Attentions have been increasingly paid to the influence of the corrosion on the ultimate strength of ship structures. In consideration of the random characteristics of the corrosion of ship structures, the method for ...Attentions have been increasingly paid to the influence of the corrosion on the ultimate strength of ship structures. In consideration of the random characteristics of the corrosion of ship structures, the method for the ultimate strength analysis of the ship stiffened panel structure subjected to random corrosion degradation is presented. According to the measured corrosion data of the bulk carriers, the distribution characteristics of the corrosion data for the stiffened panel on the midship deck are analyzed, and a random corrosion model is established. The ultimate strength of the corroded stiffened panel is calculated by lhe nonlinear finite element analysis. The statistical descriptions of the ultimate strength of the corroded stiffened panel are defined through the Monte Carlo simulations. A formula is proposed on the ultimate strength reduction of the stiffened panel as a function of the corrosion volume. The reliability analysis of the ultimate strength of the corroded deck stiffened panel is performed. It shows that both the corrosion data of the deck stiffened panel and the ultimate strength of the random corroded deck stiffened panel follow the log-normal distribution. The ultimate stress ratio of the stiffened panel is inversely proportional to the corrosion volume ratio.展开更多
研究GBBM方程ut-aΔut-bΔu+ F(u)+γu=h(x),其中F(u)=(F1(u),…,Fn(u)), F / xiFi,Fi(0)=0,Fi是R1上二阶导数连续的函数,fi(s)=d/dsFi(s),fi满足fi(0)=0,｜fi(s)｜<c(1=∑ni=1+｜s｜m),i=1,…,n,其中当n 2时,0 m<∞;当n 3时,0 m ...研究GBBM方程ut-aΔut-bΔu+ F(u)+γu=h(x),其中F(u)=(F1(u),…,Fn(u)), F / xiFi,Fi(0)=0,Fi是R1上二阶导数连续的函数,fi(s)=d/dsFi(s),fi满足fi(0)=0,｜fi(s)｜<c(1=∑ni=1+｜s｜m),i=1,…,n,其中当n 2时,0 m<∞;当n 3时,0 m 2/(n-2).在空间Rn上整体解的存在唯一性用Galerkin逼近方法和作极限的方法获得.展开更多
The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
本文利用正投影的概念将点到直线与点到平面的距离公式统一起来并作推了广。我们证明了:Ⅰ 设O≠δ=(a_1,a_2,…,a_n)∈R^n,则R^n中的点(y_1,y_2,…,y_n)到R^n的子空间W={x_1,x_2,…,x_n)∈R^n|sum from i=1 n(a_ix_i=0}的距离为|sum fr...本文利用正投影的概念将点到直线与点到平面的距离公式统一起来并作推了广。我们证明了:Ⅰ 设O≠δ=(a_1,a_2,…,a_n)∈R^n,则R^n中的点(y_1,y_2,…,y_n)到R^n的子空间W={x_1,x_2,…,x_n)∈R^n|sum from i=1 n(a_ix_i=0}的距离为|sum from i=1 n(a_iy_i)/(sum from i=1 na_i^2)^(1/2);Ⅱ 设O≠δ=(a_1,a_2,…,a_n,…)∈l^2,则l^2中的点(y_1,y_2,…,y_n,…)到l_2的子空间W={(x_1,x_2,…,x_n,…)∈l^2|sum from n=1 ∝(a_nx_n)}的距离为|sum from n=1 ∝(a_ny_n)|/(sum from n=1 ∝a_n^2)^(1/2)。展开更多
In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu（x） = -△△u（x） ＋ V（x）u（x）,for all x ∈ R^n, in the Hilbert space H = L2（R^n,H1） with the operator po...In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu（x） = -△△u（x） ＋ V（x）u（x）,for all x ∈ R^n, in the Hilbert space H = L2（R^n,H1） with the operator potential V（x） ∈ C^1 （R^n, L （H1） ）, where L （H1 ） is the space of all bounded linear operators on the Hilbert space H1, while AAu is the biharmonic differential operator and△u=-∑i,j=1^n 1/√detg δ/δxi[√detgg-1（x）δu/δxj]is the Laplace-Beltrami differential operator in R^n. Here g（x） = （gij（x）） is the Riemannian matrix, while g^-1 （x） is the inverse of the matrix g（x）. Moreover, we have studied the existence and uniqueness Theorem for the solution of the non-homogeneous biharmonic Laplace-Beltrami differential equation Au = - △△u ＋ V（x） u （x） = f（x） in the Hilbert space H where f（x） ∈ H as an application of the separation approach.展开更多
in the Solobev space E=W01,2（Q, Rn）. We assume the following conditions: （F1） F（x, u, p） is locally Hlder-continued for x; Fui（x, u, p） is locally Hldercontinued for x, u; F（x, u, p） is twice differentiabili...in the Solobev space E=W01,2（Q, Rn）. We assume the following conditions: （F1） F（x, u, p） is locally Hlder-continued for x; Fui（x, u, p） is locally Hldercontinued for x, u; F（x, u, p） is twice differentiability for p.展开更多
基金partially supported by the National Natural Science Foundation of China(Grant No.51279034)
文摘Attentions have been increasingly paid to the influence of the corrosion on the ultimate strength of ship structures. In consideration of the random characteristics of the corrosion of ship structures, the method for the ultimate strength analysis of the ship stiffened panel structure subjected to random corrosion degradation is presented. According to the measured corrosion data of the bulk carriers, the distribution characteristics of the corrosion data for the stiffened panel on the midship deck are analyzed, and a random corrosion model is established. The ultimate strength of the corroded stiffened panel is calculated by lhe nonlinear finite element analysis. The statistical descriptions of the ultimate strength of the corroded stiffened panel are defined through the Monte Carlo simulations. A formula is proposed on the ultimate strength reduction of the stiffened panel as a function of the corrosion volume. The reliability analysis of the ultimate strength of the corroded deck stiffened panel is performed. It shows that both the corrosion data of the deck stiffened panel and the ultimate strength of the random corroded deck stiffened panel follow the log-normal distribution. The ultimate stress ratio of the stiffened panel is inversely proportional to the corrosion volume ratio.
文摘研究GBBM方程ut-aΔut-bΔu+ F(u)+γu=h(x),其中F(u)=(F1(u),…,Fn(u)), F / xiFi,Fi(0)=0,Fi是R1上二阶导数连续的函数,fi(s)=d/dsFi(s),fi满足fi(0)=0,｜fi(s)｜<c(1=∑ni=1+｜s｜m),i=1,…,n,其中当n 2时,0 m<∞;当n 3时,0 m 2/(n-2).在空间Rn上整体解的存在唯一性用Galerkin逼近方法和作极限的方法获得.
基金Supported by the National Nature Science Foundation of China(11471309,11271162,and 11561062)Project of Henan Provincial Department of Education(18A110028)
基金Supported by Zhejiang Provincial Natural Science Foundation of China under Grant (No.M103069)supported by the Education Dept. of Zhejiang Province(20021022)
文摘The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
文摘本文利用正投影的概念将点到直线与点到平面的距离公式统一起来并作推了广。我们证明了:Ⅰ 设O≠δ=(a_1,a_2,…,a_n)∈R^n,则R^n中的点(y_1,y_2,…,y_n)到R^n的子空间W={x_1,x_2,…,x_n)∈R^n|sum from i=1 n(a_ix_i=0}的距离为|sum from i=1 n(a_iy_i)/(sum from i=1 na_i^2)^(1/2);Ⅱ 设O≠δ=(a_1,a_2,…,a_n,…)∈l^2,则l^2中的点(y_1,y_2,…,y_n,…)到l_2的子空间W={(x_1,x_2,…,x_n,…)∈l^2|sum from n=1 ∝(a_nx_n)}的距离为|sum from n=1 ∝(a_ny_n)|/(sum from n=1 ∝a_n^2)^(1/2)。
文摘In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu（x） = -△△u（x） ＋ V（x）u（x）,for all x ∈ R^n, in the Hilbert space H = L2（R^n,H1） with the operator potential V（x） ∈ C^1 （R^n, L （H1） ）, where L （H1 ） is the space of all bounded linear operators on the Hilbert space H1, while AAu is the biharmonic differential operator and△u=-∑i,j=1^n 1/√detg δ/δxi[√detgg-1（x）δu/δxj]is the Laplace-Beltrami differential operator in R^n. Here g（x） = （gij（x）） is the Riemannian matrix, while g^-1 （x） is the inverse of the matrix g（x）. Moreover, we have studied the existence and uniqueness Theorem for the solution of the non-homogeneous biharmonic Laplace-Beltrami differential equation Au = - △△u ＋ V（x） u （x） = f（x） in the Hilbert space H where f（x） ∈ H as an application of the separation approach.
文摘in the Solobev space E=W01,2（Q, Rn）. We assume the following conditions: （F1） F（x, u, p） is locally Hlder-continued for x; Fui（x, u, p） is locally Hldercontinued for x, u; F（x, u, p） is twice differentiability for p.
