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.     

The projective plane crossing numbers of circular graphs*

The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, respectively.     

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.     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS II： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.     

Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method

This paper considers the Geom / G / 1 queueing model with feedback according to a late arrival system with delayed access (LASDA). Using recursive method, this paper studies the transient property of the queue size from the initial state N(0⁺) = i. Some new results about the recursive expression of the transient queue size distribution at any epoch n ⁺ and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch n ⁻, and n are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered (being different from the relations given in M / G / 1 queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer network. This research is supported by the National Natural Science Foundation of China under Grant No. 70871084, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001, and the Scientific Research Fund of Southwestern University of Finance and Economics.     

THE M/M/c QUEUE WITH （e,d） SETUP TIME

The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.     

Improved Algorithm for Minimum Data Aggregation Time Problem in Wireless Sensor Networks

Wireless sensor networks promise a new paradigm for gathering data via collaboration among sensors spreading over a large geometrical region. Many applications impose delay requirements for data gathering and ask for time-efficient schedules for aggregating sensed data and sending to the data sink. In this paper, the authors study the minimum data aggregation time problem under collision-free transmission model. In each time round, data sent by a sensor reaches all sensors within its transmission range, but a sensor can receive data only when it is the only data that reaches the sensor. The goal is to find the method that schedules data transmission and aggregation at sensors so that the time for all requested data to be sent to the data sink is minimal. The authors propose a 7△/log2｜s｜＋c, new approximation algorithm for this NP-hard problem with guaranteed performance ratio which significantly reduces the current best ratio of △- 1, where S is the set of sensors containing source data, A is the maximal number of sensors within the transmission range of any sensor, and e is a constant. The authors also conduct extensive simulation, the obtained results justify the improvement of proposed algorithm over the existing one.     

Testing serial correlation in semiparametric varying coefficient partially linear errors-in-variables model

The authors propose a V _{N, p} test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed V _{N, p} test statistic. Simulation results confirm that the proposed test performs satisfactorily in estimated size and power. This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003; the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609; the Doctor's Start-up Research Fund under Grant No. 08-52204; and the Youth Science Research Fund of Chongqing Technology and Business University under Grant No. 0852008.     

THE HAMMING DISTANCES OF NEGACYCLIC CODES OF LENGTH 2^s OVER GR （2^α, m）

The Hamming distances of all negacyclic codes of length 28 over the Gaiois ring GR （2^α, m） are given. In particular, the Lee distances of all negacyclic codes over Z4 of length 2^s are obtained. The Gray images of such negacyclic codes over Z4 are also determined under the Gray map.     

ON THE CONVERGENCE OF A NEW HYBRID PROJECTION ALGORITHM

For unconstrained optimization, a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f（x） is uniformly continuous. If Δ↓f（x） is continuously differentiable pseudo-convex, the whole sequence of iterates converges to a solution of the problem without any other assumptions. Furthermore, under appropriate conditions one shows that the sequence of iterates has a cluster-point if and only if Ω＊ ≠ θ. Numerical examples are given at the end of this paper.     

ON APPROXIMATION BY REPRODUCING KERNEL SPACES IN WEIGHTED L^p SPACES

In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.     

A single server retrial queue with general retrial times and two-phase service

An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first “essential” service, whereas only some of them demand the second “optional” service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest. This research is supported by the National Natural Science Foundation of China under Grant No. 10871020.     

A modified likelihood ratio test for homogeneity in bivariate normal mixtures of two samples

This paper investigates the asymptotic properties of a modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models of two samples. The asymptotic null distribution of the modified likelihood ratio statistic is found to be χ₂², where χ₂² is a chi-squared distribution with 2 degrees of freedom. This research was supported by the National Natural Science Foundation of China under Grant No. 10661003, SRF for ROCS, SEM under Grant No. [2004]527, and the Natural Science Foundation of Guangxi under Grant No. 0728092.     

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.     

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.     

A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING*

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.     

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.     

Minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm

This paper shows that the problem of minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1 linear fractional optimization problem in polynomial time. Consequently, parametrization techniques, e.g., Dinkelbach’s algorithm, can be applied by solving a classical set covering problem in each iteration. Similar reduction can also be performed on the sup-T equation constrained optimization problems with an objective function being monotone in each variable separately. This method could be extended as well to the case in which the triangular norm is non-Archimedean. The work is supported by the National Science Foundation of the United States under Grant No. #DMI-0553310.