Parallel machine covering with limited number of preemptions简

In this paper,we investigate the i-preemptive scheduling on parallel machines to maximize the minimum machine completion time,i.e.,machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case,we show the worst case ratio is 2m.i.1 m,and we present a polynomial time algorithm which can guarantee the ratio for any 0 ≤ i ≤ m. 1. For the i-preemptive scheduling on two uniform machines case,we only need to consider the cases of i = 0 and i = 1. For both cases,we present two linear time algorithms and obtain the worst case ratios with respect to s,i.e.,the ratio of the speeds of two machines.     

Asymptotic properties of plug-in level set estimators for right censored data

We assume T1,...,Tn are i.i.d.data sampled from distribution function F with density function f and C1,...,Cn are i.i.d.data sampled from distribution function G.Observed data consists of pairs(Xi,δi),i=1,...,n,where Xi=min{Ti,Ci},δi=I(Ti Ci),I(A)denotes the indicator function of the set A.Based on the right censored data{Xi,δi},i=1,...,n,we consider the problem of estimating the level set{f c}of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators.Under some regularity conditions,we establish the asymptotic normality and the exact convergence rate of theλg-measure of the symmetric difference between the level set{f c}and its plug-in estimator{fn c},where f is the density function of F,and fn is a kernel-type density estimator of f.Simulation studies demonstrate that the proposed method is feasible.Illustration with a real data example is also provided.     

用拉普拉斯谱半径定序给定阶和匹配数的树

Let T（n,i） be the set of all trees with order n and matching number i.We determine the third to sixth trees in T（2i ＋ 1,i） and the third to fifth trees in T（n,i） for n ≥ 2i ＋ 2 with the largest Laplacian spectral radius.     

I.I.D. STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF－SIMILAR SETS

I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.     

TRIPLE INTERACTIONS OF CONORMAL WAVES FOR HIGHER ORDER SEMILINEAR HYPERBOLIC EQUATIONS

The interaction of three conormal waves for send-linear strictly hyperbolic equations of third oeder is considered. Let ∑i:i = 1,2,3, be smooth characteristic surfaces for P = Di(D^2i-△) intersecting transversally at the origin. Suppose that the solution u to Pu = f(t, x, y, D^αu), |α| ≤2 is conormal to ∑i:i = 1, 2, 3, for t < 0. The author uses Bony‘s second microlocalization techniques and commutator arguments to conclude that the new singularities a short time after the triple interaction lie on the surface of the light cone Γ over the origin plus the surfaces obtainedby flow-outs of the lines of intersection Γ （交集） ∑i and ∑i（交集） ∑j，i, j = 1, 2, 3.     

半参数变系数异方差部分线性模型下的经验似然

Consider the semiparametric varying-coefficient heteroscedastic partially linear model Y i = Xτiβ + Zτiα(Ti) + σiei,1 ≤ i ≤ n,where σ 2 i = f(Ui),β is a p × 1 column vector of unknown parameter,(Xi,Zi,Ti,Ui) are random design points,Y i are the response variables,α(·) is a q-dimensional vector of unknown functions,e i are random errors.For both cases that f(·) is known and unknown,we propose the empirical log-likelihood ratio statistics for the parameter β.For each case,a nonparametric version of Wilks’ theorem is derived.The results are then used to construct confidence regions of the parameter.Simulation studies are carried out to assess the performance of the empirical likelihood method.     

THE CHUNG-SMIRNOV LAW FOR THE PRODUCT-LIMIT ESTIMATOR UNDER RANDOM CENSORSHIP

The maximal deviation of the product limit estimator on the whole line isinvestigated.The analogue of Chung-Smirnov law of iterated logarithm is proved undervery mild conditions on censoring.An improved oonvergenoe rate is found and shown tobe best possible The result is proved by an i.i.d.representation scheme of the productlimit estimator on the whole line.Improved rates of convergence for the i.i.d.representation on compact set are also derived.     

Generalized profile LSE in varying-coefficient partially linear models with measurement errors

This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ+Zτiα(Ui)+εi , Wi=Xi+ξi,i=1, ··· , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.     

RENEWAL THEOREM FOR （L, 1）-RANDOM WALK IN RANDOM ENVIRONMENT

We consider a random walk on Z in random environment with possible jumps {-L,…, -1, 1}, in the case that the environment {ωi ： i ∈ Z} are i.i.d.. We establish the renewal theorem for the Markov chain of ＂the environment viewed from the particle＂ in both annealed probability and quenched probability, which generalize partially the results of Kesten （1977） and Lalley （1986） for the nearest random walk in random environment on Z, respectively. Our method is based on （L, 1）-RWRE formulated in Hong and Wang the intrinsic branching structure within the （2013）.     

Convergence rates in the law of logarithm of random elements

1. IntroductionLet {Xu, n 2 1} be a sequence of r.v.IS in the same probability space and put Sa =nZ Xi, n 2 1; L(x) = mad (1, logx).i=1Since the definition of complete convergence is illtroduced by Hsu and Robbins[6], therehave been many authors who devote themselves to the study of the complete convergence forsums of i.i.d. real-valued r.v.'s, and obtain a series of elegys results, see [3,7]. Meanwhile,the convergence rates in the law of logarithm of i.i.d. real-vained r.v.'s have also be…     

Fluid approximation and its convergence Rate for GI/G/1 queue with vacations

A GI/G/1 queue with vacations is considered in this paper.We develop an approximating technique on max function of independent and identically distributed(i.i.d.) random variables,that is max{ηi,1 ≤ i ≤ n}.The approximating technique is used to obtain the fluid approximation for the queue length,workload and busy time processes.Furthermore,under uniform topology,if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate,we prove by the...     

Parameter Dependence of Stable Manifolds for Nonuniform (μ, ν)-dichotomies

We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x'= A(t)x + f(t, x, λ), t≠τi and x(τ+i) = Bix(τi) + gi(x(τi), λ), i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x'= A(t)x, t≠τi and x(τ+i) = Bix(τi), i ∈ N admits a nonuniform (μ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.     

Conditions for dominated splittings

In this paper, we solve the problem proposed by Lan Wen for the case of dimM = 3. Roughly speaking, we prove that for fixed i, f has C1 persistently no small angles of index i if and only if f has a dominated splitting of index i on the C1 i-preperiodic set P＊i（f）.     

A Problem of Testing Homogeneity Against Order Constraints on Risk Differences

Consider I pairs of independent binomial variates x0i and x1i with corresponding parameters P0i and p1i and sample sizes n0i and n1i for i=1, …,I. Let △i = P1i-P0i be the difference of the two binomial parameters, where △i's are to be of interest and P0i's are nuisance parameters. The null hypothesis of homogeneity on the risk difference can be written as     

CALCULATION OF HAMILTONIAN CONSTRAINT AND MANDELSTAM IDENTITIES OVER EXTENDED KNOT FAMILIES{φi}2^2,{φi}3^4 and {φi}4^6

The actions of the Hamiltonian constraint onto the members of the extended knot families {φi}2^2, {φi}3^4 and {φi}4^6
, and the check of their invariance under the Mandelstam identities are given in the extended loop representation of loop quantum gravity.     

STRONG UNIFORM CONSISTENCY FOR DENSITY ESTIMATOR FROM RANDOMLY CENSORED DATA

Let X_1,…,X_n be a sequence of independent identically distributed random variableswith distribution function F and density function f.The X_are censored on the right byY_i,where the Y_i are i.i.d.r.v.s with distribution function G and also independent of theX_i.One only observesLet S=1-F be survival function and S be the Kaplan-Meier estimator,i.e.,where Z_are the order statistics of Z_i and δ_((i))are the corresponping censoring indicatorfunctions.Define the density estimator of X_i by where =1-and h_n(>0)↓0.     

Dimension splitting method for the three dimensional rotating Navier-Stokes equations

In this paper, we propose a dimensional splitting method for the three dimensional (3D) rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of surfaces ■i into several sub-domains, which are called the layers of the flow. Every interface i between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate (S-coordinate) system based on ■i , Navier-Stoke equations in this coordinate can be expressed as the sum of two operators, of which one is called the membrane operator defined on the tangent space on ■i , another one is called the bending operator taking value in the normal space on ■i . Then the derivatives of velocity with respect to the normal direction of the surface are approximated by the Euler central difference, and an approximate form of Navier-Stokes equations on the surface ■i is obtained, which is called the two-dimensional three-component (2D-3C) Navier-Stokes equations on a two dimensional manifold. Solving these equations by alternate iteration, an approximate solution to the original 3D Navier-Stokes equations is obtained. In addition, the proof of the existence of solutions to 2D-3C Navier-Stokes equations is provided, and some approximate methods for solving 2D-3C Navier-Stokes equations are presented.     

The Moment Convergence Rates for Largest Eigenvalues of β Ensembles

The paper focuses on the largest eigenvalues of the β-Hermite ensemble and the β-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated by the complete convergence for partial sums of i.i.d. random variables, and the proofs depend on the small deviations for largest eigenvalues of the β ensembles and tail inequalities of the general β Tracy-Widom law.     

Enumerating rooted simple planar maps

The main purpose of this paper is to find the number of combinatorially distinct rooted simpleplanar maps,i.e.,maps having no loops and no multi-edges,with the edge number given.We haveobtained the following results.1.The number of rooted boundary loopless planar [m,2]-maps.i.e.,maps in which there areno loops on the boundaries of the outer faces,and the edge number is m,the number of edges on theouter face boundaries is 2,is(?)for m≥1.G_0~N=0.2.The number of rooted loopless planar [m,2]-maps is(?)3.The number of rooted simple planar maps with m edges H_m~s satisfies the following recursiveformula:(?)where H_m~(NL) is the number of rooted loopless planar maps with m edges given in [2].4.In addition,γ(i,m),i≥1,are determined by(?)for m≥i.γ(i,j)=0,when i>j.     

DNA labelled graphs with DNA computing

Let k≥2, 1≤i≤k andα≥1 be three integers. For any multiset which consists of some k-long oligonucleotides, a DNA labelled graph is defined as follows: each oligonucleotide from the multiset becomes a point; two points are connected by an arc from the first point to the second one if the i rightmost uucleotides of the first point overlap with the i leftmost nucleotides of the second one. We say that a directed graph D can be(k, i;α)-labelled if it is possible to assign a label(l_1(x),..., l_k(x))to each point x of D such that l_j(x)∈{0,...,a-1}for any j∈{1,...,k}and(x,y)∈E(D)if and only if(l_k-i 1(x),..., l_k(x))=(l_1(y),..., l_i(y)). By the biological background, a directed graph is a DNA labelled graph if there exist two integers k, i such that it is(k, i; 4)-labelled. In this paper, a detailed discussion of DNA labelled graphs is given. Firstly, we study the relationship between DNA labelled graphs and some existing directed graph classes. Secondly, it is shown that for any DNA labelled graph, there exists a positive integer i such that it is(2i, i; 4)-labelled. Furthermore, the smallest i is determined, and a polynomial-time algorithm is introduced to give a(2i, i; 4)-labelling for a given DNA labelled graph. Finally, a DNA algorithm is given to find all paths from one given point to another in a(2i, i; 4)-labelled directed graph.