查询词典 algebra

Fuzzy logic is studied with algebraic tools in this paper. A kind of algebraic abstract of fuzzy logic, Implication Algebra on a partial ordered set, is given. The relations between Implication Algebra and other algebraic structures, such as MV-Algebra and Heyting Algebra etc., and the filter and the structure of Implication Algebra on a partial ordered set are studied.

本文的目的是使用代数工具对模糊逻辑进行研究，给出模糊逻辑的一类代数抽象，即偏序集上的蕴涵代数，研究偏序集上蕴涵代数与其它代数结构，如MV-代数，Heyting代数之间的关系，以及偏序集上蕴涵代数的滤子与其结构等。

To regulate policy composition and guarantee its correctness, an algebraic model called APoCA (attribute-based access control policy composition algebra) is proposed for composing access control policy. In APoCA, an authorization relation between entities is described at the attribute level. APoCA fertilizes the existing formal frameworks by taking into account the computation of attribute values.

为了规范策略合成和保障策略合成正确性，基于属性刻画了实体间的授权关系，通过属性值的计算结构扩展了现有的策略合成形式化框架，建立了新的基于属性的策略合成代数模型APoCA(attribute-base access control policy composition algebra)。

Chapter three: Define fuzzy congruence relation of MTL-algebra, prove that fuzzy fiter and fuzzy congruence relation is a bijective function in MTL-algebra, quotient algebra induced by congruence relation still forms a MTL-algebra; Introduce the relation between some kinds of fiters and fuzzy filters maitained above in IMTL-algebra,i.e. BR_0 algebra, which is a MTL-algebra satisfied inversely odering and involutive relation.

第三章：定义了MTL-代数中的Fuzzy同余关系，证明了MTL-代数中Fuzzy滤子与Fuzzy同余关系是——对应的，由同余关系所诱导的商代数依然构成一个MTL-代数；介绍了在满足逆序对合对应的MTL-代数-IMTL-代数，即BR_0-代数中上述几中特殊滤子，Fuzzy滤子之间的关系。

The latter is essentially derived from the geometric realization of Happels triangulated equivalence between stable module category of repetitive algebra and bounded derived category of finite dimensional algebra. In terms of this realization, we deduce that the Lie algebra realized by derived category of a finite dimensional algebra is isomorphic to the Lie algebra realized by stable module category of the corresponding repetitive algebra.

后者本质上是Happel关于重复代数的稳定模范畴和导出范畴的三角等价的一个几何实现及其应用，使用这种几何实现，我们可以证明在重复代数的稳定模范畴上定义的李代数同构于相应的导出范畴上实现的李代数。

31 Chapter 3 Number Systems and Boolean Algebra 3.2 Boolean Algebra Table 3-2 Distributivity Idempotency Absorption laws 分配律同一律吸收律 a=ab+ac a+= a+a=a aa=a a+ab=a a=a'=a'b''=a'+b' DeMorgan's laws德摩根定理计算机专业英语 3-32 Chapter 3 Number Systems and Boolean Algebra 3.2 Boolean Algebra Since a finite set of n elements has exactly 2n subsets, and it can be shown that the finite Boolean algebras are precisely the finite set algebras, each finite Boolean algebra consists of exactly 2n elements for some integer n.

由于n个元素的有限集有且只有个子集由于个元素的有限集有且只有2n个子集，而且很显然有限布个元素的有限集有且只有个子集，尔代数一定是有限集合代数，所以对某个整数n而言而言，尔代数一定是有限集合代数，所以对某个整数而言，每个有限布尔代数也有且只有2n个元素。例如，上文定义的集合T的限布尔代数也有且只有个元素。

The most famous rough algebras are Rough Double Stone Algebra, Rough Nelson Algebra and Approximation Space Algebra, and their corresponding general algebra structures are regular double Stone algebra, semi-simple Nelson algebra and pre-rough algebra respectively.

其中最有影响的粗代数分别是粗双Stone代数、粗Nelson代数和近似空间代数，它们对应的一般代数结构分别是正则双Stone代数、半简单Nelson代数和预粗代数。

Based on the outcome of Xu Yang and Qin Keyun about lattice implication algebra and lattice-valued prepositional logic LP with truth-value in a lattice implication algebra, the author studied the properties of lattice implication algebra and the α-automated reasoning method based on α-resolution principle of LP. The specific contents are as follows: The Study of Lattice Implication Algebra On the basis of previous results of lattice implication algebra, this part consists of the following three points: 1. Some properties of lattice implication algebra L were discussed, and some important results were given if L was a complete lattice implication algebra. 2. The properties of left idempotent elements of lattice implication algebras were discussed, and the conclusion that lattice implication algebra L was equals of the directed sum of the range and dual kernel of a left map constructed by a left idempotent element was proved. 3. The properties of the filters of lattice implication algebra were discussed, the theorem was shown that they satisfy the hypothetical syllogism and substitute theorem of the propositional logic. 4. The concept of weak niters of lattice implication algebras and their properties and structures are discussed. It is proved that all weak filters of a lattice implication algebra form a topology and the the implication isomorphism betweem two lattice implication algebras is a topological mapping between their topological spaces. The Study of α-automated reasoning method based on the lattice-valued propositional logic LP In this part, the author given an a-automated reasoning method based on the lattice-valued propositional logic LP.

本文基于徐扬和秦克云的关于格蕴涵代数和以格蕴涵代数为真值域的格值命题逻辑系统LP的研究工作，对格蕴涵代数以及格值命题逻辑系统LP中基于α-归结原理的自动推理方法进行了系统深入的研究，主要有以下两方面的研究成果：一、关于格蕴涵代数的研究 1、对格蕴涵代数的格论性质进行了研究，得到了当L为完备格蕴涵代数时，关于∨，∧，→运算的一些结果； 2、对格蕴涵代数的左幂等元进行了研究，证明了格蕴涵代数L可以分解为任何一个左幂等元所对应的左映射的像集合与其对偶核的直和； 3、对格蕴涵代数的滤子的性质进行了研究，证明了滤子的结构相似于逻辑学中的Hypothetical syllogism规则和替换定理； 4、给出了格蕴涵代数中弱滤子的概念，对弱滤子的性质个结构进行了研究，证明了格蕴涵代数的全体弱滤子构成一个拓扑结构，格蕴涵代数之间的蕴涵同构是相应的拓扑空间之间的拓扑映射。

The questions covering pre-algebra and elementary algebra make up the Pre-Algebra/Elementary Algebra Sub score. The questions covering intermediate algebra and coordinate geometry make up the Intermediate Algebra/Coordinate Geometry sub score. The questions covering plane geometry and trigonometry make up the Plane Geometry/Trigonometry sub score.

包含有基础初等代数和初等代数的考题构成了基础初等代数/初等代数的技能分数，涉及到中等代数和坐标几何的考题构成了中等代数/坐标几何的技能分数，而涵盖平面几何和三角函数的考题则构成了平面几何/三角函数的技能分数。

The third part proposes in Luk the concept of lattice-valued truth degrees based on the second part by generalizing truth values from the MV-unit interval(a special MV-algebra) to a general MV-algebra. And the properties of lattice-valued truth degrees suggest that this generalization is natural and reasonable. Because of the equivalence between the two algebra systems, i.e. MV-algebra and lattice implication algebra, it's natural and easy to grade the truth of formulas in lattice-valued propositional logic whose basic algebra system is the lattice implication algebra.

中。 本文第三部分在第二部分的基础上，将Luk中公式的真度值推广到了一般的MV代数上，相对于第二部分的数值真度，给出公式的格值真度，并通过格值真度的性质说明格值真度是数值真度的合理推广。

Software Description: About Personal Algebra Tutor, Enter your problems into this algebra problem solver to view step-by-step solutions and explanationsto basic algebra through pre-calculus problems.

Personal Algebra Tutor 输入你的难题到这款代数题解答器观看分步式答案以及贯穿学习微积分前必修课程的注释说明。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。