查询词典 solution formula

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。

In this paper, after taking over coupling effect between electronic spin and orbital angular momentum, to revise the formula of electronic angular momentum in Bohr's theory, and electronic speed formula is obtained in a single-electron system, and to correct the energy level formula of atomic orbit in Schr? dinger's method by relativistic effect, the theoretical improving formula is built for spectrum fine splitting calculation, the calculated values are in good agreement with experimental ones, and reflect changing law of spectrum fine splitting values.

本文在考虑了电子的自旋角动量与轨道角动量的耦合作用后，通过对Bohr理论中的电子运动角动量的修改，推导出单电子体系的电子速度公式，结合对Schrdinger的原子轨道能级表达式相对论效应修正，从而得出本文的氢及类氢离子光谱精细结构值的理论计算公式，应用此改进公式，所得的计算值与实验观测值符合得很好，计算结果也反映了氢及类氢离子光谱精细结构数据变化的规律性。

METHODS: C57BL/6J mice (15/group) were respectively received mash as AIN-93G formula, or 1% cholesterol supplemented AIN-93G formula, or 1% cholesterol and 14% long chain triglyceride rich in myristic acid supplemented AIN-93G formula, or 1%cholesterol and 14% MCT (caprylic acid/capric acid: 3/1) supplemented AIN-93G formula for 6 weeks.

分别用AIN-93G配方饲料，含1％胆固醇的AIN-93G配方饲料，含1％胆固醇和14%富含豆蔻酸的长链甘油三酯的AIN-93G配方饲料，含1％胆固醇和14％的中链甘油三酯的AIN-93G配方饲料喂养C57小鼠6周，每组15只。

By academic analyzing, it is concluded that two order discrete paraxial approximation formula of the paper, multiple transmitting formula and polynomial extrapolation formula are the different forms of continuous paraxial approximation formula, so they are with nearly equivalent precision and stability and with equivalent applicability and limitation.

据此文献[3]将傍轴近似公式归结为一类从特定的无限域模型导出的人工边界条件，并且提出了新的从一般无限域模型导出的具有普适性的、称为"多次透射公式"的局部人工边界条件。那么，是否也可以从一般无限域模型导出具有普适性的傍轴近似公式呢？

Combining Inclusion-Exclusion principle with Disjoint Sum of products formula,the new formula contains terms which correpond one by one to a class of special subnetworks. For a given newtork,terms of new formula are fewer than those of corresponding stryanarayna formula. Finally,an example illustrates our conclusion.

该公式本质上是将容斥原理公式和不交和公式融合在一起，公式中各项和网络的一类特殊子网络一一对应，与相应的Satyanarayanna公式比较，该公式包含更少的项和更少的算术运算，并给出一个算例验证上述这个结论。

Lagrange interpolation focus on the application of the formula .The comparison between the method of Transform and that of Lagrange's interpolation formula in square matrix form is made. Also the form of Lagrange's interpolation formula is generalized to include the double root case.The application of the generalized lagrange's interpolation formula in square matrix to solving state equations is found to be effective.

重点介绍了Lagrange插值公式在状态方程求解中的应用，用对角矩阵及相似矩阵的性质证明了，当状态转移矩阵中方阵的特征根相异时，拉格朗日插值公式与Laplace变换法对表达具有一致性，并用极限方法对方阵含二重根时拉格朗日插值公式的应用进行了推导。

Both upper bound formula and lower bound formula of the global truncation error of Euler method have been derived theoretically.After making certain approximat e processing,the derived upper formula changes into current upper bound formula.

从理论上推导出了欧拉方法的整体截断误差的上限公式和下限公式，作一定的近似后，得到的整体截断误差上限公式就变为现用的整体截断误差上限公式。

Finally it offers the analysis of the fault-tolerance system as well as its test verification.

这样，运行于空间环境中的系统的设计目标就是在保证系统实时性

However, it is still difficult to find out the real reason of the increase of the keratinized gingiva during the orthodontic extrusion whether it is due to the proliferation of the gingival tissue or to its elastic nature, that is because the proliferation of the fibroblasts as well as the connective tissue changes in volume and the intra-fibers spaces were all immeasurable in most of the studies.

然而，仍然难以找到真正的原因增加的角化牙龈在正畸挤压它是否是由于扩散的牙龈组织或其弹性性质，这是因为增殖的成纤维细胞以及作为结缔组织的变化量和内部纤维空格都是不可估量的，大多数的研究。