Stabilization of Euler-Bernoulli beam with a nonlinear locally distributed feedback control

This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial multiplier skill, the authors show that, corresponding to the different values of the parameters involved in the nonlinear locally distributed feedback control, the energy of the beam under the proposed feedback decays exponentially or in negative power of time t as t → ∞.     

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.     

GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS

In this paper, the authors propose a class of Dai-Yuan （abbr. DY） conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk＋1 = xk ＋ αk（sk ＋ ωk）, where the main direction sk is obtained by DY conjugate gradient method, ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.     

Construction and comparisons of simultaneous confidence intervals for the mean difference of multivariate normal distributions

<正> In this paper,Scheffé and Simplified Scheffé simultaneous confidence intervals are firstconstructed for mean difference of several multivariate normal distributions.Then the authors theoreticallyprove that when there are only two populations,Bonferroni bounds and Simplified Scheffébounds are the same and they are shorter than Scheffé bounds for p10.In the case for 3k10and 2p10,there exists n(p,k)such that Bonferroni method is better than Simplified Schefféprocedure for nn(p,k),otherwise Simplified Scheffé procedure is better.Finally,the authors findout that neither of Scheffé critical values nor Simplified Scheffé critical values are always larger thananother through numerical calculation.     

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）.     

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.     

Random evolving networks under the diameter and average connectivity constraint

In this paper, under the constraint that the average distance and the average degree （k） remain approximately constant, we studied a random scale-free network model. We found that, if the network maintains the form of its degree distribution and the maximal degree kc is N-dependent cutoff function kc（N）〈 N, the degree distribution would be approximately power-law with an exponent between 2 and 3. The distribution exponent has little relationship with the average degree, denoted by （k）. The diameter constraint can be interpreted as an environmental selection pressure, which could explain the scale-free nature of networks. The numerical results indicate that, under the diameter constraint, the preferential attachment can produce the cutoff function kc（N）〈 N and power-law degree distribution.     

Towards a theory of game-based non-equilibrium control systems

This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games.To be precise,the authors consider the infinitely repeated games between a human and a machine based on the generic 2×2 game with fixed machine strategy of finite k-step memory.By introducing and analyzing the state transfer graphes(STG),it will be shown that the system state will become periodic after finite steps under the optimal strategy that maximizes the human’s averaged payoff,which helps us to ease the task of finding the optimal strategy considerably. Moreover,the question whether the optimizer will win or lose is investigated and some interesting phenomena are found,e.g.,for the standard Prisoner’s Dilemma game,the human will not lose to the machine while optimizing her own averaged payoff when k = 1;however,when k≥2,she may indeed lose if she focuses on optimizing her own payoff only The robustness of the optimal strategy and identification problem are also considered.It appears that both the framework and the results are beyond those in the classical control theory and the traditional game theory.     

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.     

Inverse Center Location Problem on a Tree

This paper discusses the inverse center location problem restricted on a tree with different costs and bound constraints. The authors first show that the problem can be formulated as a series of combinatorial linear programs, then an O（｜V｜^2 log ｜V｜） time algorithm to solve the problem is presented. For the equal cost case, the authors further give an O（｜V｜） time algorithm.     

Induced Subgraph in Random Regular Graph

Let Gn,d be a random d-regular graph with n vertices, where d = o（n）. Given a fixed graph H, YH denotes the number of induced copies of H in Gn d In this paper, the authors determine the threshold of the event ＂YH 〉 0＂, and also obtain the induced subgraph counts inside the threshold interval.     

RELIABILITY OF LINEAR （n,f, k） SYSTEMS WITH WEIGHTED COMPONENTS

The (n, f, k): F(G) system consists of n components and the system fails (works) if and only if there are at least f failed (working) components or at least k consecutive failed (working) components. These system models can be used in electronic equipment, automatic payment systems in banks, and furnace systems. In this paper we introduce and study the (n, f, k):F and (n, f, k): G systems consisting of weighted components. Recursive equations are presented for reliability evaluation of these new models. We also provide some conditions on the weights to represent weighted-(n, f, k) systems as usual (n, f, k) systems.     

PHASE TRANSITION IN SEQUENCE UNIQUE RECONSTRUCTION

In this paper, sequence unique reconstruction refers to the property that a sequence is uniquely reconstructable from all its K-tuples. We propose and study the phase transition behavior of the probability P（K） of unique reconstruction with regard to tuple size K in random sequences （iid model）. Based on Monte Carlo experiments, artificial proteins generated from lid model exhibit a phase transition when P（K） abruptly jumps from a low value phase （e.g. 〈 0.1） to a high value phase （e.g. 〉 0.9）. With a generalization to any alphabet, we prove that for a random sequence of length L, as L is large enough, P（K） undergoes a sharp phase transition when p ≤ 0.1015 where p = P （two random letters match）. Besides, formulas are derived to estimate the transition points, which may be of practical use in sequencing DNA by hybridization. Concluded from our study, most proteins do not deviate greatly from random sequences in the sense of sequence unique reconstruction, while there are some ＂stubborn＂ proteins which only become uniquely reconstructable at a very large K and probably have biological implications.     

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).     

The conditional diagnosability of shuffle-cubes

<正> In the application of multiple-processor systems some processors or links in a system maynot function properly,thus the fault diagnosis is one of the most important issues in the analysisand maintenance of those systems.For the practical fault diagnosis systems,the probability that allneighboring processors of a processor are faulty simultaneously is very small.Thus,the conditionaldiagnosability,which is a new metric for evaluating such systems,assumes that every fault set doesnot contain all neighbors of any processor in the system.In this paper,the authors show that then-dimensional shuffle-cube has the conditional diagnosability of 4n-15 for n = 2 (mod 4) and n ≥ 10.     

Complete monotonicity of the probability of ruin and de Finetti’s dividend problem

This paper studies the complete monotonicity of the probability of ruinψin the the classical risk model and the classical risk model that is perturbed by a diffusion.As a byproduct,the authors give an alternative proof to a result on the optimal dividend problem due to LoefFen(2008).     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

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.     

Random continuous model of scale-free networks

There are a lot of continuous evolving networks in real world, such as Internet, www network, etc. The evolving operation of these networks are not an equating interval of time by chance. In this paper, the author proposes a new mathematical model for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution of which counting process determines the operating number, and has proved that this system self-organizes into scale-free structures with scaling exponent γ = 3+ α/m.     

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.