a sequence of real numbers and {ɛ _k , k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {ɛ _k , k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter α when {ɛ _k , k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ ₀ = 1, ψ _k = 0, k ≥ 1.     

Superconvergence of mixed covolume method on quadrilateral grids for elliptic problems

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h~2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h~2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L~2 norm.Numerical experiments illustrating the theoretical results are provided.     

Solutions for singular p-Laplacian equation in R n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation −∆ _p u = f(x)u ^−α + λg(x)u ^β in R ^N ; where N ≥ 3, 1 < p < N, λ > 0, 0 < α < 1, max(p, 2) < β + 1 < p* = \fracN_pN - p \frac{{{N_p}}}{{N - p}} . We prove that there exists a critical value ¤ such that the problem has at least two solutions if 0 < λ < Λ; at least one solution if λ = Λ; and no solutions if λ > Λ.     

EXTENDED CLUSTERING COEFFICIENTS：GENERALIZATION OF CLUSTERING COEFFICIENTS IN SMALL-WORLD NETWORKS

The clustering coefficient C of a network, which is a measure of direct connectivity between neighbors of the various nodes, ranges from 0 （for no connectivity） to 1 （for full connectivity）. We define extended clustering coefficients C（h） of a small-world network based on nodes that are at distance h from a source node, thus generalizing distance-1 neighborhoods employed in computing the ordinary clustering coefficient C = C（1）. Based on known results about the distance distribution Pδ（h） in a network, that is, the probability that a randomly chosen pair of vertices have distance h, we derive and experimentally validate the law Pδ（h）C（h） ≤ c log N / N, where c is a small constant that seldom exceeds 1. This result is significant because it shows that the product Pδ（h）C（h） is upper-bounded by a value that is considerably smaller than the product of maximum values for Pδ（h） and C（h）. Extended clustering coefficients and laws that govern them offer new insights into the structure of small-world networks and open up avenues for further exploration of their properties.     

CONVERGENCE PROPERTIES OF THE DEPENDENT PRP CONJUGATE GRADIENT METHODS

In this paper, a new region of βk with respect to ;βk^PRP is given. With two Armijo-type line searches, the authors investigate the global convergence properties of the dependent PRP conjugate gradient methods, which extend the global convergence results of PRP conjugate gradient method proved by Grippo and Lucidi （1997） and Dai and Yuan （2002）.     

The recursive solution of queue length for <Emphasis Type="Italic">Geo/G</Emphasis>/1 queue with <Emphasis Type="Italic">N</Emphasis>-policy

This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n~-,n~+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n~-,n~+,n and departure epoch D_n).     

Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain

<正> This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the associated linear problem,the IBVP is shown to be locallywell-posed in the space H~s(0,1) for any s≥0 via the contraction mapping principle.     

A NEW FAMILY OF TRIVALENT CAYLEY NETWORKS ON WREATH PRODUCT Zm ～ Sn

We propose a new family of interconnection networks （WGn^m） with regular degree three. When the generator set is chosen properly, they are isomorphic to Cayley graphs on the wreath product Zm ～ Sn. In the case of m ≥ 3 and n ≥3, we investigate their different algebraic properties and give a routing algorithm with the diameter upper bounded by [m/2]（3n^2- 8n ＋ 4） - 2n ＋ 1. The connectivity and the optimal fault tolerance of the proposed networks are also derived. In conclusion, we present comparisons of some familiar networks with constant degree 3.     

H ∞ control of networked multi-agent systems

This paper concerns the disturbance rejection problem arising in the coordination control of a group of autonomous agents subject to external disturbances. The agent network is said to possess a desired level of disturbance rejection, if the H _∞ norm of its transfer function matrix from the disturbance to the controlled output is satisfactorily small. Undirected graph is used to represent the information flow topology among agents. It is shown that the disturbance rejection problem of an agent network can be solved by analyzing the H _∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. An interesting result is that the disturbance rejection ability of the whole agent network coupled via feedback of merely relative measurements between agents will never be better than that of an isolated agent. To improve this, local feedback injections are applied to a small fraction of the agents in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. Finally, extensions to the case when communication time delays exist are also discussed. This research is supported by the Natural Science Foundation of China under Grants Nos. 10832006 and 60674093.     

Removable ears of 1-extendable graphs

<正> Carvalho,Lucchesi and Murty proved that any 1-extendable graph G different from K_2and C_(2n)has at least Δ(G)edge-disjoint removable ears,and any brick G distinct from K_4 and■hasat least Δ(G)-2 removable edges,where Δ(G)denotes the maximum degree of G.In this paper,weimprove the lower bounds for numbers of removable ears and removable edges of 1-extendable graphs.It is proved that any 1-extendable graph G different from K_2 and C_(2n)has at least χ′(G)edge-disjointremovable ears,and any brick G distinct from K_4 and■has at least χ′(G)-2 removable edges,whereχ′(G)denotes the edge-chromatic number of G.     

An SEIRS epidemic model with two delays and pulse vaccination*

Pulse vaccination is an effective and important strategy to eradicate an infectious disease. The authors investigate an SEIRS epidemic model with two delays and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, the authors obtain that the infectious population dies out if R△ 〈 1, and the infectious population is uniformly persistent if R^△ 〉 1. The results indicate that a short period of pulse vaccination or a large pulse vaccination rate is a sufficient condition to eradicate the disease.     

H ∞ filtering for continuous-time systems with pointwise time-varying delay

The problem of H_∞filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper.By applying an innovation analysis in Krein space,a necessary and sufficient condition for the existence of an H_∞filter is derived in two methods:One is the partial differential equation approach,the other is the reorganized innovation analysis approach.The former gives a solution to the proposed H_∞filtering problem in terms of the solution of a partial differential equation with boundary conditions.The later gives an analytical solution to the proposed H_∞filtering problem in terms of the solutions of Riccati and matrix differential equations.     

Upwind finite volume element methods for one-dimensional semiconductor device

A fully discrete implicit Euler upwind finite volume element method is derived and studied for one-dimensional semiconductor device. Upwind scheme is introduced to deal with the convection-dominated diffusion equations in the semiconductor model. With different time steps for the electrostatic potential and the other unknown quantities, the computational procedure of the method is obtained. The local mass conservation laws are preserved under the framework of the upwind finite volume element schemes. A first-order accuracy in the L ²-norm is proved. Numerical experiments are given to validate the usefulness and efficiency of the method.