定义方程

In this article,we showed the algebraic structure of syntactic categories based on monoid and defined categorial equation whose solutions are described by consistency and correlation .

摘要］ 本文给出了建立在含幺半群基础上的范畴语法的代数结构，定义了范畴方程和它的解并对范畴方程的解作了分类：相容性的相关性。

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

The purpose of this paper is to prove the existence of non-oscillatory solutions to second-order neutral time-lag differential equation with positive/negative coefficient by using contraction-image principle through defining an operator from a bounded,closed,and convex subset into Banach space.

通过定义有界闭凸子集到B anach空间上的一个算子，应用压缩映像原理讨论了带有正负系数的二阶中立型时滞微分方程非振动解的存在性，得到该方程非振动解存在的一个充分条件。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

The asymptotic behavior of the weak solution is obtained when an enthalpy function is made in L(superscript 2 subscript +) and a differential inequality is proved after using Cauchy inequality, Poincare inequality and the definition of weak solution.

在L(上标2 下标+)空间上构造了一个熵函数，利用带ε的Cauchy不等式和poincare不等式及弱解的定义，推导出了此函数满足的一个微分方程不等式，通过求解微分方程，证明了弱解的渐近性问题。

On the one hand, Lagrange hit upon the new idea to redefine the complete integral when he was inspired by his study on the first-order partial differential equation with the method of variation of constants.

在分析、比较欧拉和拉格朗日完全积分定义的基础上，依据原始文献，重点考究了拉格朗日重新定义偏微分方程完全积分的原因和动机。

On the basis of analyzing the lilnitations of the conventional flow equation for rotameter , ac-cording to principle of mechanical energy conservation and transform for real fluid, a new generalflow equation Q=for rotameter has been developed.This equation includes the rota-form factor β to reflect the influence of rota-form on flowmeasurement.

在分析转子流量计习用流量方程局限性的基础上，根据实际流体机械能守恒与转换原理，定义了反映转子形状特征对流量测定影响的转子几何形状因子β；经过推导，最终获得了转子流量计一种新的普遍流量方程Q＝。

In the first charpter,response variable is generalized to q dimensions, we propose the concept of QMLE and quasi function in nonlinear models, then under mild conditions, we prove that there exists the solution_n with probability 1 for sufficiently large n, and obtain the strong consistency, some results of asymptotic normality, meanwhile consistent estimator of σ~2 for QMLE for heterosedastic nonlinear models is presented.

在第一章中，我们首先将响应变量由一维推广到了多维，得出了非线性模型的极大拟似然估计的定义和拟似然方程，然后在一定的条件下，证明了当样本量n充分大时，拟似然方程以概率1有解？？_n且收敛于参数的真值(即定理1.2)，并且给出了极大拟似然估计的渐近正态性(即定理1.3，1.4)，最后考虑了异方差非线性模型的离差参数σ~2的相合估计(即定理1.5)。

In the method, the equation of vorticity is simplified and combined with the definitions of vorticity and divergence , and then restrained by the equation of continuity to set the system of retrieval equations. Three-dimensional wind vector, vorticity and divergence can be got by solving the system of equations. Preliminary test has proved that it is feasible.

该方法从动力学角度出发，将柱坐标中的垂直涡度方程适当简化后，联系涡度散度的定义式，再以大气连续方程作约束，得到一个反演方程组，求解方程组就可得到不同高度层上的三维风场以及涡度、散度，初步检验证明其是可行的。

For the definition of two damage variables,damage variable and damage evolution equation are derived respectively.

针对两种损伤的定义，给出了损伤变量和损伤演化方程，同时用损伤力学定义了边坡的安全系数为极限损伤与最大损伤变量之比，并给出了应用算例。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。