Empirical likelihood confidence intervals for the differences of quantiles with missing data

Suppose that there are two nonparametric populations x and y with missing data on both of them. We are interested in constructing confidence intervals on the quantile differences of x and y. Random imputation is used. Empirical likelihood confidence intervals on the differences are constructed. Supported by the National Natural Science Foundation of China (No. 10661003) and Natural Science Foundation of Guangxi (No. 0728092).     

LIMIT CYCLES AND CENTER-FOCUS OF NONLINEAR SYSTEMS

The authors consider the nonhnear systems x=h(y)-F(x),y=-g(x) in which g(x) may be not differentiabte and the system can be nonsymmetric. Some conditions which en-sure that there exists an infinite number of limit cycles are obtained. A problem about center-focus put forward by R. Conti has been answered.     

A NEW PROPERTY OF BINARY UNDIRECTED de BRUIJN GRAPHS

1.IntroductionThen-dimensionalbinarydirecteddeBruijngraph,denotedbyB(n),hasthevertex-set{xlxz'xu:xiE{0,1}}.TherearetwoarcsfromavertexxlxZ'xutothevenicesxzxa'x.-lx.0andxZx3'x.-l-c.1.Then-dimensionalbinaryundirecteddeBruijngraph,denotedbyUB(n),isobtainedfromB(n)bydeletingtheorientationofthearcsandthenomittingmultipleedgesandloops.ItiswellknownthatUB(n)hasdiameternandconnectivitytwo.ThedeBruijngraphshavebeenwidelyusedincodingtheory[6].Theyhavebeenalsoproposedasapossiblegoodcomputeri…     

Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection

A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given.     

ON THE EXPONENT SET OF PRIMITIVELOCALLY SEMICOMPLETE DIGRAPHS

A locally semicomplete digraph is a digraph D=(V,A) satisfying the following condi-tion for every vertex x∈V the D[O(x)] and D[I(x)] are semicomplete digraphs. In this paper,we get some properties of cycles and determine the exponent set of primitive locally semicompleted digraphs.     

LINEARIZED OSCILLATIONS OF DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS

The necessary and sufficient conditions for the oscillations of every solution of the nonlinear delay equation x(t) f(x(t l)) g(x([t-k]))=0 are oblained.     

分数填补下两总体分位数差异的经验似然置信区间

设有两个非参数总体,其样本数据不完全,用分数填补法补足缺失数据,得到两总体的"完全"样本数据,在此基础上构造两总体分位数差异的经验似然置信区间.模拟结果显示,分数填补法可以得到更加精确的置信区间.     

A Conjecture Concerning the Pure Exponential Diophantine Equation a^x ＋ b^y = c^z

Let a, b, c, r be fixed positive integers such that a^2 ＋ b^2 = c^r, min（a, b, c, r） 〉 1 and 2 r. In this paper we prove that if a ≡ 2 （mod 4）, b ≡ 3 （mod 4）, c 〉 3.10^37 and r 〉 7200, then the equation a^x ＋ b^y = c^z only has the solution （x, y, z） = （2, 2, r）.     

一个耦合系统自由边界问题的整体古典解

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｄｉｓｃｕｓｓｔｈｅｇｌｏｂａｌｃｌａｓｓｉｃａｌｓｏｌｕｔｉｏｎｏｆａｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｑｕａｓｉｓｔａｔｉｏｎａｒｙｐｒｏｂｌｅｍ .Ｔｈｅｐｒｏｂｌｅｍｃｏｍｅｓｆｒｏｍｔｈｅｄｉｓｃｕｓｓｉｏｎｏｆａｇｒｏｗｔｈｍｏｄｅｌｏｆｓｅｌｆｍａｉｎｔａｉｎｉｎｇｐｒｏｔｏｃｅｌｌ(ｓｅｅ [1— 3])ｉｎｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｃａｓｅ .Ｔｈｅｐｒｏｔｏｃｅｌｌｃａｎｂｅｖｉｓｕａｌｉｚｅｄａｓｈａｖｉｎｇａｐｏｒｏｕｓｓｔ…     

Confidence intervals for quantile estimation using Jackknife techniques

We consider the inference on quantiles, Q _y (β), with jackknife techniques, in finite populations of a variable, Y, using the quantile information on an auxiliary variable, X. Jackknife techniques are applied to estimate quantiles and the behaviour of these estimators is analyzed. Their properties are studied for simple random sampling. We also examine the confidence intervals obtained with jackknife variances.     

On the Diophantine System a^2 ＋ b^2 = c^3 and a^x ＋ b^y = c^z for b is an Odd Prime

Let a, b and c be fixed coprime positive integers. In this paper we prove that if a^2 ＋ b^2 = c^3 and b is an odd prime, then the equation a^x ＋ b^y = c^z has only the positive integer solution （x, y, z） = （2,2,3）.     

SOLVING SYMMETRIC MONOTONE LINEAR VARIATIONAL INEQUALITIES BY SOME MODIFIED LEVITIN-POLYAK PROJECTION METHODS

Some modified Levitin-Polyak projection methods are proposed in this paper for solving monotone linear variational inequality x∈Ω，（x′-x)^T(Hx c)≤0，for any x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality.     

An approximate expression related with RSA fixed points

Let T=T(n,e,a)be the number of fixed points of RSA(n,e)that are co-prime with n=pq,and A,B be sets of prime numbers in (1,x)and(1,y) respectively.An estimation on the mean-value M(A,B,e,a)=1/(#A)(#B)∑p∈A,q∈B,(p.q)=1 logT(pq,e,a)is given.     

Solutions and Multiple Solutions for p（x）-Laplacian Equations with Nonlinear Boundary Condition

The authors study the p（x）-Laplacian equations with nonlinear boundary condition. By using the variational method, under appropriate assumptions on the perturbation terms f1 （x, u）, f2（x, u） and h1（x）, h2（x）, such that the associated functional satisfies the ＂mountain pass lemma＂ and ＂fountain theorem＂ respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.     

分数填补下两总体分位数差异的半经验似然推断

在完全随机缺失机制情形,利用分数填补法填补缺失值,然后用经验似然方法构造两总体分位数差异的半经验似然比统计量,证明其渐近服从加权X~2分布并构造了相应的半经验似然置信区间.     

SOLUTIONS OF THE EQUATION x^m＋y^m=z^m IN SL2z

This paper solves an open problem of Vaserstein. The main result is: the equation x^m y^m=z^m has a solution in SL2z if and only if m is not divisible by 4 or 6 and m is not congruent to 3 modulo 6.     

Applications of an Explicit Formula for the Generalized Euler Numbers

The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.     

A Note on the Mean Value of Numbersof the Solutions of x^α≡ 1（modn）

Let T = T(p, q, α) be the number of solutions of the congruence x^α ≡ 1 (mod p^ηq^θ). Let A and B be sets of primes satisfying x₁ < p ≤ x₂ and y₁ < q ≤ y₂, respectively. A mean value estimation of is given. Supported by National Natural Science Foundation of China (No. 19971024) and Zhejiang Provincial Natural Science Foundation of China (No. 199047)     

On the Rankin-Selberg problem: higher power moments of the Riesz mean error term

LetΔ_1(x;φ) be the error term of the first Riesz mean of the Rankin-Selberg problem. We study the higher power moments ofΔ_1(x;φ) and derive an asymptotic formula for the 3-rd, 4-th and 5-th power moments by using Ivic's large value arguments and other techniques.     

Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval

Abstract This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value prob-lem for scalar viscous conservations laws u_t+f(u)_x=u_(xx) on[0,1],with the boundary condition u(0,t) =u_,u(1,t)=u_+ and the initial data u(x,0)=u_0(x,0)=u_0(x),where u_≠u_+ and f is a given function satisfyingf'(u)>0 for u under consideration.By means of energy estimates method and under some more regular condi-tions on the initial data,both the global existence and the asymptotic behavior are obtained.When u_u_+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shockwaves,which means that │u_-u_+│is small.Moreover,exponential decay rates are both given.