近似公式

The basic concept in these sections is replacing backward Euler's method by modified backward Eulers's method to approximate the characteristic differential equation and discretizing the convection-diffusion equation at the middle point of the approximate characteristic curve, which will make the convective term get up to second order accuracy.

这三节的基本离散方法是用改进的Euler公式代替向后Euler公式来近似特征微分方程，并且将近似特征线的中点作为离散节点，使得对流项的离散精度提高到二阶，对于扩散项，将其转移到待求时间层进行离散。

In this paper, Galerkin method is employed. First, test functions to satisfy natural boundary conditions are selected. Then the approximate analytic formulations of the system frequency are derived. Meanwhile the approximate analytic formulation of the limit velocity is got.

采用直接法，首先选取满足自然边界条件的试函数，而后求出了系统固有频率的近似解析公式，同时也得到了极限流速的近似解析公式。

We discuss asymptotically best linear unbiased estimators of the Logistic population based on selected order statistics and give the formula of computing the ABLUE, the variance and the covariance of the ABLUE in limit, and properties of the ABLUE, and so on. We give the optimum chosen of spacing which is the ABLUE with maximum asymptotic relative efficiency based on complete sample when selected order statistics number is less than 10, and obtain its maximum asymptotic relative efficiency.

讨论基于Logistic总体Ⅱ型截尾样本的若干个样本分位数的总体分布参数的近似最佳线性无偏估计；给出了该近似最佳线性无偏估计的计算公式，估计方差与协方差的极限表达式及估计量的大样本性质等；给出了全样本，样本分位点个数固定，但不超过10情形下，使上述近似最佳线性无偏估计有最大相对联合估计效率时，样本分位数选取法及最大相对联合估计效率；为大样本情形下，该近似最佳线性无偏估计的应用提供了理论依据。

This makes more and more people pay more attention to studies and applications of numerical simulation in thermal recovery. In this research, we have developed a reliable mathematical model for thermal recovery, which takes a full consideration of the effect of viscos, gravitical and capillary forces on the three-phase flow of gas, water and oil, the effect of the temperature on the medium characteristics of liquid and solid, the phase equilibrium of gas-liquid in each component, heat transportation including connection, conduction and radiation as well as heat losses in both the overburn and underlying strata. In the space discreation of the mathematical model, we have proposed a new method based on the improvement of the conventional nine-points difference approximation, which has a higher difference accurancy.

本项研究以热力采油的主要机理为基础，充分考虑在粘性力、重力和毛管力作用下油水气三相流动，考虑温度对各种流体和固体介质物性的影响，考虑每一组分中汽液两相的相平衡，考虑热在地层中的传导、对流和辐射以及上下盖层的热损失，利用热力学第一定律、质量守恒定律和流体迁移定律，建立了正确可靠的注蒸汽数学模型；在对数学模型进行空间离散时，利用控制有限体积积分法，对以往的九点差分近似作了合理的改进，使其具有较高的差分近似精度：结果表明，该公式的近似精度要比以往文献中所给的九点差分近似精度高，可以认为，在油藏数值模拟中，如果遇到非均质情况，使用这种九点差分近似更合理。

In this thesis the process of constructing the non-perturbative Hamiltonian theory is de-scribed and is applied to estimate the vacuum condensate. It contains the following contents:At the very beginning, by using the path integral method and eliminating the gluon freedom, aGCM action 〓 of current quarks including lower order current-current coupling was derivedfrom the QCD Lagrangian and the effective Hamiltonian operator that could hardly be doneby the normal methods was derived. After doing this, the broken vacuum is introduced whichincludes quark-antiquark condensate through the generalized Bogoliubov-Valatin transformation,the effective Hamiltonian of constituent quark was derived. The detailed formulas containingthe spatial current-current coupling term for the effective Hamiltonian and gap equations wasworked out by parameterizing the correlation kernel as a quadratic potential. And then, the gapequation was solved and the quark-antiquark condensate of vacuum was studied both in the casesof instantaneous interaction and retarded interaction. In the end, the effective Hamiltionian withtwo-body quark-quark interaction was derived with one-body approximation, and with the helpof the functional integral method the coupling non-linear dynamic equations for systems withnuclear matter was derived. Finally, these equations were solved by selfconsistent method andthe effect of nuclear matter on vacuum condensate was studied. The spatial current-current coupling term is too difficult to handle, hence the correlationkernel is assumed to be not important and usually omitted in the pure vacuum condensate, andthe instantaneous interaction generally is adopted. Retaining the spatial current-current termand partial retardation effect, the quark pairs condensate in pure vacuum was studied, and theeffect of quark mass was also studied. At present, little study is focused in the case with nuclearmatter and spatial current-current term also omitted. Under the approximation with partialspatial current-current term, the effect of nuclear matter on vacuum condensate was studied.

本论文描述了量子色动力学整体色对称模型哈密顿量方法的构建过程，得到了反映正反夸克对凝聚真空结构的关于组分夸克的有效哈密顿量算符，它隐含了胶子作用，并且准确至流-流耦合项；接着，通过参数化哈密顿量中的夸克作用关联核，导出平方禁闭势参数化选择的哈密顿量的具体公式和能隙方程；随后，应用公式，编程求解，考察了瞬时作用下和部分延迟作用下真空的正反夸克对凝聚，在计算中保留了空间流-流耦合作用；之后，导出瞬时势和延迟势下包含二体作用项的哈密顿量公式，并采用单体化近似，通过泛函变分方法得到核物质存在时耦合的非线性动力学方程；在保留部分空间双流耦合作用的近似下，求解核物质的动力学方程，考察核物质密度对真空凝聚的影响，以往考察真空凝聚，对关联核的选用，由于空间流-流耦合项不易处理，也认为作用不大，常忽略该项，并且常采用瞬时作用；本文保留空间双流项和部分延迟作用，考察了真空情形的夸克对凝聚，还考察了夸克质量对纯真空凝聚的影响，以往对核物质存在情形的真空凝聚考察很少，也都忽略空间流-流项，本文在考虑部分空间流-流项近似下，考察了核物质存在对真空凝聚的影响。

In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative.

该文通过对圆形断面均匀流方程与临界流方程的数学变换，分别得到其正常水深与临界水深的牛顿迭代公式，同时，通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算，利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式，并以此近似计算式为初值，用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。

According to the characteristic that the definition point of the Q matrix of wave front is always located on the extremum point on the axis of the beam, a three-dimensional formula for the rectificative factor of phase in complex ray paraxial approximation is proposed, which calculates the rectificative factor of phase directly without considering the calculation of the main directions and curvatures and the rotation of the coordinates, thus simplifying the paraxial approximation calculation by the complex ray expansion method.

根据波前Q矩阵的定义点总位于波束轴上极值点的特点，提出了三维复射线近轴近似相位校正因子计算公式。该公式不用考虑主方向和主曲率的计算和坐标旋转，直接计算相位校正因子，从而简化了复射线展开法的近轴近似计算。

In addition, laser Raman scattering and low temperature photoluminescence measurements are carried out, the GaSb-like LO mode, AlSb-like LO mode and the coupled mode between LO phonon and plasmon are observed. According to the dependence of the GaSb-like LO mode frequency on Al composition, an empirical formula was obtained for determining the Al composition.

用激光喇曼散射和低温光致发光研究了材料的光学性质，观察到了类GaSb的LO模和类AlSb的LO模以及LO声子与等离子体激元的耦合模L，并根据类GaSb的LO模随Al组分x的变化规律，得到一个计算Al组分的近似公式。

Based on collected data of more than handred exist ships for deep sea trawlers , the main parameters are analysed.

在收集大型远洋拖网渔船百余艘实船资料的基础上，对其主要参数进行了分析，探索了它们之间的关系，得出了一些近似公式，可用于设计工作中，也可作为船型论证的基础。

After the deduction of high order temporal and special difference approximation to the wave equation, the snapshots of wave propagation in an infinite monoclinic media and synthetic three components surface and VSP data for a flat layered model are presented.

推导了交错网格中时间和空间上的高阶差分近似公式，并针对二维单斜各向异性介质，给出了具体的空间差分网格的形式。在上述理论的基础上，利用交错网格高阶有限差分技术，首次对单斜各向异性介质中波的传播特性进行了模拟。

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。