离散随机变量序列完备及非完备样本最大值的联合分布

设离散随机变量三角阵列{X_(n,k),K≤n,n≥1}存在数据缺失,对给定的n,M_n=max{X_(n,k),K≤n}为第n行的最大值,(~(M)_n)为该行观测到的随机变量的最大值,研究了离散型随机变量的分布函数某一参数变动时(~(M)_n),M_n)的联合渐近分布.

Abstract：

For triangular array discrete random variables {X_(n,k), k ≤ n,n ≥1},there may exist data missing observation. Denote M_n=max{X_(n,k),k ≤ n}the partial maximum and (~(M)_n) is the maximum of the observed random variables in the nth row.In this paper,the asymptotic joint distributions of (~(M)_n),M_n) of some discrete random variables are obtained as their parameters vary along with sample size.     

关于反向Hardy-Hilbert积分不等式的推广

通过引入参数及估算权函数,建立了反向Hardy-Hilbert积分不等式的推广式,证明了:若p＜0,1/p+1/q=1,2-q＜λ＜2-p,α≥-β,f(t),g(t)≥0,且0＜∫∞α(t+β)1-λfp(t)dt＜∞ 0＜∫∞α(t+β)1-λgq(t)dt＜∞则∫∞α∫∞αf(x)g(y)/(x+y+2β)λdxdy＞{∫∞α[kκ(p)-θλ(q)(α+β/t+β)q+λ-2/q](t+β)1-λfp(t)dt}1/p{∫∞α[kλ(p)-p/p+λ-2(α+β/t-β)p+λ-2/p](t+β)1-λgq(t)dt}1/q其中θλ(q)=∫011/(1+u)λuq+λ-2/q-1du,且常数因子kλ(p)=B(p+λ-2/p,q+λ-2/q)为最佳值.     

一类带有非线性边界条件和Hardy项的凸凹非线性问题

通过对偶喷泉定理,证明了当参数λ很小且1< q< 2 < p ≤ 2*=2N/N-2,0 ≤μ≤μ*时,方程-△u+u-μu/｜χ｜2=｜u｜p-2 u∈Ω、{0}δu/δv=λ｜u｜q-2u u∈δΩ有无穷多个解.     

一类非局部近共振问题多重解的存在性

通过变分方法在光滑有界域Ω上研究由常数a,b0,参数λ0及连续函数f(x,u)共同决定的非局部问题:{-(a-b integral from Ω|▽u|~2dx)Δu+bλu~3=f(x,u)x∈Ω u=0 x∈Ω利用Ekeland变分原理和山路引理得到该问题近共振情形多重解的存在性.     

顺序统计量的几乎处处中心极限定理

{Xn, n≥1}是独立同分布随机变量序列, M(1)n, M(2)n分别表示{X1, X2, …, Xn}的第一个最大值与第二个最大值. 若存在 an＞0, bn 使得 P(Mn(1)≤anx+bn)w/→G(x) 成立(其中 G(x)为极值指数分布), 则对 x＞y 有limN→∞1/log N∑Nn=11/nI{M(1)n≤un, M(2)n≤vn}=G(y){log G(x)-log G(y)+1} a.s.其中un=anx+bn, vn=any+bn.     

p-Lapacian方程关于Fuík谱共振问题解的存在性

当(a,b)∈{λ_1}×[λ_1,+∞)或(a,b)∈[λ_1,+∞)×{λ_1}时,在f至多线性增长的情况下,运用环绕定理证明了p-Laplacian方程{-Δ_pu=au_+~(p-1)-bu_-~(p-1)+f(x,u)-h(x)x∈Ωu=0 x∈Ω至少存在1个弱解.     

脉冲泛函微分方程三个正周期解的存在性

用锥不动点定理,建立了形如的{y'(t)=-a(t)y(t)+g(t,y(t-τ(t)))t3tj y(tj+)=y(tj-)+Ij(y(tj))t∈z脉冲泛函微分方程3个正周期解存在的充分条件,其中,α∈ C(R,R+),τ∈ C(R,R),g∈ C(R×[0,∞),[0,∞)),α,τ,g是ω-周期函数.

Abstract：

By using a fixed point theorem in cones,some sufficient conditions are established for the existence of three positive periodic solutions for a kind of nonautonomous functional differential equations with impulses and delays of the form {y'(t)=-a(t)y(t)+g(t,y(t-τ(t)))t3tj y(tj+)=y(tj-)+Ij(y(tj))t∈z where α∈ C(R,R+),τ∈ C(R,R),g∈ C(R×[0,∞),[0,∞)),and α,τ,gareω-periodic functions,and ω> 0 is a constant.     

顺序统计量的几乎处处中心极限定理

{Xn,n≥1}是独立同分布随机变量序列, Mn^（1） , Mn^（2）分别表示{X1 , X2, …, Xn }的第一个最大值与第二个最大值．若存在an〉0,bn使得P（Mn^（1）≤anx＋bn）→wG（x）成立（其中G（x）为极值指数分布）,则对x〉y有lim N→∞1/logN∑Nn=1 1/nI{Mn^（1）≤Mn^（2）≤vn}=G（y）{logG（x）-log G（y）＋1}a.s,其中un=anx＋bn,vn=any＋bn.     

完全二部图K4,n的点强可区别全染色

设G=(V,E)是简单图,f是从VUE到{1,2,…,k}的一个映射,其中k是正整数.对任意x∈V,令C(x)={f(x)}U{f(y)| y∈V,y和x相邻}U{f(e)| e∈E,e和x相关联},称之为x在f下的色集合.若:(i)对任意u v∈E,f(u)≠f(v),有f(u)≠f(uv),f(v)≠f(uv);(ii)对任意uv,uw∈E,7v≠w,有f(uv)≠f(uw);(iii)对任意u,v∈V,u≠v,有C(u)≠C(v),则称f是图G的一个使用了k种颜色的点强可区别全染色,简记为k-VSDTC.称xvst(G)=min{k|G存在肛VSDTC}为G的点强可区别全色数.得到了完全二部图K4.n(n＞4)的点强可区别全色数.     

p-Lapacian方程关于Fuík谱共振问题解的存在性简

当（a,b）∈{λ1}×[λ1,+∞)或（a,b）∈[λ1,+∞)×{λ1}时,在f至多线性增长的情况下,运用环绕定理证明了p-Laplacian方程{-Δpu=au+p-1-bu-p-1+f（x,u）-h（x）x∈Ωu=0 x∈Ω至少存在1个弱解.     

Transformation of a star into a planet in a millisecond pulsar binary

Millisecond pulsars are thought to be neutron stars that have been spun-up by accretion of matter from a binary companion. Although most are in binary systems, some 30% are solitary, and their origin is therefore mysterious. PSR J1719-1438, a 5.7-millisecond pulsar, was detected in a recent survey with the Parkes 64-meter radio telescope. We show that this pulsar is in a binary system with an orbital period of 2.2 hours. The mass of its companion is near that of Jupiter, but its minimum density of 23 grams per cubic centimeter suggests that it may be an ultralow-mass carbon white dwarf. This system may thus have once been an ultracompact low-mass x-ray binary, where the companion narrowly avoided complete destruction.     

Action at a distance along a DNA

A number of ways are known by which an event at one location on a DNA molecule can affect an event at a distant location on the same molecule. Three classes of mechanisms are described for such distal actions: tracking or translocation of a protein along a DNA, the association of two proteins bound at separate sites to form a DNA loop in between, and distal interactions that are affected by the topology of the DNA. The basic characteristics of each type of mechanism are discussed in terms of the known physicochemical properties of DNA. The various modes of action at a distance are often interrelated. Examples include the formation of positively and negatively supercoiled DNA loops by tracking and the strong effects of DNA topology on looping.     

Development of a receptor on a foreign nerve fiber in a Pacinian corpuscle

When the sensory fiber of a Pacinian corpuscle (in cat mesentery) is transected (at the inferior mesenteric nerve) transduction fails within 30 hours: the nerve ending produces no generator potentials in response to mechanical stimulation. Electrically elicited nerve impulse conduction continues for at least another 18 hours. A transducer mechanism develops on a regenerating nerve fiber when this fiber enters the denervated corpuscle. Such transducer development takes place on myelinated fibers from the inferior mesenteric nerve, which normally supplies corpuscles, as well as on myelinated hypogastric nerve fibers, which normally do not go to corpuscles, including fibers larger than the original corpuscle afferents.     

Conversion of a peroxiredoxin into a disulfide reductase by a triplet repeat expansion

Pathways for the reduction of protein disulfide bonds are found in all organisms and are required for the reductive recycling of certain enzymes including the essential protein ribonucleotide reductase. An Escherichia coli strain that lacks both thioredoxin reductase and glutathione reductase grows extremely poorly. Here, we show that a mutation occurring at high frequencies in the gene ahpC, encoding a peroxiredoxin, restores normal growth to this strain. This mutation is the result of a reversible expansion of a triplet nucleotide repeat sequence, leading to the addition of one amino acid that converts the AhpC protein from a peroxidase to a disulfide reductase. The ready mutational interconversion between the two activities could provide an evolutionary advantage to E. coli.     

离散型三维竞争系统中某群体竞争获胜的条件

研究了离散型三维竞争系统的模型结构与稳定性,得到了这类竞争系统中各类平衡点的坐标及其性质,获得了系统在某些边界上的平衡点渐近稳定的充分条件和不稳定的充分条件,并由此得到了系统中的某群体在竞争过程中竞争获胜淘汰所有对手的条件和参与竞争的各个群体永不和谐的充分条件.