相关乘积

Based on this, to the recent years the related questions which appear frequently in the middle school mathematics competition, nimble utilization the aliquot concept, the relative prime nature, the combinatorial nature, the factorization, as well as the conclusion of the continual integer product nimbly can by aliquot knowledge and the methods, and so on, carried on the proof and the explanation.

在此基础上，对近年来在中学数学竞赛中频繁出现的相关问题，灵活运用整除概念、互素性质、组合性质、因式分解以及个连续整数的乘积能被整除的结论等知识和方法，来进行证明与解答。

The main results are as follows:We review the existing Monte Carlo control variates estimators of the price of Asian options and propose a new one. According to pratical needs, we define efficiency as the inverse of the product of the variance of an estimator and its computational time and make it a standard for comparisons to draw the following conclusions: Firstly, the more control variates correlate with arithmetic average Asian options, the larger is the efficiency of an estimator with these control variates, but among which the geometric average option plays the most important role; Secondly, an estimator with more control variates is better than one with less ones only when the time to maturity is long and the volatility is high.

在综合已有研究工作的基础上，本论文的主要创新成果如下：（1）我们回顾了已有的亚洲期权价格的蒙特卡罗控制变量估计，并提出了一个新的控制变量估计，且从客观实际出发，将估计值的方差和计算时间的乘积的倒数定义为效率并以它为标准比较各估计，得到以下结论：与算术平均亚洲期权相关程度越大的控制变量构成的估计的效率越大，而其中起主要作用的控制变量为几何平均亚洲期权的价格；只有在到期时间较长且标的资产的波动率较大时，元素多的多元控制变量估计比元素少的效率大。

Results reveal that the spatial correlation properties of MIMO channel are dependent on the PAS, the antenna pattern and the geometric configuration of the array. When the PASs at the base station and the mobile station are independent, the spatial correlation matrix of the MIMO channel is the Kronecker product of the spatial correlation matrix at the BS and the MS. The temporal correlation properties of the MIMO channel are determined by the PAS at the MS, antenna pattern and the traveling speed of the MS. Based on the analysis of the physical essence, the temporal correlation properties are equivalent to the spatial correlation properties at the MS. The joint spatio-temporal correlation properties at the BS and the MS are quite different. When the PASs at the BS and the MS are independent, the spatial correlation at the BS is independent on the temporal correlation, but this is not true for the spatial correlation at the MS.

分析与计算的结果表明，MIMO信道的空间相关特性由角度谱、阵元的方向图、阵元间距以及阵列几何结构决定，并且当发射端与接收端的空间统计特性相互独立时，MIMO信道的空间相关矩阵可以表示为发射阵列空间相关矩阵与接收阵列空间相关矩阵的Kronecker乘积：信道的时间相关仅与MS端的角度谱、阵元方向图以及MS的运动速度有关，通过对信道时间相关的物理本质的研究，说明了时间相关与MS端空间相关的等价性；MIMO信道的空-时联合相关特性在BS端和MS端具有不同的特点，当发射端与接收端的空间统计特性相互独立时，BS端的空间相关与时间相关是独立的，而由于信道的时间相关与MS端的空间相关具有相同的物理本质，MS端的空间相关与时间相关不是独立的。

Moreover, we prove the linear combination and product measure of probability measures with negative correlation are preserved.

最后证明了具有负相关的概率测度的线性组合及乘积测度仍是负相关的。

Motivated by the newψfunctional stability,we can establish some new kinds of stabilities which are different from the exponential stability.With the help of semimartingale convergence theorem,stochastic calculous,moment inequality,Burkholder-Davis-Gundy inequality,Gronwall inequality etc.,we find that the product ofψfunction and the solutions of neutral equations will approach a nonempty set if some specific conditions are satisfied.

我们应用半鞅收敛定理、随机微积分的相关知识以及矩不等式、Burkholder-Davis-Gundy不等式和Gronwall不等式等技巧，得到中立型随机泛函微分方程的解与特定的"ψ函数"的乘积在一定的条件下将趋向某非空集合这一结论，并建立了该中立型方程的随机LaSalle型定理。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

For signals that exhibit a weak or moderate long-term persistence,an OIVPM-MDL structure identification method is proposed based on overdetermined instrumental variable product moment and minimum description length criteria,and for signals with a strong long-term correlation between samples a combinative approach of inverse fractional filtering and the OIVPM-MDL method is also described.

本文研究了滤波分形差分高斯噪声过程的结构辨识问题，针对存在较弱和适中的长期间相关的信号，提出了一种基于超定辅助变量乘积矩和最小描述长度准则的OIVPM－MDL结构辨识方法；针对存在强长期间相关的过程，提出了分形反滤波与OIVPM－MDL的组合定阶方法。

The phase and group velocities of Lamb waves in the aluminum plate related to the frequency and the thickness of the plate because of the material characters. However, for the carbon fiber composite lamina, the situation was of difference, in which the velocities were with regarded to the frequency and thickness as well as the propagational direction and the fiber orientation.

输入铝板和碳纤维板的材料参数，即可得出铝板和碳纤维材料单层板中Lamb波的频散曲线，铝板为各向同性材料，其中的Lamb波相群速度只与频率板厚的乘积相关，碳纤维板为各向异性材料，其中的Lamb波相群速度不仅与频厚积有关，还与Lamb波传播方向、碳纤维的铺层方向相关。

This paper aims to study some important problems of clutter modeling and simulation, which include as follow:According to the principle that each quadrature component of K-distributed clutter can be modeled, exactly or approximately, by a weighted sum of products of two independent Gaussian variables, a new method for modeling and simulation of correlated coherent K-distributed clutter is presented.

本文对海杂波的分析与建模中的几个关键问题进行了研究，主要包括以下内容：根据K分布杂波的两个正交分量可由两列相互独立的高斯矢量的加权乘积和精确或近似构成的原理，本文提出了一种新的相关相干K分布杂波建模与仿真方法。

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers,the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.

为了求得用于研究双包层光纤激光器输出特性的更为精确的解析解，根据稳态速率方程组，针对典型的双包层光纤激光器参量，在估计了上能级粒子再发射项和抽运光产生的影响后，采用保留再发射贡献主导部分的办法以提高可积分近似方程的精确度，明确地提出了要获得光纤激光器输出功率的解析表达式的关键在于求出损耗系数与光场乘积的积分值，简洁地求得了输出功率和抽运光斜线效率的显函数解析表达式，并对其相关问题进行了讨论，以915nm，920nm和975nm的抽运光为例，当输出激光为1090nm时，得出975nm抽运光产生的斜率效率最高并可高达约87%。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。