数学模型

The previous research, in which macro-kinetics of ammoniation of phosphoric acid was measured in a double magnetic stirring reactor,found that the reaction between wet phosphoric acid and gaseous ammonia was a rapid reaction controlled by the gas-film mass transfer.

本文采用数学模型法，根据氨化反应过程的机理，通过小试建立数学模型并经合理简化，再通过中试对模型进行修正和完善，最后用工业大装置加以验证，使所得的模型可用于工业放大。

Show model combines growth model, math model and VR technologies to design the proper object structure of each organ of virtual plant. First of all,research background, research content of virtual plant area and Virtual Reality technology are introduced. The concept of VR and research content of virtual plant are defined. Secondly, we analyze math model of virtual plant, including Bezier curve, NURBS curved surface, fractal system, L-system and Catenary curve. Thirdly, we give show model of virtual plant in detail. Finally, the design of the platform and growth model on XML script is introduced , and how to show the virtual plant in the platfrom is discussed too.

本文首先介绍了虚拟植物领域的研究背景、研究内容和虚拟现实技术，明确了虚拟现实的概念和虚拟植物的研究范畴，然后介绍了虚拟植物器官的数学模型，对各个器官展开了拓扑结构分析，建立有针对性的数学模型，先后介绍了Bezier曲线，NURBS曲面，分形系统，L-系统和悬链线曲线，接着详细分类介绍了虚拟植物器官的显示模型，最后介绍了虚拟作物平台的设计，平台中基于XML脚本的生长模型，以及虚拟作物在作物平台中的显示。

With the investigation of the domestic and foreign literature systematically, the bases on the domestic and foreign present research and the comprehensive utilizations of the various knowledge of fluid mechanics in porous medium, reservoir engineering, mathematical physics, perforation completion, numerical simulation and so on, this article takes numerical simulation of gas reservoir of water solubility as the research aim which has completed following research works and obtained the corresponding research results: it analyzes the nature of the Water-soluble gas and formation water as well as the influent factors of the solubility through the study of massive materials; It establishes mathematical models three-dimension, the dual medium, the gas-water phase through the way of finite difference in the migration of water-soluble gas, which describes the entire process of release, migration and production in formation, where it considered the problems of variable bubble point; According to the numerical models of gas reservoir of water solubility it provides solution procedure that based on black oil model; It discovers that there will obtain the good effects in the lowly speed of development through simulation; the reinjection of formation water may largely enhance the produce degree of water-soluble gas when we consider reinjection in simulator; It considered the influence of perforated completion on development so as to increase the simulator"s versatility, It discovers that the simulator may reflect the conditions of development when we exanimate he simulator"s reliability with the empirical datum.

本文以水溶性气藏数值模拟研究为研究目标，在系统调研国内外文献、深入分析国内外研究现状的基础上，综合利用渗流力学、油气藏工程、数学物理方法、射孔完井以及数值模拟理论等多方面的知识，完成了以下研究工作并取得相应的研究成果；①通过对大量的资料调研，分析了水溶气、地层水性质、储层地质性质以及影响气体在水中溶解度的因素。②考虑到由于高压产生的大量水力裂缝，采用有限差分方法建立水溶气运移的三维、双重介质、气-水两相全隐式数学模型，该模型描述了水溶气在地层中的释放、运移和采出的整个过程。③在原有黑油模型的基础上，根据水溶性气藏数值模型编制了该数值模型的求解程序，该程序可以求解单重、双重介质两种情况。④通过模拟不同开采速度对水溶气开发效果的影响，发现开采速度较慢的时候可以取得较好的开采效果。⑤在模拟器中考虑了注水对水溶性气藏开发的影响，地层水回注可以大幅度提高水溶气的采出程度。⑥为增加模拟器的通用性，在模拟器中考虑了射孔完井方式对开采的影响。⑦检验模拟器计算的可靠性，发现在使用实验数据对水溶性气藏进行模拟时，模拟器可以很好的反映气藏开发的状态。

According to mechanism of ECBM/CO2 sequestration, a mathematical model was developed. In the mathematical model, two-phase flow, multiple gas components and mixed gas sorption, impact of coal matrix shrinkage and swelling on permeability, pressure loss in wellbore were studied.

给出了多分支井模拟CO2注入开采数学模型，模型考虑了气水两相流动、多组分气体吸附、煤基质膨胀和收缩对渗透率的影响以及分支水平井井筒压降；根据数学模型得到了相应的数值模型和计算程序，进行了模拟计算对比。

In this paper, the propagation and focus properties for several modes describing hollow beam are analyzed, and the focus properties for hollow gaussian mode are particularly discussed. Furthermore, a new mode, high-order Bessel-Gauss mode, is put forward to describe hollow beams. The results for high order Bessel-Gauss beams propagating through lens focusing system and free space are derived by terms of Collins integral formula.

本文分析了几种描述空心光束数学模型的传输特性和聚焦特性，着重讨论了描述非中空光束的数学模型的聚焦特性；同时提出了一种描述完全中空的空心光束的新模型――高阶贝赛耳高斯模型，并且运用Collins积分公式，分析了这种新模型的空心光束的传输特性和聚焦特性。

The study methods: Based on digital printing and offset printing technology principle, the basic parameters having effect on the ink-jet printing output quality were analyzed. And the mathematics models between the ink quantity and the solid density, and the relation between the gamma and printing contrast were established. The relation among the output dot area coverage, the original dot area coverage and the dot-gain percent was analyzed. And the mathematics models of printing characteristics curves and dot-gain curves were established. The factors influencing the dot-gain were analyzed, and then the dot-gain compensation function was acquired. All the models were verified by the method of regression analysis. And the precisions of the models were obtained by the correlation coefficient and multiple correlation coefficients.

研究方法：根据数码印刷以及胶版印刷的工艺原理，分析了影响喷墨印刷输出质量的基本参数，建立墨量与样张实地密度、γ与相对反差的数学模型；分析输出网点面积率、标定网点面积率以及网点扩大率三者之间的关系，建立网点扩大曲线和印刷阶调复制曲线的数学模型，并对网点扩大的影响因素进行了分析，导出了网点扩大补偿函数；运用回归分析方法分析模型，并用相关系数和复相关系数检验回归模型的显著性；使用灰平衡方程，结合回归法得出灰平衡控制曲线。

Flat plate steady mathematical model and non steady symmetric model are presented, the analytical solution of temperature of powder is derived on the basis of non steady symmetric model in spheroidal coordinates with the methods of mathematical transformation and principle of superposition .

对点火问题进行研究，给出了两种点火的数学模型；平板定常模型和球对称非定常模型。从火药颗粒的球对称非定常模型出发，利用叠加原理和数学变换导出了火药颗粒表面温度的分析解。该研究对深入研究点火理论和起始弹道学有一定的作

This thesis,starting from working out the arrest points and the infl ection points of the function curves of the grey mathema tical model GM(1:1 )and its residual correction model and residual period model, derives the conditions for empliying these grey models to obtain a higher class of accuracy,thus enabling the user to decide which model should be used in the light of the state of given initial sequency data.

从求得灰色数学模型GM(1.1)及其残差指数修正模型和残差周期修正模型函数曲线的驻点与拐点入手，导出使用这些灰色模型取得较高精度的条件，让使用者可依据初始序列数据的态势决定采用哪种数学模型，并且在结果未揭示以前便可大体上估计到拟合精度是否令人满意。

At last, the software for upper machine and lower machine is introduced.Chapter 3, on the basis of the experiment on the nano feeding control platform, the mathematic modal of drive parts is established considering that the nano feeding under large feeding force has some open air temperature random disturbance phenomenon which influences the feed precision.

第三章，首先对建立数学模型的分步拟合方法进行了介绍，接着，在实验的基础上，通过拟合的方法得出纳米级热驱动部件输入功率与输出位移的数学传递函数以及外界温度干扰与输出位移的数学传递函数，最后建立了干扰情况下的纳米级热驱动部件数学模型。

In order to understand the operation safety and pipe service life span of rear superhearter, the essay established dynamic mathematic model of single piece of screen of rear superhearter, including the following sub-models: flue gas side model, steam side and metal pipe wall mathematic model, flow calculation model and wall temperature calculation model.

为了更好地了解后屏过热器运行的安全性和管子使用寿命，本文建立了后屏过热器中单独一片屏的动态数学模型，其中包括以下几个子模型：烟气侧模型、蒸汽侧和金属管壁的数学模型、流量计算模型和壁温计算模型。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。