作为半连续格的推广，引入了拟半连续格和拟半代数格的概念，讨论了它们的一些基本性质。
As generalizations of semicontinuous lattices and semialgebraic lattices, the concepts of quasi-semicontinuous lattices and quasi-semialgebraic lattices are introduced.
作为推论，给出了格蕴涵代数的某些结构性定理。
As consequences it is given some of structure theorems of lattice implication algebras.
给出的格蕴含代数的公理系统，并给出另一个公理系统。
Simplify the axiom system of lattice implication algebras, which was given by y.
因此，构造新的格蕴涵代数对人工智能的研究具有重要意义。
Therefore, the forming of new lattice implication algebras plays an important role in artificial intelligence research.
同时，对格蕴涵代数之全体的结构进行了全面的研究。
Finally, the set of a lattice implication algebra are studied.
并对“近世代数”（吴品三）、“抽象代数”（徐诚浩）中有关模格维数几个定理证明的遗漏，作了某些补证。
The paper also gives some corrections to several theorems and their proofs about the dimension of the modular lattice ih the books" Modern Algebra" by Wu and "Abstract Algebra" by Xu.
其结果描述了这些代数内部结构的特征，同时也为从语义的角度进一步研究格值逻辑系统提供了一个新的途径。
Those results describe the characterizations of interior structures of those algebras, and also offer a new way for further researching lattice-valued logic systems from the semantics.
逐步阐明格论，概述影响整数最优化的代数几何学思想，并讨论整数最优化的几何学。
Develops the theory of lattices, Outlines ideas from algebraic geometry that have had an impact on integer optimization, and discusses the geometry of integer optimization.
从代数动力学算法的观点考察了辛几何算法和龙格-库塔算法的保真问题。
The symplectic geometric algorithm and the Ronge-Kutta algorithm are examined from the viewpoint of the algebraic dynamical algorithm.
对系统应用第一类拉格朗日方程，得到系统位形坐标的微分—代数方程组。
Apply Lagrange equation of the first kind to the system, and get a set of the differential - algebraic equations (DAEs) of its absolute coordinates.
根据逻辑代数方程理论，提出了格蕴涵代数方程的概念。
According to the theory about logic algebraic equation, the notion of lattice implication algebraic equation was proposed.
提出了格蕴涵同态像的概念，证明了格蕴涵同态像是格蕴涵代数；
The concept of lattice implication homomorphism image, which is proved to be a lattice implication algebra, is introduced.
作为一个推论给出：蕴涵半格构成一个代[代数]簇。
As a consequence of the above result, we have that implicative semilattices form an algebraic variety.
针对二维三温能量方程九点格式离散后形成的非线性方程组，研制了高效求解的代数解法器。
We developed a high performance algebraic solver for nonlinear systems discretized from two-dimensional energy equations with three temperatures by a nine point scheme.
给出了格蕴涵代数、MV代数、R 0代数等一些格上蕴涵代数之间的关系，并建立了它们的对偶代数。
This paper gives out that the relationship among lattice implication algebras, MV algebras, R0 algebras and other implication algebras based on lattices, and their dual algebras are established.
数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的。
Numerical experiments show our AMG method is robust and efficient for solving the quadratic Lagrangian finite element system.
讨论粗糙集代数与格蕴涵代数的关系以及由粗糙集代数构造格蕴涵代数的方法。
The relation between rough set algebra and lattice implication algebra was studied, and the method of constructing lattice implication algebra from rough set algebra was presented.
本文中，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。
In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.
格蕴涵代数中素滤子的概念被引入。
The concept and some of fundamental properties of prime filters in lattice implication algebras are introduced.
证明了离散格是一个布尔代数，给出了离散格的表示定理。
It is proved that this lattice is a Boolean algebra, and the representation theory of discretization lattice is given.
亚里士多德是传统逻辑的创始人。弗雷格，德国著名的数学家，逻辑学家，是现代数理逻辑的创始人。
Aristotle was the founder of traditional logic, and G-Frege, a famous mathematician of German, was the founder of modern mathematical logic.
结果在拉格朗日的视野中，微积分是关于函数的一种代数形式演算，而函数是由一个解析表达式给出并且均可展成幂级数。
Results in perspective of Lagrange, the calculus was a kind of algebraic calculation of the function given by an analytical expression, which could be developed into power series.
目的探讨拉格朗日微积分代数化方案的基本内涵、实质及影响。
Aim To explore the basic connotation, essence and influence of Lagrange's algebraic program of calculus.
本文针对带有间断系数的三维椭圆问题，讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法。
In this paper, we consider a quadratic Lagrangian finite element equation arising from discretizations of 3d elliptic problem with jump coefficients under any tetrahedral partition.
本文针对带有间断系数的三维椭圆问题，讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法。
In this paper, we consider a quadratic Lagrangian finite element equation arising from discretizations of 3d elliptic problem with jump coefficients under any tetrahedral partition.
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