查询词典 solution set of equation

In this paper, we will investigate the matrix equation in composition over a complete Brouwerian lattice. First, we give an equivalent condition for the solvability of this equation, i.e. theorem 2.2.3 in this paper: The matrix equation in composition over a complete Brouwerian lattice is solvable iff is the minimal solution of this equation.

本文主要探讨完备Brouwer格上的型矩阵方程，首先给出该类矩阵方程可解的一个等价条件，即本文的定理2.2.3：完备Brouwer格上的型矩阵方程可解的充要条件是是它的解，且是最小解。

This dissertation is devoted to a very important equation system among differential equation systems------quasi-linear equation system, as is a important topic of equation system(especially when discussed shock wave solution), Often appear in such research fields as Hydrokinetics, the semiconductor establishes in physical theory ,Chemical reaction theory , project, Biology , Communication and Ecology etc.

中文摘要：本论文主要研究了微分方程中的一类很重要的方程组——拟线性方程组，它是微分方程的一个重要的课题，常常出现在流体动力学、半导体设置的物理理论、化学反应理论、工程、生物、通信和生态等研究领域中。

An inhomogeneous Benjamin-Davis-Ono-Burgers equation including topographic forcing and turbulent dissipation is derived in terms of the quasi-geostrophic vorticity equation, an approximate analytic solution of the BDO-Burgers equation with a small dissipation is obtained, the time variations of mass and energy of the algebraic solitary waves are discussed, and finally, the forced BDO-Burgers equation is integrated numerically and the numerical solutions are given for a given basic flow with a weak shear and a localized topographic forcing.

利用包括地形外源和湍流耗散的准地转涡度方程导出了包含强迫项和湍流耗散项的非齐次强迫BDO-Burgers方程，求出了小耗散存在情况下BDO-Burgers方程的近似解析解，讨论了代数孤立波的质量和能量的守恒关系，最后，对给定的弱切变基本气流和局地地形强迫，数值积分强迫BDO-Burgers方程，求得了不同参数下的数值解。

The bubble-point method and tridiagonal matrix method are proposed as solution of MESH equations(Material equation, phase Equilibrium equation, Summation equation, Heat equation), through which equations could be solved quickly and steadily, and the composing mole fraction at the top of tower and Key composition profiles and temperature of every stage are given.

提出采用三对角矩阵法和泡点法(BP，Bubble Point)相结合作为模型求解的解决方案，可快速稳定地求解复杂的MESH方程组，并给出塔顶液相组分组成和各塔板的关键组分分布及温度分布。

This one-way wave equation fits eikonal equation and transport equation corresponding to full acoustic wave equation in travel-time and first order amplitude. According to the perturbation theory often used in inverse solution, we split the velocity field into intraformational constant velocity background and variable velocity disturbance. Then we calculate time-shift quantity of migration and amplitude correction coefficients for wavefield depth continuation in total uniform formation and each formation.

基于反问题求解中常用的摄动理论，把速度场分裂为层内常速背景和变速扰动，求得整个均匀层波场深度延拓的偏移时移量及振幅校正系数、各层的偏移时移量及振幅校正系数，从而得到一个基于傅里叶有限差分法的双域保幅叠前深度偏移算子方程。

Material and MethodsRA Rabbit Model group: 15 early RA rabbits of the same weight and variety Control group:10 normal rabbits of the same weight and varietyMethods of making RA rabbit model:elect 15 normal rabbits of the same weight and variety, dissolve Ovalbumin in 0.9% sodium chloride solution, to make the solution of 20mg/ml concengtration, blend the same quantity of complete Freund′s Adjuvant equably ,inject the mixed solution into endermic tissue of the rabbit′s scapular section, making the rabbits allergic, inject 1 ml of the mixed solution to one rabbit every time, inject 1 ml of the mixed solution in 5 different places of the rabbit′s scapular section, inject the rabbit one time every week,inject 3 weeks continuously,it turned out to be that the rabbits will be allergic, inject Ovalbumin blent with the 0.9% sodium chloride solution into the knee joint cavity of the rabbits in the fourth week, 5 mg Ovalbumin every knee joint cavity,two knees of every rabbit of the 15 rabbits are both injected,the arthrosis diameter and the exterior temperature of the knees will be added obviously in 24 hours,and they will drop gradually,at the time of the 14th or 21th day, the arthrosis diameter and the exterior temperature of the knees will get to the balance time,the incidence rate of RA is 100%.after the RA model succeeds,it is the early time of RA from the first week to the fourth week,after the fourth week,it is the late time of RA, the cartilage of the femoral condyle and the subchondral bone cortices will be changed unrecoverily.

资料与方法RA模型组：早期RA家兔模型15只，品种及体重接近。对照组：正常家兔10只，品种及体重接近。RA家兔模型制作方法：选取15只成年家兔，体重、品种接近，将卵蛋白溶解于生理盐水，配成浓度为20mg/ml的溶液，与等量完全弗氏佐剂混匀，注入家兔肩胛区皮下致敏，每只家兔每次注射1ml，于肩胛区5个不同区域注射，每周一次，连续注射3周而致敏，第4周向膝关节腔注射卵蛋白生理盐水溶液，每只关节腔注射5mg卵蛋白，15只家兔膝关节全部注射，24h内此关节直径和表面温度大幅度上升，以后缓慢下降，至14～21d达到平台期，发病率达100%。造模成功后第1～4周为早期改变，第4周以后出现不可逆的关节软骨及骨破坏。采用高频超声对RA模型组与对照组的膝关节髌上囊液体厚度、滑膜及股骨髁软骨厚度及软骨下骨皮质的回声情况进行对比观察。结果RA组模型组膝关节髌上囊积液及滑膜的厚度明显厚于对照组，其股骨髁软骨的厚度与对照组相比无明显差异，其软骨下骨皮质与对照组相比无明显改变。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

The polymeric sol is obtained by process of preparing a calcium salt solution, containing calcium ethoxide dissolved in organic acid, and a phosphate solution, containing triethyl phosphite or triethyl phosphate dissolved in the organic acid, mixing the calcium salt solution with the phosphate solution to produce a mixed solution, and aging the mixed solution.

本发明的磷酸钙化合物的聚合物溶胶是通过如下步骤制备的：制备含有溶解在有机酸中的乙醇钙的钙盐溶液和含有溶解在该有机酸中的亚磷酸三乙酯或磷酸三乙酯的磷酸盐溶液；及将该钙盐溶液和该磷酸盐溶液混和制得混合溶液，并老化该混合溶液。

An alkaline solution containing mercaptides is regenerated in an improved process wherein the alkaline solution to be regenerated containing a suitable oxidation catalyst is contacted with an oxygen-containing solvent which is immiscible with said alkaline solution in a reaction zone comprising a plurality of fibers positioned longitudinally within a conduit, whereby the two liquids are in contact while concurrently flowing through said reaction zone during which the mercaptides contained in the alkaline solution are oxidized to disulfides and are simultaneously extracted from the alkaline solution into the solvent solution.

包含 mercaptides 的碱解决在一个改良的程序被再产生在何处碱的解决被再产生包含一个适当的氧化催化剂与被说反应的碱的解决组成一个纤维的多数地域纵观地放置在一个导管里面的对一个包含氧的溶剂感到不能相混合的一起连络，那里当协同地流动过说的反应地域的时候，这二种液体保持接触在哪一个期间包含在碱的解决 mercaptides 被使氧化到 disulfides 而且同时地从碱的解决到有偿付能力的解决被吸取。

The oil shale ash is disintegrated into fine powder less than 150 eye to be calcined at a certain temperature, then sulfuric acid solution is added for performing acid dipping, after solid-liquid separation and solid residue removal, aluminum sulfate solution is obtained and is then filtered after sodium hydroxide solution is added in, further metallic ions as Ca2 , Mg2 , Fe3 , Fe2 and the like are filtered from the solution, thereby sodium aluminate solution is obtained, gas of carbon dioxide is communicated into the sodium aluminate solution to obtain aluminum hydroxide sediment, and after drying and calcining aluminum hydroxide powder is obtained.

将油页岩灰渣粉碎至＜150目的细粉，在一定温度下煅烧，加入硫酸溶液进行酸浸，固液分离，去除固体残渣，得硫酸铝滤液，加氢氧化钠溶液后过滤，滤除溶液中的Ca 2 、Mg 2 、Fe 3 、Fe 2 等金属离子，得偏铝酸钠溶液，向偏铝酸钠溶液通入二氧化碳气体，得到氢氧化铝沉淀，经烘干、煅烧得到氢氧化铝粉末。

If you were not , and OS X just booted normally, have no fear.

如果你没有，和OS X刚刚启动通常，没有恐惧。

I only want to preserve our all .

我只想保存好我们的一切