Some Limit Theorems in Geometric Processes

Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n = 1, 2,…} for which there exists a real number a > 0, such that {an-1 Xn, n = 1,2, …} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.     

On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes

Abstract For the multidimensional ARMA system A(z)y_k=C(z)w_k it is shown that stability(det A(z)≠0,z:│z│≤1)of A(z) is equivalent to the trajectory boundedness in the mean square sense(MSS)which,as a rule,is a consequence of a successful stochastic adaptive control leading the closed-loop of an ARMAXsystem to a steady state ARMA system.In comparison with existing results the stability condition imposed onC(z)is no longer needed.The only structural requirement on the system is that det A(z) and det C(z) have nounstable common factor.     

Periodic Solution of a Nonautonomous Diffusive Food Chain System of Three Species with Time Delays

Abstract By using the continuation theorem of coincidence degree theory,the existence of a positive periodicsolution for a nonautonomous diffusive food chain system of three species. dx_1(t)/dt=x_1(t)[r_1(t)-a_(11)(t)x_1(t)-a_(12)(t)x_2(t)]+D_1(t)[y(t)-x_1(t)], dx_2(t)/dt=x_2(t)[-r_2(t)+a_(21)(t)x_1(t-r_1)-a_(22)(t)x_2(t)-a_(23)(t)x_3(t)], dx_3(t)/dt=x_3(t)[-r_3(t)+a_(32)(t)x_2(t-r_2)-a_(33)(t)x_3(t)], dy(t)/dt=y(t)[r_4(t)-a_(44)(t)y(t)]+D_2(t)[x_1(t)-y(t)]+D_2(t)[x_1(t)-y(t)],is established,where,r_i(t),a_(ii)(t)(i=1,2,3,4),D_i(t)(i=1,2),a_(12)(t),a_(21)(t),a_(23)(t)and a_(32)(t) are all positiveperiodic continuous functions with period w>0,T_i(i=1,2)are positive constants.     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

可逆测度与拟可逆测度的等价性

本文讨论了一类速度函数的可逆与拟可逆测度间的关系,证明了在[2]的条件下,可逆测度与拟可逆测度是等价的。     

Volterra积分微分方程大系统的渐近稳定性

一个大系统通常是由若干孤立子系统经过互联而构成的,所以有关大系统的问题,可以通过对每个孤立子系统,以及它们之间的互联关系的分析来解决。由常微分方程所描述的大系统和由差分方程描述的离散大系统平衡态的稳定性问题,已有了许多成果。但对Volterra积分微分方程大系统的讨论还不多见。这里拟采用向量V-泛函及微分不等式方法讨论它的渐近稳定性。     

一族Liouville可积的有限维Hamilton系统

本文生成了一族Liouville可积的Hamilton相流彼此可交换的有限维Hamilton系统,并且给出了一串对合的显式公共运动积分及其一组对合的显式生成元.     

带时滞观测线性离散系统的递推滤波

本文讨论带时滞观测线性离散系统的滤波问题,提出利用联合分布函数,得到滤波递推格式.这种方法还适用于一般的带有状态时滞的线性离散系统.     

农业总产值构成的关联分析方法

本文利用灰色系统理论建立了省级农业总产值构成的关联分析模型，并给出了应用实例。通过该模型，我们可以分析全省各市农业产值的发展对全省农业总产值的影响，从而为下一步更好地调整农业发展规划提供决策依据．     

兰州重离子加速器

 兰州重离子加速器是由注入器(SFC)和主加速器(SSC)组成的加速系统。离子源产生的重离子束,由注入器预加速,经前束流线传输并匹配到主加速器,在主加速器内加速到最高能量后引出,经后束流线传输到实验终端。 加速后的各种离子束,主要用于重离子核物理研究,例如,用于重离子核反应机制、核结构以及新核素的合成等。另外,重离子束对许多非核科技领域的研究,例如,对材料科学、原子物理学、辐射生物学、辐射医学等领域的研究,已展现出日益广阔的前景。