查询词典 solution set of equation

Firstly, four geometric loop equations are set up by using vector method in complex number fields. Secondly, three constraint equations are used to construct the Dixon resultants, which is a 6×6 matrix and contain two variables to be eliminated. Extract the greatest common divisor of two rows and two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant.

首先使用矢量法和复数法建立4个几何约束方程式；再使用Dixon结式法对3个方程式构造一个含有2个变元的6×6 Dixon矩阵，提取其中2行列元素的公因式，将新矩阵的行列式展开后得到二元高次多项式方程，该方程与剩下一个方程使用Sylvester结式消去一变元，得到一元高次方程。

In the case of simply supported ends, the Galerkin method is used to simplify the integro-partial-differential equation into an integro -differential equation. The equation is further simplified into a set of ordinary differential equations by introducing an additional variable. Finally, the numerical methods in modern nonlinear dynamics such as phase plane trajectory, power spectrum and Lyapunov exponents are adopted to investigate the dynamical behavior of the beam.

对于两端简支的情形，采用Galerkin方法简化为常微分－积分方程；然后通过引进附加变量的方法进一步简化为常微分方程；最后利用相平面图、功率谱和Lyapunov指数等非线性动力学中的数值方法识别梁的动力学行为。

The absolute solution of Jiaojia ERP is put forward, the system models are established, and the solution are explained in detail. The business program of Jiaojia gold mine is reengineered based on the theory of "business centers", and the program-oriented compressed organization is framed. The index group and the solution of mine total quality management are setup. Then the optimize program of SCM and its components are designed on the guidance of "Horizontal Integration". The data of Jiaojia gold mine are reengineered based on the data warehouse technology. The information integration can be available after the establish of the business oriented databases, the subject integration oriented data marts, the application oriented data warehouses, the code databases and metadata, as weil as the OLAP system. The mathematics models and data mining modes are set up to function for the decision support of ERP system. The model of programming Master Production Schedule driven by geological resources and marked is figured out, so as to the models for material requirements planning and other decision supports are set up. The models provide service in forms of model storehouse, method storehouse, and algorithm tools center. The agent center is introduced to process the models' organizing, service, as well as self-study. The function system of Jiaojia gold mine ERP is figured out. By combining the development characteristics of Clients/Server and Browse/Server, the general framework and every sub systems are described in detail, including the function, structure, arrangement, modality, and so on.

主要内容如下：（1）深入论述了黄金矿山实施ERP的可行性，并结合应用需求将ERP理论在深度和广度上进行了拓延，建立了黄金矿山ERP系统的理论基础：以资源与市场共同驱动的供应链管理；黄金矿山的双重物流体系；以地质资源有效利用为目标的生产控制体系；黄金矿山财务管理的成本控制核心理论等；（2）提出焦家金矿ERP系统的整体解决方案，构建ERP系统模型，并进行了细节方案的设计：基于"作业过程核心"理论重新规划焦家金矿的业务流程，在此基础上设计面向流程的"扁平化"组织机构；建立了矿石全面质量管理的指标体系和实施方案；以"横向一体化"为指导思想，提出供应链管理各组成部分的全面优化方案；（3）以数据仓库技术为核心完成焦家金矿的数据规划，分别建立面向业务的数据库、面向主题集成的数据集市和面向主题应用的数据仓库，设计代码数据库和元数据库，定义OLAP方式，实现焦家金矿的全面信息集成；（4）针对ERP系统中的决策支持功能，建立了相应的数学模型和数据挖掘模型，提出了地质资源和市场共同驱动的主生产计划模型制定过程，进一步建立了物料需求计划的线性规划模型，以及其它决策支持模型；提出以模型库、方法库和算法工具为核心的模型服务方式，并设计了代理机制完成模型的组织、服务和自学习过程；（5）构建焦家金矿ERP系统的功能体系，针对C/S和B/S模式系统的开发特点，分别对功能体系架构以及各子系统的功能、结构、层次和形式进行详细设计。

By synthetically analysizing the physical and chemical properties of all components and particle size, the content of F2641 in the JOB-iC is determined by gravimetric analysis after F2641 is seperated from HMX,TATB and PNP through ? alkali reflux. Determination conditions is set as follows the sample is boilingly refluxed for six hour in a constant temperature bath after adding lOOm! 8.0 ?? 0.1% NaOH. The solvent DMF saturated by TATB is used for extracting HMX,F21 and PNP from the sample and TATB is seperated by crucible filter G4. The mass precent of TATB is determined by extraction fractionation. The mass percent of PNP is measured by multiwavlength linear regression ultraviolet spectrophotometry. The testing conditions are set as follows:multiwavlength constitution: X=267nxn, 275nm, 283nm, 29mm, 299nm,the application scope of the Lambert-Beer law: the concentration of PNP is O.005?0.O25mgIml, the concentration of HMX is 0.060.3Omg/ml,absorption coefficents of PNP and HMX are solved by the slope of linear regression curve of absorbency- concentration of standard solution of PNP and HMIX for measuring wavelengthes,on the basis of the Lanibert-Beer law and absorbancy additivity principle, the slope of linear regression curve of A/E(1) and E1 of PNP and HMX solution is regarded as the concentration of PNP in the solution.

根据传爆药中各组分的物理、化学性质及主体炸药的粒度大小，进行综合分析，确定了采用碱回流重量法测定JOB-1C 中F_(2641)的含量，测定条件：加入100ml浓度为8.0±0.1％的氢氧化钠，在恒温水浴中煮沸回流6h；采用溶剂萃取法测定JOB-1C中TATB的含量，选择TATB饱和的二甲基甲酰胺为萃取溶剂，用G4坩埚式过虑器进行萃取分离；采用多波长线性回归紫外分光光度法测定JOB-1C中PNP的含量，通过实验确定了多波长组合：λ=267nm，275nm，283nm，291nm，299nm；朗波—比耳定律的适用范围为PNP浓度：0.005～0.025mg/ml，HMX浓度：0.06～0.30mg/ml；在测定波长下，对PNP、HMX标准溶液的吸光度—浓度进行线性回归，由回归曲线的斜率得出PNP、HMX的吸收系数；根据朗波—比耳定律和吸光度加和性原理，在测定波长下，对PNP、HMX 两组分混合溶液A_i/E_HMX(i与E_PNP(i/E_HMX(i进行线性回归，回归曲线的斜率即为混合溶液中PNP的浓度。

At last, we provide the upper semi-continuity and compactness of the spectral scalar solution set mapping under some suitable conditions, and the necessary and sufficient conditions to guarantee the lower semi-continuity of the spectral scalar solution set mapping by virtue of the concept of essential solution.

最后，给出了谱标量解集映射满足上半连续且紧的充分条件及下半连续的充分必要条件。

The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. The advantage is that the cost function variation is independent of the flow field variation, with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow-field evaluations. So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.

虽然他们的研究成果大多数都可以在公开性文献上看到，但是其中一些具体的细节问题的处理方法却没有透露，比如：伴随方程如何离散求解才能减小最终梯度计算中的误差，使得设计过程有效地进行；伴随方程与流动方程的边界条件是不同的，如何合理地处理伴随方程的边界条件，才能推动设计过程朝着设计目标而发展；在减阻问题中目标函数如何定义，求解梯度的具体数学公式如何推导，如何通过数值方法来实现它们等。

In Chapter 1, two solutions to the elliptical boundary value problem have been constructed through a monotone iterative process, and they might be identical. In Chapter 2, the author expresses the local solution to the parabolic initial boundary value problem taking advantage of Green function. In Chapter 3, the asymptotic solution to the initial value problem of Duffing equation is obtained and the method for finding the approximate solution to the inverse problem is put forward.This paper is planned with a view to the author's research means.

从研究结果看：第一章通过单调迭代过程构造出椭圆型方程的边值问题的两个解，并且指出二者可能是同一个解；第二章利用格林函数给出了抛物型方程的初边值问题的局部解的解析表达式；第三章中，先对Duffing方程的初值问题写出解的渐近展开式，再对其反问题提出一种求近似解的方法。

Based on linear bending theory of thin elastic plate and fundamental solution constructed with the general solution principle of biharmonic equation, a meshless method was developed for establishing a computational format of numerical solution of thin plate bending.

基于弹性薄板的线性弯曲理论和重调和方程的一般解理论构造的基本解，建立无网格法求解薄板弯曲问题的数值计算格式。

However,authors still do not find the relevant references on convergence and symmetric problems of the semi-analytical solution.Based on the semi-analytical solution for Hamilton canonical equation theory,the formulations of the clamp and simply supported and symmetric boundary conditions on the Hamiltonian element are derived by the variational principle.Several numerical examples show that with increase of meshes,the convergence rate of the semi-analytical solution is faster than the convergent rate of traditional finite element method based on displacement.

①在厚度上没有任何位移和应力模式的假设，由于传递矩阵方法的引入，从理论上讲，不受板壳厚度或层合板壳层数的限制；②采用弹性力学的Hamilton正则方程半解析法，可以克服边界的局部化效应[8]；③由于在平面内或圆柱壳的曲面内采用了有限元法，所以一般的板壳问题不受结构侧面边界条件的限制，在复杂工程板壳问题上具有广泛的应用领域。

Firstly, we combine the theories of monotone operator and maximal monotone operator's Yosida approaching with domain method to prove the solution's existence of single input-output equation in R n in the similar economical backgrounds in present articles and then gain the solution's continuity by exterior approaching method,at last we give the responding economical meaning about the solution's existence and continuity.

就R n空间中消耗为单调单值型的投入产出方程，在现有文献类似的经济背景之下，利用单调算子的理论以及极大单调算子的Yosida逼近结合邻域逼近法给出了投入产出方程的解的存在性的证明，然后利用外部逼近法结合方程截断技巧证明了投入产出方程的解的连续性，最后给出了相对应于存在性和连续性的经济解释。

The second is to cut a mere 100 calories from your diet , which is the equivalent of a tablespoon of butter.

第二个就是从你的饮食中减少一百卡路里，只是相当于一大汤匙的黄油。

This is where the Rorschach test comes in.

现在，罗氏测试就出现了。