algebraically

1. This can be done numerically by computer or algebraically as follows.
   这可借计算机用数值去完成或像下面那样用代数来完成。
2. It is much easier to indicate how to find the mean by expressing the procedure algebraically.
   用代数的方法来表现这个过程，就更容易说明平均数是如何求得的。
3. The two stresses can then be added algebraically to obtain the resultant.
   然后将两种应力代数相加就得到合应力。
4. Let's say you have to go through three or four operations to get a final number, well, do it algebraically.
   让我们说，你不得不通过3-4个操作，才能得到最终的数，好吧，用代数方法求解。
5. The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.
   证明了任一环有代数封闭的扩张环，且实封闭域上的四元数体是代数封闭的，给出了代数封闭环的若干性质。
6. We solve for A steady state algebraically.
   我们用代数方法解决A稳态。
7. In this paper, we discuss the classification of3-dimensionally commutative algebras on algebraically closed field.
   研究了代数闭域上三维交换代数的分类。
8. First interpret it combinatorially, and then derive it algebraically from the multinomial theorem.
   先用组合方法阐述，然后从多项式定理利用代数方法推导。
9. By using the homogeneous balance principle ( HBP) and Hermite transform, various kinds of exact solutions to a stochastic nonlinear evolution equations can be algebraically obtained in terms of the exact solutions of heat conduction equation with variable coefficients.
   利用齐次平衡原则及厄尔米特变换，借助于变系数热传导方程的各种精确解，用代数的方法获得了一随机非线性发展方程组的各种精确解。
10. The thermal group flux is calculated algebraically from fast group flux and detector activations.
    热群通量可根据快通量计算值及活性测量值经过简单代数运算求出。
11. From the famous Gabriel's theorem, a basic connected finite dimensional associative algebra A over an algebraically closed field can be looked as a quotient of a path algebra decided by a connected finite quiver Q.
    由Gabriel定理，代数闭域上基的，连通的有限维结合代数A同构于一个由连通有限箭图Q确定的路代数的商代数。
12. It is proved moreover, that the K N K metric is algebraically special and of Petrov type D.
    并利用GoldbergSachs定理的推论，证明了KNK度规是代数特殊的PetrovD型。
13. Further by Evans function method and detailed semigroup estimates, we prove that each wave with non-critical or critical speed is locally algebraically stable in some weighted spaces, which further explains some asymptotic phenomena obtained by numerical simulation.
    进一步，将Evans函数方法、适当的空间分解、半群方法和经典的谱分析方法相结合，我们分别得到了具有临界和非临界波速的行波解在多项式加权空间里的局部渐近代数稳定性。
14. Compressible flow around an NACA 0012 airfoil at high angle of attack is numerically simulated by solving the two-dimensional Navier-Stokes equations in a body-fitted system, the grid system is C-type grid generated algebraically.
    以求解二维N-S方程数值模拟NACA0012翼型大攻角状态的可压绕流特性；N-S方程是在贴体坐标系中给出的，以代数方法生成C型网格系统。
15. Discusses algebraically and geometrically the properties of the ruled surfaces in the Euclidean three-space, especially, the principal normal surfaces on which there are some special curves, such as Mannheim curves, Bertrand curves and general helices.
    在三维欧氏空间中，作为特殊曲线，Mannheim曲线、Bertrand曲线以及一般螺线具有良好的几何和代数性质.讨论了三维欧氏空间中特殊曲线的主法线曲面。
16. Two sets of algebraically explicit analytical solution are derived for the partial differential equation set describing the one dimensional unsteady gas-liquid two phase flow.
    对气液两相非定常一元流动方程组导出了两套代数显式解析解。
17. The Cohomology of Semi-simple Algebraic Groups Over an Algebraically Closed Field of Characteristic O
    在特征数0的代数闭域上半单纯代数群的上同调群
18. A path-following algorithm for solving linear complementarity problems based on algebraically equivalent transformation
    基于代数等价变换的线性互补问题内点算法
19. In the first chapter, we discuss the fully graded algebras over discrete valuation ring with an algebraically closed residue field of characteristic p.
    第一章中，我们研究了剩余域是代数闭域的离散赋值环上的完全分次代数；
20. Two algebraically explicit analytical solutions of the governing equation set for the coupled heat and mass transfer process of rapid drying in porous media are derived.
    对多孔介质快速干燥过程的传热与传质耦合方程组导出了两套代数显式解析特解。
21. We give a number of one-step two-order and three-order hybrid formulae which are algebraically stable in the end.
    最后，给出了若干一步二阶、三阶代数稳定的混合方法公式。
22. Interior-point Algorithms for Uniform P-function Nonlinear Complementary Problem Based on Algebraically Equivalent Path
    基于代数等价路径的一致P-函数非线性互补问题的可行内点算法
23. In this paper, two results with functions that are low order instead of all constants in the algebraically dependent theorem of two meromorphic functions by F. Gross are established.
    本文将F.GROSS关于两个亚纯函数代数相关定理作一推广，给出了两个亚纯函数在级较低的亚纯函数域上的代数相关性，并讨论了整函数的情形。
24. An algebraically explicit analytical solution for governing equations of heat and mass transfer process in wet capillary porous media is derived.
    对含湿毛细多孔介质传热与传质过程的基本主控方程，以建议使用的加法分离变量法导出了一套代数显式解析特解。
25. Algebraically explicit analytical solution for heat and mass transfer in wet porous media
    含湿毛细多孔介质传热与传质基本方程的一组代数显式解析解
26. In this paper, two algorithms are given for attitude determination with double geostationary satellites system, and their two solutions problem is geometrically and algebraically proved.
    给出了双星姿态测量的两种算法，并从几何和代数两个方面证实其存在双值问题；
27. The relation between the normal sublattice and the associate molecular lattice of the molecular lattice I ￣ x is discussed, it is proved that and is algebraically homomorphic;
    考察了分子格I~x的正规子格与相关分子格之间的关系，证明与是代数同构的；
28. This paper proves that any one-step and two-step hybrid methods with explicit predictor is not algebraically stable.
    本文证明了基于显式预报的一、二步混合方法不是代数稳定的。
29. On the Algebraically Dependent of Entire and Meromorphic Functions
    关于整函数和亚纯函数的代数相关
30. Assume A is a finite dimensional hereditary algebra over an algebraically closed field.
    设A是代数闭域上的有限维遗传代数，A（1）是A的重复代数。

adv

1. in an algebraic manner
   1. algebraically determined