查询词典 solution set of equation

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

Aiming at the problem that solution FEMequation set needs too much memory, segregated solotion methOd has beenadopted and for the first in China E l em ent- B y- E lement has been introduc edwhen solving flow field parameter equation sets. EBE technology need notassemble and store the global stiffness matrix, and minish effectively memoryrequires of solution equation set, moreover it has inherent high parallelity, andadvance equation solution.

针对求解流场有限元方程组占用计算机内存资源过多、限制求解规模的缺点，采用分离式求解法，在求解流场各参数方程时，在国内首次引入EBE技术，EBE技术不必组集和存储总刚矩阵，能有效地减小了方程组求解时对内存空间的要求，同时EBE技术具有内在的高度并行性，能有效提高方程组的求解速度。

Multiple trials is the basic concept of many parallel simulated annealing. It is to perform multiple trials at the same time to search acceptable solutions. The division simulated annealing with no communication and The clustering simulated annealing are two common types of parallel simulated annealing methods. The division simulated annealing with no communication makes each processor generate its own adjacent solution from its own current solution and compute the acceptance probability for a adjacent solution. Each of the processors searches solutions without communicating each other. Clustering simulated annealing makes each processor generate its own adjacent solution from a common current solution and compute the acceptance probability for each adjacent solution. Then, it decides which adjacent solution should be used to replace current solution according to a pre-specified rule.

许多平行模拟退火法之理论依据为多向试验，利用同一时间探索更多方向的试验来拓展搜寻的广度或深度，不进行沟通的分工模拟退火法(the division simulated annealing with no communication)以及丛集模拟退火法(the clustering simulated annealing)皆为平行化的模拟退火法，前者定义为各个处理器针对各自的起始解进行搜寻，产生各自的搜寻序列，在搜寻过程中处理器不进行任何沟通，各处理器仅针对自身之目前解进行搜寻；而后者定义为让所有处理器针对同一目前解进行运算搜寻各自的可能解，并各自决定其产出解之接受机率，最后根据事先决定之规则进行沟通比较，挑选其中一个可接受解取代目前解。

Therefrom; heating said waste edible oil from which solid materials have been removed to a predetermined temperature, thereby removing moisture and materials of odor contained in the waste edible oil therefrom by evaporation; dissolving in alcohol a catalyst containing at least one type or more types of alkaline material selected from a group comprised of at least potassium hydroxide, potassium carbonate and potassium alcoholate, thereby preparing an alcoholic solution containing the catalyst; mixing said waste edible oil from which said solid materials, moisture and materials of odor have been removed with said alcoholic solution containing the catalyst and stirring the waste edible oil and alcoholic solution, thereby accelerating a catalytic reaction between the waste edible oil and the alcohol and obtaining a reaction product between the waste edible oil and the alcohol; separating said reaction product into a light solution and a heavy solution; mixing the light solution obtained in the separation step with a solid absorbent, thereby impurities such as residual catalyst, odor material, moisture contained in the light solution being absorbed by the solid absorbent; and separating and removing said solid absorbent from a mixture of the solid absorbent having absorbed the impurities and the light solution.

完成前述对象，根据这项发明的特点是获得的柴油燃油从废油脂透过几个步骤：去除固体材料包含在一个废油脂倾倒，从餐厅，食品厂，民政等因此；暖气说，废油脂从哪个固体材料已被调离到一个预定的温度，从而消除了水分和材料的气味，载于废油脂因此由蒸发；溶解在酒精的催化剂至少含有一种或更多类型的碱性材料选定由一组组成的至少氢氧化钾，碳酸钾和钾，醇，从而准备一醇溶液中含有催化剂；混合说，废油脂从哪个说，固体材料，含水率和材料的气味已被剔除与说，酒精性解决方案载有催化剂和搅拌废物食用油及含酒精的解决办法，从而加速催化反应之间的废油脂及酒精和获得反应产物之间的废油脂及酒精；分开说，反应产物成为一个轻型的解决方案和沉重的解决方案；混合轻解决方案，获得了在分离一步一个坚实的吸水性，从而杂质，如残留的催化剂，气味的物质，水分，载于轻解决方案，被吸收的固体吸收剂；分离和消除说，固体吸附剂从混合物对固体吸收剂吸收了杂质和轻便的解决办法。

Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.

利用矩阵技巧和所建立的矩阵理论，给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外，还有重要的应用价值。在具有对合反自同构的正则环上，给出了四类矩阵方程组有双对称解，中心对称解，斜中心对称解，广自共轭解，斜广自共轭解，自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。

By using constructive methods and complicated techniques of matrices, necessary and sufficient conditions for the existence of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, skewbisymmetric solution and various interlaced solutions over a finite central algebra Ω to systems of generalized Sylvester matrix equations overΩ are presented.

利用构造方法和复杂的矩阵技巧，研究了有限维中心代数上的多项式环Ω上的广义Sylvester矩阵方程组在Ω上有自共轭解，斜自共轭解，广自共轭解，斜广自共轭解，中心对称解，斜中心对称解，双对称解，斜双对称解及其各种交错解的充要条件。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

The equation for item level from item slot is a logarithmic equation and the equation from item level to weapon DPS would require an exponential equation, therefore an equation from item slot value, the value prior to item level, to weapon DPS would be a linear equation.

武器DPS是物品等级中一个很有趣的属性，因为它似乎有多种计算方法。最近加入的传家宝物品可以提出和回答这个问题。物品等级在57以前的时候，它的计算方法和蓝装的线形公式一样，传家宝武器不是线形增长的，似乎是介于线形和多项式增长之间。在58-67的时候，传家宝武器的DPS随物品等级成指数增长。在68-80的时候，武器DPS也是成指数增长，但是速度不同。在100-226之间的史诗物品成相同的指数增长。

The asymptotical properties of KdV equation and KP equation exhibit the soliton behavior when some conditions are satisfied, and in some cases the parameter matrices describing the interaction between two solutions is quite simple. Two kinds of solutions of the second coupled equations of AKNS hierarchy are provided and applied to NLS equation. A systemical way of construction of special solutions is also tried for DS equation. Most of the results on a scalar equation can often be directly generalized to some matrix equation, and the difference between the ω in scalar form and ω in matrix form lies only in the replacement of vector p, q by matrices p, q.

对KdV方程和KP方程渐近性质的讨论显现出解在一定条件下的孤子特性，从而使得一些情形下，同类解的相互作用体现在参数矩阵上变的较简单；我们给出了AKNS方程的两类不同解，并约化到NLS；对DS方程，我们从另一个方面初步探讨了形式化推导矩阵方程特解的方法；把这些有关标量ω的结果推广到ω为矩阵上往往只要把p，q变为矩阵即可，进而可以再推广到方程组上。

Foods high in this vitamin include oily fish such as salmon, tuna and, and fish liver oils.

维生素D含量高的食物包括诸如大麻哈鱼、金枪鱼和鲭鱼之类的油鱼以及鱼肝油。

We need you to cosign our public letter demanding that press intimidation cease immediately, and that all charges be dropped.

我们需要您cosign我们的公共信，要求记者立即停止恐吓，并要求所有收费下降。