带Hardy-Sobolev临界指数和权函数的半线性椭圆问题的非平凡解

借助环绕定理和非线性分析技巧,研究如下一类带Hardy-Sobolev临界指数和权函数的半线性椭圆方程 - Δ u-μ u |x|2 =λu+K(x) |u|2*(s)-2u |x|s , x∈Ω; u=0, x∈Ω, 解的存在性,其中Ω是 R N具有光滑边界的有界开区域,0∈Ω,N≥5,0≤s≤2, 0≤μ≤ N-2 2 2, λ>０,K(x)是 上有界正函数.     

一类含Hardy项的三维Kirchhoff型问题的两个正解

研究如下的三维Kirchhoff型问题{-(a+b∫Ω| ▽u | 2dx)△u=| u|q-1u+λ |u|p-2u/|x|s, x∈Ω,u=0, x∈(a)Ω,其中,Ω是R3中具有光滑边界的有界区域,0∈Ω,0＜q＜1,0≤s＜1,4＜p＜2*(s)=2(3-s),a,b,λ＞0.运用变分方法,证明当λ＞0足够小时,这一方程至少有2个正解.     

一类形如f（x）｜g（x）｜函数的导数求法

本文试图利用f（x）｜g（x）｜导数之间的关系,以及关于求可导函数与不可导函数的乘积的导数定理,给出形如,f（x）｜g（x）｜的函数的导数的一种求法。     

一类奇异非线性Kirchhoff型问题的正解

考虑如下问题:{-(a+b∫Ω︱▽u︱2dx)Δu=f(x)/up,inΩ;u>0,inΩ;u=0,onΩ.其中,a,b>0,1相似文献   

一类耦合系统的最优控制解的存在性证明

主要讨论如下最优控制解的存在性问题,即对给定的正数T和已知函数uT(x)∈L2(Ω),寻找一个最优控制q(·)∈L∞(0,T)满足0≤q(t)≤1,使得J(q)=∫Ω|u(x,T)-uT(x)|2dx+δH∫T0|q(t)|2dt,达到最小,其中δ0为一给定常数,(,u)为下列耦合方程组初边值问题的解:{t+?×[a(x,t)?×]=F(x,t)(x,t)∈QT(1.1)u-▽(k(x,u)▽u)=q(t)a(x,t)|▽×(x,t)QT(1,2)N×(x,t)=N×G(x,t),u(x,t)=g(x,t)x∈?Ω,0tT(1,3)(x,0)=H0(x),u(x,0)=u0(x)x∈Ω(1.4)其中QT=Ω×(0,T],Ω为有界区域,?=(?/?x1,?/?x2,?/?x3),H=(H1,H2,H3),G(x,t),g(x,t)为给定函数,0(x),u0(x)为给定初始函数,N为边界?Ω的法向导数。     

异构分簇无线传感器网络中节点通信半径的研究

研究了在异构分簇无线传感器网络中,如何优化簇内节点的通信半径,从而最小化网络的总能耗.定义节点的能量消耗模型为E=a(dα+c)、网络半径为 R 、层数为 K .对节点通信半径不可调的网络,证明了α=2、c≤4R2时,或α=4、c≤4R2、K≤ 6 R时,最小化网络总能耗的簇内节点通信半径的上界为 α c/(α-1) .对于节点通信半径可调的网络,在α=2时,提出了自内而外依次最小化每层簇内节点的平均能耗来确定节点通信半径的算法.     

反映扩散方程的全局吸引子的存在性

文章讨论了抛物型方程μt-△μ λ|μ|αμ=f(x) g(u)在Ω×(0,∞)上,在满足初值条件u(x,0)=u0(x)∈L和零边界条件下,解对时间的连续性和唯一性,得到了解的连续半群S(t):L→LP((A)p≥1),由此得到了方程解的全局吸引子.     

带有低阶项的非散度椭圆方程解的二阶导数的高阶可积性

研究如下形式的非散度椭圆方程Lu=n∑i,j=1aij(x)(ε)2u/(ε)xi(ε)xj+n∑i=1bj(x)(ε)u/(ε)xi+c(x)u=h(x)解的二阶导数的高阶可积性,其中系数aij(x)有界且具有小BMO范数,bi(x),c(x)∈Ln(Ω),Ω为Rn(n≥3)中的有界光滑域.     

具有多个非线性源项与临界初始状态的半线性波动方程的初边值问题

研究具有多个非线性源项的半线性波动方程utt-△u=f(u)=∑ak|u|pt-1u from k=1 to l具有临界初值E(0)=d,I(u0)<0的初边值问题。我们证明了,若f(u)满足假设(H),u0(x)∈H01(Ω),u1(x)∈L2(Ω),E(0)=d,I(u0)<0且(u0,u1)≥0,则此问题不存在整体弱解,从而解决了这一公开问题,从实质上补充了文献[10]的结果。     

一类非线性四阶波动方程整体弱解的存在性

应用Galerkin和位势井理论结合的方法研究一类非线性四阶波动方程uu＋△2u｜u｜p1u=0初边值问题整体弱解的存在性,得到了较好的结果。     

一个含临界指数的拟线性椭圆型方程的注记

研究了如下的拟线性椭圆型方程:△pu+uq+λup*-1=0,u∈W1o,p(Ω), (1λ)其中,Ω2是RN中具有光滑边界的有界区域,△pu=div( |▽u|p-2▽u),N≥3,2≤p＜N,0＜q＜1,p*=NP/N-P.设λ*(Ω,p,q)是拟线性椭圆型方程(1λ)可解的参数集的上确界.运用变分方法,在不要求具有对称性质的一般区域Ω上得到了λ*(Ω,p,q)的一个可以精确计算的下界.     

中立型高阶偏微分方程解的振动性与渐近性

本文研究了一类中立型高阶偏微分方程在第一和第三边值条件下解的振动性质,得到了方程所有解u(x,t)振动或者limt→ ∞乙赘u(x,t)dx=0的一些充分性判别准则。     

带黏性项的强阻尼波动方程解的指数衰减性

讨论的是一类带有黏性项的强阻尼波动方程,Uu-△u-α△u1＋∫01g（t-τ）△u（τ）dτ＋ε︱u1︱p-1u1-︱u︱m-1u。对于ε≠1,α≠0的情况证明方程解的存在性和指数衰减性。     

Angular region: a measure of underdamped behavior

The natural modes of an underdamped dynamical system are given by the characteristic numbers of the quadratic operator pencil

$\text{P(s)=s}{}^2\text{I+sB+A,}$

where the operator A depends on the dissipative and reactive elements of the system, while B depends solely on the reactive elements. The operator P(s) for every applied stimulus vector signal x must satisfy:

$\text{(Bx,x)}{}^2\text{<4(Ax,x).}$

A measure of underdamped behaviour is suggested by predetermining an angular region |φ| containing all natural modes of the system,

$\text{|}\text{tan}\text{φ|?}\text{[4(Ax,x)?(Bx,x)}{}^2\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(Bx,x)}\text{.}$

When a comparison between positive operators A and B is available, say B²=KA, then

$\text{|}\text{tan}\text{φ|?}\text{√(4?K}{}^2\text{)}\text{K}\text{.}$

The paper is motivated by Duffin-Krein-Gohberg's earlier mathematical contributions.     

Indirect reference intervals for haematological parameters in capillary blood of pre-school children

IntroductionIndirect estimation of reference intervals (RIs) is straightforward and inexpensive procedure for determination of intra-laboratory RIs. We applied the indirect approach to assess RIs for haematological parameters in capillary blood of pre-school children, using results stored in our laboratory database.Materials and methodsWe extracted data from laboratory information system, for the results obtained by automatic haematology analyser in capillary blood of 154 boys and 146 girls during pre-school medical examination. Data distribution was tested, and logarithmic transformation was applied if needed. Reference intervals were calculated by the nonparametric percentile method.ResultsReference intervals were calculated for: RBC count (4.2-5.4 x10¹²/L), haemoglobin (114-146 g/L), MCH (25.0-29.4 pg), MCHC (321-368 g/L), RDW-SD (36.1-43.5 fL), WBC count (4.5-12.3 x10⁹/L), neutrophils count (1.7-6.9 x10⁹/L) and percentage (29.0-69.0%), lymphocytes count (1.6-4.4 x10⁹/L) and percentage (21.9-60.7%), PLT (165-459 x10⁹/L), MPV (8.1-11.4 fL) and PDW (9.2-14.4%). Gender specific RIs were calculated for monocytes count (male (M): 0.2-1.6 x10⁹/L; female (F): 0.1-1.4 x10⁹/L) and percentage (M: 2.5-18.3%; F: 1.8-16.7%), haematocrit (M: 0.34-0.42 L/L; F: 0.34-0.43 L/L), MCV (M: 73.4-84.6 fL; F: 75.5-84.2 fL) and RDW (M: 12.1-14.3%; F: 11.7-13.9%), due to observed gender differences in these parameters (P = 0.031, 0.028, 0.020, 0.012 and 0.001; respectively). Estimated RIs markedly varied from the literature based RIs that are used in the laboratory.ConclusionsIndirect method employed in this study enables straightforward assessment of RIs in pre-school children. Herein derived RIs differed from the literature-based ones, indicating the need for intra-laboratory determination of RIs for specific populations and sample types.     

Irradiation swelling,creep and thermal fatigue behaviors of LMFBR pressure vessels

The behaviors of irradiation swelling, irradiation creep and thermal-cycling fatigue induced by fast neutron fluence and developed in the LMFBR pressure vessels are analyzed on the basis of experimental data. From the interactions of the irradiation swelling, irradiation creep and thermal-cycling fatigue, the failure criterion for the design and safety surveillance of the pressure vessels can be expressed as a(frbuilt|t/t_c)^u+b(frbuilt|N/N_f)^v+c(?/?_s)^w=1, where t is time, t_c is creep rupture time, N is number of cycles, N_f is number of cycles to failure, ? is strain, ?_s is swelling strain to failure, and a, b, c, u, v and w are parameters or constants. The tangential tensile strain produced by the irradiation creep, thermal-cycling fatigue and hydrostatic pressure of the liquid sodium coolant may be combined together with the irradiation swelling strain ? as a whole. The inter-relationships between the behaviors of irradiation swelling, irradiation creep and thermal-cycling fatigue developed in the LMFBR pressure vessels are discussed.     

逆向国际化企业创新搜索平衡对双元性的影响

结合逆向国际化企业的特征,从网络嵌入和知识源利用两个维度解构该类企业的创新搜索策略,并结合战略匹配理论探讨了两种创新搜索平衡模式（国内聚焦和国外多源搜索、国内多源和国外聚焦搜索）对组织双元性的差异性影响,以及因果与效果推理在其中的调节效应。采用多元层次回归的方法对245家企业问卷数据进行实证检验,研究发现：（1）两种搜索模式对组织双元性都具有正向影响;（2）因果推理和效果推理均负向调节上述关系;（3）整合因果和效果推理能够增强国内多源和国外聚焦搜索平衡对组织双元性的影响,而对国内聚焦和国外多源搜索平衡与双元性的正向调节作用仅得到部分验证。研究结果进一步深化了整合决策理性作用下创新搜索平衡对组织双元性构建的作用机理的认识,为逆向国际化企业创新实践提供了新思路。