最大下界

If all the flows getting into the system were constrained by the leaky-bucket parameters, the maximum cell delay and the buffer content bound were got when the capacity of the crosspoint was enough, and the maximum cell delay and the buffer capacity bound which can guarantee the maximum cell delay were also got when the content of the crosspoint was not enough.

在各数据流都由令牌桶参数约束的条件下，得到了交叉点缓存容量足够大情况下的最大信元时延和缓存临界容量大小，还得到了交叉点缓存容量不足够大情况下的最大信元时延以及保证信元具有时延上界的缓存临界容量大小。

We make the following assumption for When 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of Least squares estimate have been discussed in many documents. Considered 2 is nonnegative definite matrix, this thesis derives Best linear unbiased Estimate of parameter matrix B and estimable parameter function KBL under the meaning of matrix nonnegative definite and the property of maximum probability of BLUE is investigated.

当∑＞0时，众多文献讨论了回归系数阵的各种估计及LSE的有效性，本文考虑了当∑≥0的情形，给出了回归系数阵B及其可估参数函数KBL的在矩阵非负定意义下的最优估计，研究了它的一个最大概率性质，并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件，在此基础上给出了均值矩阵的最小二乘估计与BLUE的偏差估计，定义了LSE相对于BLUE的一个相对效率，并给出了它的界。

The greatest lower bound of A is also called the infimum of A.

A的最大下界边称为A的下确界。

Firstly, we give a new upper bound of a mixed graph′s largest Laplacian eigenvalue, which is more precise. And also we give a lower bound of a mixed connected graph′s largest Laplacian eigenvalue.

首先给出了混合图的最大Laplace特征值的一个新的上界，并且用实例说明我们的结果与以往结果相比更精确，同时也给出了一个连通混合图的最大Laplace特征值的一个新的下界。

We determine the bounds on the upperand lower orientable strong radius and strong diameter of graphs satisfyingthe Ore condition. Let G_1, G_2 be any connected graph, we present the exactvalue of srad(G_1×G_2), consider the relationship between sdiam(G_1×G_2) andr(G_1×G_2), d (G_1×G_2). Moreover, we determine the values of the lower orientablestrong diameters of some special graphs. Furthermore, we give the exact value ofSDIAM, a lower bound for SDIAM, an upper and lowerbound for SRAD and SRAD, respectively.

对满足Ore条件的图，给出了最小强半径、最大强半径的上、下界；对笛卡尔乘积图G_1×G_2，确定了G_1×G_2的最小强半径与G_1×G_2的半径以及G_1和G_2的最小强直径之间的关系，并进而确定了一些特殊笛卡尔乘积图的最小强直径的值，确定了SDIAM的值，SDIAM的下界，SRAD和SRAD相应的上、下界。

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

Through establishing the priori estimates for the approximation solutions, we pove the existence of global generalized solution by using the compactness principle and obtain the global property for the generalized solutions in the space L〓. At the last, a new method is used to prove the uniqneness which is a good results, at some extense, under generalize conditions.

运用De Giorgi的最大模估计方法，证明了解的整体上界估计和准衰减型的估计，进一步，在边值和初值具有正的下界条件下，证明了解的一致下界估计，得到了深刻结果。

Lithologic character of Eogene syste is interbedded sandstone and mudstone primarily, including the thin layer oil shale, Neocene- Quaternary system is set of rivers deposits. Based on this, through the reaserch of ateral correlation and distribution characteristics of every structural layers show that: Paleozoic synthem overall thickness of relatively stable.The residual thickness of Mesozoic synthem is difference in the horizontal, Residues in the horizontal thickness of greater difference, to the greatest thickness achieve to 4500m. Eogene syste has obviously fault depression basin deposition characteristic, the thickness of many sags achieve to 3000 m ,from Neocene, the stratum crosswise mop tended to be stable.

在此基础上，通过对各构造层横向对比以及展布特征的研究表明，古生界构造层整体厚度相对稳定，冷武-奥陶系残留厚度在1200m左右，石炭-二叠系残留厚度在800m左右；中生界构造层残留厚度在横向上差异较大，最大厚度达到4500m，其中，下-中三叠统仅发育于南部小部分地区，最大厚度在1000m以上，侏罗系-下白垩统整体具有南厚北薄的展布特征，南部冠北洼陷厚度最大，达到3500m；新生界古近系具明显的断陷式盆地沉积特征，多个洼陷厚度在3000m以上，新近纪以后地层横向展布趋于稳定。

Using the independence number and the girth, the upper bound of the Betti deficiency is obtained. A better lower bound on the maximum genus of a graph is obtained and a previous result is improved.

利用图的独立数和围长，得到了一个Betti亏数的上界，进而得到了最大亏格的一个比较好的下界，改进了黄元秋先前的一个结果。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。