小时间区间中的条件扩散过程

本文讨论具有一致连续系数条件扩散过程的大偏差性质。设X(t)是具有Dirichlet空间(ξ、H_0~1(P_0~d))的扩散过程,其中 ξ(f,g)=1/2 integral from n=R~d to (〈▽f,▽g〉(x)dx)。 P_a~e是过程x_6(t)=x(∈t)满足条件x_6(0)=x,x_6(1)=y的律。那么当∈→0时,(P_(?)~(?),y)具有大偏差性质,且具有速率函数 J_(x,y)(ω)=1/2 integral from n=0 to 1(〈(?)(t),a(-1)(ω(t)),(?)(t)〉dt-1/2 d~2(x,y)。     

SOME GENERALIZATION OF GRONWALL-BIHARI INTEGRAL INEQUALITIES AND THEIR APPLICATIONS

The interest of this paper lies in the estimates of solutions of the three kinds of Gronwail-Bihari integral inequalities:(Ⅰ) y(x)≤f(x) sum from i=1 to n(g_i(x)integral from n=0 to x(h_i(d)y(s)ds)),(Ⅱ) y(x)≤f(x) g(x)φ(integral from n=0 to x(h(s)w(y(s))ds))(Ⅲ) y(x)≤f(x) sum from i=1 to n(g_i(x)integral from n=0 to a(h_i(s)y(s)ds g_(n 1)φ(integral from n=0 to x(h_(n 1)(s)w(y(t))ds)).The results include some modifications and generalizations of the results of D. Willett, U. D. Dhongade and Zhang Binggen. Furthermore, applying the conclusion on the above inequalities to a Volterra integral equation and a differential equation, the authors obtain some new better results.     

一类非线性Volterra积分微分方程组及褶积型积分方程组的解之延展和界值

对非线性Volterra型积分微分方程组x'(t)=f(t,x(t))+sum from j=1 to m(integral from n=0 to t(A_j(t,s)g_j(s,x(s))ds)),t∈R_+ (1)以及褶积型积分方程组y(t)=F(t)+sum from j=1 to m(integral from n=0 to t(B_j(t-s)G_j(s,y(s))ds)),t∈R_+ (2)我们得到了如下结果:定理1 若方程组(1)满足下列条件1)f(t,η),g_j(t,η)∈c[R_+×R~n,R_n],A_j(t,s)∈c[R_+×R_+,R~(n×n)],它们使得(1)     

OSCILLATORY AND ASYMPTOTIC BEHAVIORS OF FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper the author discusses the following first order functional differentialequations: x'(t) +integral from n=a to b p(t, ξ)x[g(t, ξ)]dσ(ξ)=0, (1) x'(t) +integral from n=a to b f(t, ξ, x[g(t, ξ)])dσ(ξ)=0. (2)Some suffcient conditions of oscillation and nonoseillafion are obtained, and two asymptolioproperties and their criteria are given. These criferia are better than those in [1, 2], and canbe used to the following equations: x'(t) + sum from i=1 to n p_i(t)x[g_i(t)] =0, (3) x'(t) + sum from i=1 to n f_i(t, x[g_i(t)] =0. (4)     

积分中值定理中ξ值的渐近性

本文给出当b→a时积分的第一中值定理integral from a to b f(x)dx=f(ξ)(b—a)的中值ξ的性态。即当f’(a)≠0时有而当f′(a)=f″(a)=…=f~(n-1)(a)=0,F~(n)(a)≠0时有积分第一中值定理推广形式integral from a to b f(x)g(x)dx=f(ξ) integral from a to b g(x)dx的中值ξ也具有类似的性态。     

关于线性算子的高阶饱和

设f(x)∈C_(2π)。而f(x)～sum from k=0 ( )A_k(f_1k)≡α_0/2 sum from k=1 ( )(α_kcoskx b_ksinkx)。 又设 U_n(f,x)=1/πintegral from -πto π(f(x t)u_n(t)dt,) 其中u_n(t)=1/2 sum from k=1ρ_k~(n)coskt满足条件: integral from 0 to k(|u_n(t)|dt=O(1),)ρ_k~(n)→1(n→∞;k=1,2,…,)。设m是正整数,ρ_0~(n)=1。记~mρ_k~(n)=sum form v=0 to ∞ ((-1)~(m~(-v))(m v)ρ_k v~(n) (k=0,1,…,)。)T.Nishishiraho考虑了在ρ_k~(n)=O(k>n)的情况下U_n(f,x)的饱和问题,证明了。 定理A 设{_n}是收敛于0的正数列,使得     

算子样条函数磨光法

1.引言 本文仍按逼近δ函数的观点,对表达式 f(x)=integral from n=-∞ to ∞(δ(x-t)f(t)dt两端,施以磨光逼近算子M_h,导至磨光公式 M_hf(x)=integral from n=-∞ to ∞(K_h(x-t)f(t)dt.(1)     

具有齐性核Marcinkiewicz积分交换子的Lipschitz估计

本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)上的有界算子并且也是Lp(Rn)到Lq(Rn)上的有界算子.     

ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du)) integral from n=■Q to (G(x,u))

In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du)) integral from n=(?)Q to (G(x,u)), u∈W~(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.     

关于求解第二类Volterra积分方程的Picard迭代收敛性的一点注记

考虑第二类Volterra积分方程: φ(x)+integral from n=0 to x(K(x,y)φ(y)dy)=f(x),x∈[0,L],(1)其中f(x)∈C([0,L]),核函数 K(x,y)对y可积,且     

关于凸函数的Hadamard不等式的拓广(英文)

设,是区间[a,b]上连续的凸函数。我们证明了Hadamard的不等式 f(a+b/2)≤1/b-a integral from a to b (f(x)dx)≤f(a)+f(b)/2可以拓广成对[a,b]中任意n+1个点x_0,…,x_n和正数组p_0,…,p_n都成立的下列不等式 f(sum from i=0 to n (p_ix_i)/sum from i=0 to n (p_i))≤|Ω|~(-1) integral from Ω (f(x(t))dt)≤sum from i=0 to n (p_if(x_i)/sum from i=0 to n (p_i),式中Ω是一个包含于n维单位立方体的n维长方体,其重心的第i个坐标为sum from i=i to n (p_i)/sum from i=i-1 (p_i),|Ω|为Ω的体积,对Ω中的任意点t=(t_1,…,t_n) ω(t)=x_0(1-t_1)+sum from i=1 to n-1 (x_i(1-t_(i+1))) multiply from i=1 to i (t_i+x_n) multiply from i=1 to n (t_i)。不等式中两个等号分别成立的情形亦已被分离出来。 此不等式是著名的Jensen不等式的精密化。     

一类二阶泛函微分方程解的渐近性

对各类二阶微分方程解的性质,自1971年Hammett以来已有许多讨论,如[1]—[10]本文讨论二阶时滞泛函微分方程 (r(t)x′(t))′+sum from i=0 to n (P_i(t)g_i′(x(t-τ_i(t))))+sum from i=0 to n (q_i(t)g_i(x(t-τ_i(t))))=f(t) (1)的解的渐近性质,其中;r(t)、q_i(t)、g_i(x)、τ_i(t)、f(t)连续;p_i(t)连续可微;当p_i(t)不恒为0时,g_i(x)连续可微;当x≠0,xg_i(x)>0;g_i(x)关于x单调不减;F(u)=integral from n=to to u (|f(s)|ds)<∞;g_0(x)=x,τ_0(t)=0。     

方程+f(x)■+g(x)=p(t)的调和解

本文不作假设integral from 0 to ±∞ (f(x)+|g(x)|dx=±∞),得到方程(?)+f(x)(?)+g(?)=p(t)调和解的存在性,以及当integral from 0 to ±∞(g(x)dx=+∞时,其解的正向有界性和当g(x)=x,f(x)>0时,其调和解的渐近稳定性、唯一性。     

二重积分■f(x,y)dxdy的对称性计算技巧

<正> 在定积分计算中常用到一个重要的结论是:f(x)是区间[-a,a]上的连续函数,则integral from n=-a to a (f(x)dx=2 integral from n=0 to a (f(x)dx),当f(x)为偶函数时, integral from n=-a to a (f(x)dx=0,当f(x)为奇函数时, 这个重要结论常说成“偶倍奇零”,它可以推广到对称区域D上的二重积分∫∫f(x,y)dxdy的计算问题中。为此,下面假设被积函数f(x,y)在对称区域D上连续,给出二重积分||f(x,y)dxdy的对称性计算的一般性结论。结论1 设积分区域D关于x轴对称,则     

LARGE DEVIATIONS FOR SYMMETRIC DIFFUSION PROCESSES

Let a(x)=(a_(ij)(x)) be a uniformly continuous, symmetric and matrix-valued function satisfying uniformly elliptic condition, p(t, x, y) be the transition density function of the diffusion process associated with the Diriehlet space (, H_0~1 (R~d)), where(u, v)=1/2 integral from n=R~d sum from i=j to d(u(x)/x_i v(x)/x_ja_(ij)(x)dx).Then by using the sharpened Arouson's estimates established by D. W. Stroock, it is shown that2t ln p(t, x, y)=-d~2(x, y).Moreover, it is proved that P_y~6 has large deviation property with rate functionI(ω)=1/2 integral from n=0 to 1<(t), α~(-1)(ω(t)),(t)>dtas s→0 and y→x, where P_y~6 denotes the diffusion measure family associated with the Dirichlet form (ε, H_0~1(R~d)).     

Positive Solutions of Hammerstein Nonlinear Integral Equations

In this paper we consider the Hammerstein nonlinear integral equation (x)=integral from G (K(x,y) f(y,(y))dy=A(x)) (1) where G is a bounded closed domain in R"; the function f(x,u) is non-negative,continuous on G×[0,+∞) and f(x,0)≡0; the kernel k(x,y) is non-negative continuous on G×G. Obviously, A acts in the space C(G) and is completely continuous. Theorem 1 Suppose that (i) lim u~(-1)f(x,u)=0 and lim u~(-1)f(x, u)=+∞     

应用于地震学中的一种行之有效的积分方法

本文在Filon积分思想的基础上,讨论了在地震学中广泛使用的两种带参积分 I_0(r)=integral from n=a to b (f(x)Ja(rx)dx), I_1(r)=integral from n=a to b (f(x)J_1(rx)dx),的数值求积方法,与其他方法相比,此法具有精度高,速度快的特点.     

条件L泛函的核估计及其Bootstrap逼近

设(X,y)为取值于 R~d×R~1的随机变量,X 具有边缘分布 F(x),Y 关于 X 的条件分布为 F(y|x).对于条件 L 泛函θ_1(x)=integral from n=0 to 1 J(y)F~(-1)(y|x)dy(1)θ(x)=integral from n=0 to 1 J(y)F~(-1)(y|x)dy+sum from j=1 to k a_jF~(-1)(p_j|x)(2)在[1]中曾给出了它们的近邻估计,并讨论了估计的渐近性质(其中 F~(-1)(x)=inf{t:F(t)≥x}).在本文中,我们将用核函数方法构造它们的另一类估计,并讨论估计的一些渐近性质.设(X_1,Y_1),(X_2,Y_2),…是(X,Y)的一个样本列,取 w_n_i(x)=K((x-X_i)/h_n)/sum from i=1 to n K((x-X_i)/h_n),其中 K 为 R~d 上的概率密度函数,并有0相似文献   

关于Smale提出的积分逼近效率的一般结论

设?~k是[0,1]上的CooeB空间,Q:?~k→R是至少具有k-1次代数精度的求积泛函.设J:f|→integral from n=0 to 1 (f(t)dt),h=1/n。通过由等式 M_hf(t)=h sum from i=0 to (n-1)(f(ih+th)),?f∈C[0,1],?t∈[0,1]确定的线性算子M_h:C[0,1]→C[0,1],定义Q的复化求积泛函QM_h。在?~k中的     

含有n个滞量的三维微分差分方程组周期解的存在性

本文研究含有n 个滞量的三维微分差分方程组x(t)=sum from i=1 to ∞(1/i)f[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]y(t)=sum from i=1 to ∞(1/i)g[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)](τ_i>0)z(t)=sum from i=1 to ∞(1/i)h[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]周期解的存在性,给出了方程组周期解周期的取值范围.推广并改进了文[1]的结果.