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)。     

圆周自映射的v极限集

设 f:s~1→s~1为连续映射。f 的回归点集和非游荡集分别记为 R 和Ω.xes~1,令v(x)=ω(x)∩α(x),其中ω(x)(α(x)为 x 的ω-(α-)极限集.令Γ=(?)v(x),若 y(?)s~1,记∧(y)=(?)ω(x).我们证明了:(1)Γ=∧(Ω)=∧(∧)=∧(Γ);(2)Ω-Γ是 s~1中无处稠密的可数集;(3)若以 x 为端点的每个开弧至少包含某个轨道中的的两点,则 x∈Γ;(4)若Γ-R≠φ,则Γ-R 为不可数集;(5)如(?)-R≠φ,则(?)-R 为无限集;(6)Γ=R 当且仅当(?)~(+)∩(?)~(-)=R.其中(?)~(+)((?)~(-))表示 R 的右(左)闭包。     

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)).     

第九届美国数学邀请赛(AIME)试题及解答

1.已知:xy x y=71,x~2y xy~2=880,x,y为正整数,求x~2十y~2. 2.矩形ABCD,AB=4,CB=3,点A=p_O,P_1,…,P_(168)=B把AB边分为168个相等的小段,点C=Q_o,Q_1,…,Q(168)=B把CB边分成168个相等的小段,做线段P_kQ_K,1≤k≤167,在AD,CD上同样重复上述过程,再引对角线AC,求这335条线段长度之和。 3.把(1 0.2)~(1000)按二项式定理展开,且令c_1000~0(0.2)~0 C_1000~1(0.2)~1 … C_1000~k(0.2)~1000=A_o A_1 … A_1000,其中A_=C_1000~1000(0.2)~k,k=0,1,2,…,1000,问使A_k最大时k是多少?     

第五届全国大学生数学夏令营数学竞赛试题

<正> 1.xoy 平面上有两个圆C_1:(x-1)~2+(y-1)~2=1,C_2:(x+2)~2+(y+2)~2=4,求作一个在全平面连续,且满足0≤f(x,y)≤1的二元函数,f(x,y),使得,f(x,y)在C_1之内部取值1,在 C_2之内部取值零.2.你能否求出最小正数 k,使得下列不等式成立:     

甩瓦累-布然平均逼近连续函数

<正> §1.总说§1.1 设 f(x)∈C_(2π),f(x)～a_0/2+sum form n=1 to ∞ a_ncosnx+b_nsin nx≡sum form n=0 to ∞ A_n(x)记 S_n(f,x)=sum form v=0 to n A_v(x).称σ_(n,p)(f,x)=1/p+1 sum form v=n-p to n S_v(f,x)为 f(x)的瓦累-布然平均.记△_u~kf(x)=sum form v=0 to k (-1)~v(?)f[x+(k-2v)u].称函数ω_k(f,t)=(?)|△~u_kf(x)|为 f(x)的 k 阶连续模.简记ω(f,t)=ω_1(f,t).假如 f(x)的共轭函数     

上期课外练习解答

高一年级1.(1)B≠φ时,-2√2相似文献   

一类值得注意的函数——复合函数

如果y是u的函数,记为y=f(u),u又是x的函数,记为u=g(x),且g(x)的值域与f(u)的定义域的交集不空,则确定了一个y关于x的函数y=f[g(x)],这就是函数y=f(u)与u=g(x)的复合函数,而y=f(u)称为外函数,u=g(x)称为内函数.本文举例介绍复合函数问题的一些常见类型及解法. 1.求复台函数的定义域 关键是正确分析函数的复合层次,由里向外或由外向里逐层解决. 例1 已知f(x)的定义域为[0,1)若F(x)=f[log1/2(3-x)],则函数的定义域是     

y=Asinωx和y=Acosωx的几何性质

函数y=Asin(ωx φ) k或y= Acos(ωx φ) k的最值、周期、单调代数性质等是大家都比较熟悉的.本文介绍它们的几个几何性质,供同学们学习参考.性质如图1和图2,M,N,P是函数y =Asinωx或y=Acosωx(A>0,ω>0)的图象上的三个相邻的两个最高点和一个最低     

趣味数学几例

1.今年元旦是星期日,试问今年元旦后的第1984~(1984)天是星期几。解:∵1984~(1984)=(283×7+3)~(1984) =7m+3~(1984),m∈N。而 3~6≡1(mod7),3~(1984)=3~4×3~(6×330) 3~4≡4(mod7),∴1984~(1984)≡4 (mod7)。答:今年元旦后的第1984~(1984)天是丛期四。 2.若f(x+1)=|x-1|,求f(1984)。解:令 x+1=1984,则x-1=1982, ∴ f(1984)=1982。 3.已知 f(x)=3x+1,g(x)=2x-1,h(g〔f(x)〕)=f(x)。求h(1984)。解:∵ f(y)=3y+1, ∴ g〔f(y)〕=2(3y+1)-1=6y+1, 故h(6y+1)=3y+1。令6y+1=1984,     

Detecting nuclear materials smuggling: using radiography to improve container inspection policies

This paper proposes a layered container inspection system for detecting illicit nuclear materials using radiography information. We argue that the current inspection system, relying heavily on the Automated Targeting System (ATS) and passive radiation detectors, is inherently incapable of reliably detecting shielded radioactive materials, especially highly enriched uranium (HEU). This motivates the development of a new inspection system, which is designed to address a fundamental flaw of the ATS-based system, allowing for improved defense against sophisticated adversaries. In the proposed inspection system, all cargo containers go through x-ray imaging equipment first. From the x-ray image, a hardness measure of the container is computed. This hardness measure characterizes how likely it is that shielded HEU, if it does exist in the container, will not be detected in a subsequent passive detection step. Depending on the value of the hardness, the lower-hardness containers are sent to passive detection and the high-hardness containers are sent directly to active detection. This paper explores the trade-off between the detection probability of the new inspection system and the expected sojourn time a container spends in the system. The solution details and decision-making tools for using such a system are provided. Comparisons are made between the proposed system and the current ATS-based nuclear inspection system.     

交通运输系统协调发展理论与模型研究

提出了交通运输系统协调度的评价分析模型.从系统论的观点出发,提出了交通运输系统协调理论的概念,探讨了交通运输系统随时间而不断演化变迁的规律,给出了交通运输系统协调发展基本步骤;并根据协调学原理,讨论了交通运输系统的协调性问题,提出了系统协调发展模型,对交通运输子系统内部及子系统之间及系统整体的协调发展问题进行了研究,探讨了交通运输可持续发展的系统协调管理过程,为进一步研究交通运输系统的可持续发展奠定了基础.     

A multi-ary number communication system based on hyperchaotic system of 6th-order cellular neural network

This paper proposes the hyperchaotic system of 6th-order cellular neural network (CNN), realizes its synchronization based on state observer. In addition, a multi-ary number communication system based on this hyperchaotic system is given in this paper. This communication system has the features of large capacity of signals transmission and high security.     

A Normal Form for Systems of Implicit Ordinary Differential Equations

This contribution deals with the application of computer algebra based methods to the analysis of dynamic systems described by implicit ordinary differential equations. This type of system defines a submanifold of a certain jet space. We solve the problem whether this submanifold admits a parametrization by an explicit system, i.e. any solution of the original system is a solution of the explicit one and vice versa. Since this approach requires the formal integrability of the implicit system, a sketch of an algorithm for the computation of the formally integrable system is presented.     

Hopf bifurcation analysis of integro-differential equation with unbounded delay

The complexity of a nonlinear dynamical system is controllable via a selection of system parameters. One representative behavior of such a complex system can be illustrated by Hopf bifurcation. This paper presents a Hopf bifurcation analysis of a kind of integro-differential equations with unbounded delay. Based on the Hopf bifurcation principle, a set of relationships among system parameters are obtained when a periodic orbit exists in the system. A numerical analysis is applied to solve the integro-differential delay equation. This paper proves the existence of Hopf bifurcation in the corresponding difference equations under the same system parameters as that in the integro-differential delay equations.     

Global smooth solution for a kind of two-fluid system in plasmas

A kind of two-fluid system in plasmas is studied in this paper. This system describes rich dynamics of a plasma, including the interactions between the ion acoustic wave and the plasma wave. When ignoring the effect of the high-frequency electric field, such system reduces to the ion type Euler–Poisson system. We prove that for this kind of two-fluid system, small perturbations around the equilibrium state lead to a global smooth solution. This result generalizes the recent work given by Guo and Pausader.     

On multiserver feedback retrial queue with finite buffer

This paper deals with a multiserver feedback retrial queueing system with finite waiting position and constant retrial rate. This system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition for stability of the system is investigated. Some important system performance measures are obtained using matrix geometric method. The effect of various parameters on the system performance measures are illustrated numerically. Finally, the algorithmic development of the full busy period for the model under consideration is discussed.     

年龄相关的种群扩散系统广义解的正则性

证明了年龄相关的种群扩散系统广义解的正则性,为进一步讨论该系统最优控制的存在性奠定了理论基础,也为种群系统控制问题的实际研究提供了数学理论和方法.