Model checking for general linear error-in-covariables model with validation data

In this paper, model checking problem is considered for general linear model when covariables are measured with error and an independent validation data set is available. Without assuming any error model structure between the true variable and the surrogate variable, the author first apply nonparametric method to model the relationship between the true variable and the surrogate variable with the help of the validation sample. Then the author construct a score-type test statistic through model adjustment. The large sample behaviors of the score-type test statistic are investigated. It is shown that the test is consistent and can detect the alternative hypothesis close to the null hypothesis at the rate n ^−r with 0 ≤ r ≤ 1/2. Simulation results indicate that the proposed method works well.     

Nonconforming finite element method for nonlinear parabolic equations

<正> A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L~2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.     

DEGREE CONDITIONS FOR GRAPHS TO BE FRACTIONAL （a, b, n）-CRITICAL GRAPHS

Let G be a graph, and a and b be integers with a ≤ b. A graph G is called a fraetional （a, b, n）-critical graph if after any n vertices of G are deleted the remaining subgraph has a fractional [a, b]-factor. In this paper two degree conditions for graphs to be fractional （a, b, n）-eritical graphs are presented, and the degree conditions are sharp in some sense.     

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.     

Empirical likelihood confidence region for parameters in linear errors-in-variables models with missing data

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin (1976) is considered in this paper. A constrained empirical likelihood confidence region for a parameter β ₀ in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β ₀. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation’s conclusion.     

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.     

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).     

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.     

A COMPARATIVE STUDY OF DATA MINING METHODS IN CONSUMER LOANS CREDIT SCORING MANAGEMENT

1. Introduction Data mining (DM), sometimes referred to as knowledge discovery in database (KDD), is a systematic approach to find underlying patterns, trends, and relationships buried in data. Data mining has drawn much attention from bothresearchers and practitioners due to its wide applications in crucial business decisions. Basically, the research on DM can be classified into two categories: methodologies and technologies. According to Curt (1995), the technology part of DM consists of…     

Simulating the supply disruption for the coordinated supply chain

There are many disruptive accidents in the supply chain operations system and achieving the coordination of supply chain is main objective for supply chain research. While disruptive accidents have increasingly influenced the coordinated operation of the supply chain, existing research literature on the supply chain coordination is setting in a stationary environment. The answer for how the disruptive accidents affect the coordinated supply chain is given in this paper. Based on the benchmark supply chain which is coordinated by the negative incentive mechanism, we study the impacts of supply disruption on the supply chain system by using simulation approach in which two different distribution function of random variable are used to express the supply disruption. Comparison between these two simulation results and possible coordination mechanism under the supply disruption are proposed. From the perspective of supply chain risk management, we provide the inspiration for the manager.     

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.     

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 ∞ 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.     

Testing <Emphasis Type="Italic">k</Emphasis>-edge-connectivity of digraphs

This paper presents an algorithm that tests whether a given degree-bounded digraph is k-edge-connected or ɛ-far from k-edge-connectivity. This is the first testing algorithm for k-edgeconnectivity of digraphs whose running time is independent of the number of vertices and edges. A digraph of n vertices with degree bound d is ɛ-far from k-edge-connectivity if at least ɛdn edges have to be added or deleted to make the digraph k-edge-connected, preserving the degree bound. Given a constant error parameter ɛ and a degree bound d, our algorithm always accepts all k-edge-connected digraphs and rejects all digraphs that is ɛ-far from k-edge-connectivity with probability at least 2/3. It runs in $ O\left( {d\left( {\frac{c} {{\varepsilon d}}} \right)^k log\frac{1} {{\varepsilon d}}O} \right) $ O\left( {d\left( {\frac{c} {{\varepsilon d}}} \right)^k log\frac{1} {{\varepsilon d}}O} \right) (c > 1 is a constant) time when input digraphs are restricted to be (k-1)-edge connected and runs in $ O\left( {d\left( {\frac{{ck}} {{\varepsilon d}}} \right)^k log\frac{k} {{\varepsilon d}}O} \right) $ O\left( {d\left( {\frac{{ck}} {{\varepsilon d}}} \right)^k log\frac{k} {{\varepsilon d}}O} \right) (c > 1 is a constant) time for general digraphs.     

Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system

<正> This paper shows how the so called von Karman model can be obtained as a singular limitof a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity,provided a regularizing term through a fourth order dispersive operator is added.Introducing dampingmechanisms,the authors also show that the energy of solutions for this modified Mindlin-Timoshenkosystem decays exponentially,uniformly with respect to the parameter k.As k→∞,the authors obtainthe damped von Karman model with associated energy exponentially decaying to zero as well.     

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.     

Robustness analysis of leader-follower consensus

In this paper, robustness properties of the leader-follower consensus are considered. For simplicity of presentation, the attention is focused on a group of continuous-time first-order dynamic agents with a time-invariant communication topology in the presence of communication errors. In order to evaluate the robustness of leader-follower consensus, two robustness measures are proposed: the L ₂ gain of the error vector to the state of the network and the worst case L ₂ gain at a node. Although the L ₂ gain of the error vector to the state of the network is widely used in robust control design and analysis, the worst case L ₂ gain at a node is less conservative with respect to the number of nodes in the network. It is thus suggested that the worst case L ₂ gain at a node is used when the robustness of consensus is considered. Theoretical analysis and simulation results show that these two measures are sensitive to the communication topology. In general, the “optimal” communication topology that can achieve most robust performance with respect to either of the proposed robustness measures is difficult to characterize and/or obtain. When the in-degree of each follower is one, it is shown that both measures reach a minimum when the leader can communicate to each node in the network. This work is supported by the National Natural Science Foundation of China under Grant No. 60774005.     

IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS

The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameterdependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

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.