非自治二阶哈密顿系统周期解的存在性

利用临界点理论中的极大极小作用原理获得了非自治二阶哈密顿系统{ǔ=▽F(t,u(t),a.e.t∈[0,T] u(0)-u(T)=ú(0)ú(T)=0周期解的存在性结果.其中T>0,F:[0,T]× RM→R满足:对每个x∈RN,F(t,x)关于t是可测的;对几乎处处的t∈[0,T],F(t,x)关于x是连续可微的;存在a∈C(R+,R+)和b∈L1(0,T;R+)使得| F(t,x)|≤a(|x|)b(t)| ▽F(t,x)|≤a(|x|)b(t)对所有的x∈RN和几乎处处的t∈[0,T]都成立.

Abstract：

The existence of periodic solutions is obtained for nonautonomous second order Hamiltonian systems{ǔ=▽F(t,u(t),a.e.t∈[0,T] u(0)-u(T)=ú(0)ú(T)=0- where T ＞ 0,and F:[0,T]× RN →R satisfies assumption:which says that F(t,x)is measurable in t for every x ∈ RN and continuously differentiable in x for a.e.t ∈[0,T],and there exist a ∈C(R+,R+),b ∈L1(0,T;R+)such that｜ F(t,x)｜≤a(｜x｜)b(t)｜ ▽F(t,x)｜≤a(｜x｜)b(t)for all x ∈ RN and a.e.t ∈[0,T].The existence of solutions is proved by the minimax method in critical point theory.     

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.     

一类带有临界指数增长项的Kirchhoff型方程正的基态解的存在性

研究了一类带有临界指数增长项的Kirchhoff型方程{-(a+b∫Ω|▽u|2dx)Δu=f(x,u)+u5 x ∈Ωu=0x∈Ω其中a,b0,Ω是R3中的有界区域,f是次临界的且满足一定的条件.在较弱的条件下,利用山路定理获得了方程的正基态解.     

一类Kirchhoff型方程解的多重性

研究一类Kirchhoff型方程烄-(a+∫b|u|2dxu+)p-1 x∈ΩΩ)Δu=-λ|u|q-2 u+a1u+b1(u=0 x∈Ω其中,Ω是R3中具有正则边界的有界区域;1q2,4p6;a,b,a1和b1均为正数;λ是正参数.利用山路定理和极小化理论得到方程至少存在3个解:1个非负非平凡解和2个非正非平凡解.     

一类非局部问题解的存在性与多重性

考虑一类非局部问题{-(a-b integral from Ω|▽u|~2dx)Δu=λg(x)x∈Ω u=0 x∈Ω其中a0,b0,ΩR~N是有界开集,λ0且g∈H~(-1)(Ω)\{0},这里H~(-1)(Ω)是Sobolev空间H_0~1(Ω)的对偶空间.应用Ekeland变分原理和山路引理证明了:存在λ_*0,使得:(ⅰ)当λ∈(0,λ_*)时,该非局部问题至少有3个不同的解;(ⅱ)当λ=λ_*时,该非局部问题至少有2个不同的解;(ⅲ)当λλ_*时,该非局部问题至少有1个解.     

带有临界指数的Kirchhoff方程正解的存在性

利用Nehari流形方法,研究了在N=4的情况下,带有临界指数的Kirchhoff方程{-(a+b∫_Ω|▽u|~2dx)Δu=u~3+λu~q x∈Ω u=0 x∈Ω正解的存在性.     

高维空间中一类奇异Kirchhoff型问题正解的存在性

利用变分方法研究了在四维及以上空间中的一类次临界奇异Kirchhoff型问题{-（a+b∫a|▽u|2dx）Δu=f（x）up+g（x）u-γ x∈Ω,u=0 x∈Ω并获得了该问题正解的存在性.     

带有凹凸非线性项的Kirchhoff型方程解的多重性

利用集中紧性原理和对偶喷泉定理,研究了一类带有凹凸非线性项的Kirchhoff方程{-(a+b∫Ω|▽u|~2dx )Δu=|u|~4u+μ|u|~(q-2)u x∈Ω u=0 x∈?Ω获得了该方程有无穷多个解.其中Ω为R~3中边界光滑的有界开集,且a,b0,1q 2,μ0.     

关于RN 上非齐次四阶椭圆方程的注记

运用临界点理论中的Ekeland变分原理研究了非齐次四阶椭圆方程Δ2u-Δu+V(x)u=f(u)+h(x)u∈H2(RN)解的存在性,其中V∈C(RN,R)满足infx∈RNV(x)≥a1>0,这里a1>0是一个常数,更进一步,对每个M>0,meas({x∈RN:V(x)≤M})<∞,这里meas表示RN中的Lebesgue测度;f∈C(R,R+),f(0)=0,并且当z<0时f(z)≡0;limz→0f(z)/z=0,limz→+∞f(z)/z=l<+∞.     

带有梯度项的非线性双曲方程正解的爆破

研究了具有齐次Dirichlet边界和变指标反应项的非线性双曲方程ut-div（｜△u｜^p-2△u）=｜△u｜^q（x）（p〉2）在（x,t）∈Ω×（0,T）（T〉0）内非负解的爆破性质,并运用特征函数方法得到方程解在有限时刻爆破的条件。     

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.     

带杠杆千斤顶的设计

带杠杆千斤顶是基于地震、矿难、车祸等场合的救援或自救而自主研发的一种新型、简便、实用、高效的救援装置。由于其构造简单、携带方便,对于空间狭小且地表复杂的救援非常实用,亦可民用或作为工厂维修工具。本文对设计的原理方案、产品优点及使用进行了系统的说明。     

一类生化开关模型的定性分析

本文研究一类生化开关模型其中ｘ≥０，ｙ≥０；ａｉ，ｂｉ，ｃｉ（ｉ＝１，２）为正参数、给出了系统（１）具有开关行为的充要条件．     

Identification of a sex pheromone from a spider

The compounds (R)-3-hydroxybutyric acid and its dimer, (R)-3-[(R)-3-hydroxybutyryloxy]-butyric acid, have been identified as sex pheromones of a spider. These compounds elicit web reduction behavior by males of Linyphia triangularis (Clerck) on the webs of unmated adult females.     

Capture of a single molecule in a nanocavity

We describe a heptameric protein pore that has been engineered to accommodate two different cyclodextrin adapters simultaneously within the lumen of a transmembrane beta barrel. The volume between the adapters is a cavity of approximately 4400 cubic angstroms. Analysis of single-channel recordings reveals that individual charged organic molecules can be pulled into the cavity by an electrical potential. Once trapped, an organic molecule shuttles back and forth between the adapters for hundreds of milliseconds. Such self-assembling nanostructures are of interest for the fabrication of multianalyte sensors and could provide a means to control chemical reactions.     

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.     

一类p-Ginzburg—Landau泛函的C^1,a口收敛

研究了一类p-Ginzburg-Landau（p〉0）模型的渐近性态.通过局部分析的技巧,推出了泛函的正则性估计.在此基础上,利用Euler方程解的正则性估计及渐近行为,得到了极小元的C1,α收敛.     

Discrimination of successiveness: a test of a model of attention

Interpreting attention as a periodic phenomenon, we show its relevance to discriminating the successiveness of signals presented to separate sense modalities. Experiments confirm the expected linear relation between the probability of discriminating pairs of successive from pairs of simultaneous signals and make it possible to infer the period of attention.