An application of Ritt-Wu’s zero decomposition algorithm to the pseudo null Bertrand type curves in Minkowski 3-space

The Bertrand curves were first studied using a computer by Wu (1987). The same problem was studied using an improved version of Ritt-Wu’s decomposition algorithm by Chou and Gao (1993). This paper investigates the same problem for pseudo null Bertrand curves in Minkowski 3-space $ \mathbb{E}_1^3 $ \mathbb{E}_1^3 .     

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.     

Relation between wiener numbers of quasi-hexagonal chains and quasi-polyomino chains

<正> Let Q_n and B_n denote a quasi-polyomino chain with n squares and a quasi-hexagonalchain with n hexagons,respectively.In this paper,the authors establish a relation between the Wienernumbers of Q_n and B_n:W(Q_n)=1/4[W(B_n)-8/3n~3+(14)/3n+3].And the extremal quasi-polyominochains with respect to the Wiener number are determined.Furthermore,several classes of polyominochains with large Wiener numbers are ordered.     

Large sample and robust properties of $$ \tilde L^2 $$-median

As a competitive depth, $ \tilde L^2 $ \tilde L^2 -depth is modified from L ²-depth. Its induced median is called $ \tilde L^2 $ \tilde L^2 -median. Basic properties of the median and its sample version are provided. Especially, the strong consistency of sample median is gained under weaker condition. Robustness of the median and its sample version is discussed. Besides ease of computation, it is shown that $ \tilde L^2 $ \tilde L^2 -median has both good large-sample and robust properties. Simulation studies are also given to compare the breakdown point of $ \tilde L^2 $ \tilde L^2 -median with that of other depth-induced medians.     

Asymptotic Normality of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Fixed Design*

In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n Xi（yi -μ（Xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nXiXi′, Xi are bounded p × q regressors, and yi are q × 1 responses.     

Good p-ary quasic-cyclic codes from cyclic codes over $$\mathbb{F}_ p + v\mathbb{F}_ p$$

This paper introduces a Gray map from（F_p + uF_p）ⁿ to F_p²ⁿ,and describes the relationship between codes over F_p + vF_p and their Gray images.The authors prove that every cyclic code of arbitrary length n over F_p + vF_p is principal,and determine its generator polynomial as well as the number of cyclic codes.Moreover,the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.     

A MacWilliams type identity on Lee weight for linear codes over \mathbb{F}_2 + u\mathbb{F}_2^*

In this paper,the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F₂ + uF₂ is determined.As an application of this identity,the authors obtain a MacWilliams type identity on Lee weight for linear codes over F_2^m+ uF_2^m.Furthermore,the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.     

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.     

A general iterative method of fixed points for equilibrium problems and optimization problems

The purpose of this paper is to present a general iterative scheme as below:

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.     

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.     

CLT of wavelet estimator in semiparametric model with correlated errors

This paper considers the semiparametric regression model j/j= Xif3+g（U）+Vi（1 < i < n）, where（x_i,t_i） are known design points,/3 is an unknown slope parameter,g（·） is an unknown function, the correlated errors Vi=∑_j=-∞^∞c_je_i-jwith∑_j=-∞^∞|c_j|<∞,and e_i negatively associated random variables.Under appropriate conditions,the authors study the asymptotic normality for wavelet estimators ofβand g（·）.A simulation study is undertaken to investigate finite sample behavior of the estimators.     

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.     

SEMI ON-LINE SCHEDULING PROBLEM FOR MAXIMIZING THE MINIMUM MACHINE COMPLETION TIME ON TWO UNIFORM MACHINES

Ia this paper, we consider a semi on-line version on two uniform machines Mi, i = 1, 2, where the processing time of the largest job is known in advance. A speed si（s1 = 1, 1 ≤s2 = s） is associated with machine Mi. Our goal is to maximize the Cmin. We give a Cmin 2 algorithm and prove its competitive ratio is at most 2s＋1/s＋1 We also claim the Cmin 2 algorithm is tight and the gap between the competitive ratio of Cmin2 algorithm and the optimal value is not greater than 0.555. It is obvious that our result coincides with that given by He for s =1.     

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.     

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.     

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 THE MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.     

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.     

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.