代数等价

In chapter 2, we introduce weak hopf π coalgebra and two kinds of special subalgebra over it.Some basic properties are studied to make a basis for the following chapter.

第三章主要是在弱Hopf群余代数上建立Yetter-Drinfeld模，探讨其性质并给出它的等价条件，从而对其结构有更本质的认识。

In Chapter 4, we define the induction of divisors and prove the existence of Galgebras of complete induction; through the analysis of Mackey formula, we give an equivalent characterization of the relationship between Green correspondence and free projectivity.

在第四章中，我们定义了除子的诱导，证明了完备诱导的G-代数的存在性；通过分析Mackey公式，给出了Green对应和自由投射关系的等价刻画。

Zadeh put forward, make MTL-algebra"s filter conception fuzzified, provide the conceptions and properties of fuzzy filter, obtain the structure of all fuzzy, filters, prove that the set of all fuzzy filters forms a complete distribution lattice; Provide several fuzzy Boolean filter"s equivalent forms, introduce fuzzy positive implicative filter, fuzzy obstinate filter and fuzzy ultra filter, discuss some property characteristics and terms that transform each other under certain terms to obtain them.

Zadeh提出的模糊集思想使MTL-代数的滤子概念模糊化，给出了Fuzzy滤子的概念和性质，得到了全体Fuzzy滤子的结构，证明了全体Fuzzy滤子之集构成完备的分配格；给出了Fuzzy布尔滤子的若干等价形式，并且引入了Fuzzy正蕴涵滤子，Fuzzy固执滤子和Fuzzy超滤的概念，得出了它们的一些性质特征以及在一定条件下之间相互转化的条件。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

Additionally, we propose an algebraic diagonalization method which is equivalent to Bogoliubov-Valatin transformation in a sense.

此外，我们介绍了一种新的对角化方法——代数对角化，它在一定程度上等价于Bogoliubov变换。

This article present an unification arithmetic for a kind of mixture equations made up of some differential and algebra equations.

提出了一种求解微分代数混合方程组的统一算法，证明了统一算法所求出的懈与原方程组的解具有等价性。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

In this paper the Karnaugh map for simplifying logic functions is used in computing canonical covers based on the equivalence between the theory of functional dependencies and logic algebra.

本文依据函数依赖理论与逻辑代数对应部分的等价性，引入化简逻辑函数的卡诺图法求函数依赖集的规范覆盖。

Using a method of algebraic transformation such as power series expansion, it is found that, three crop water production functions, the Jensen mold, Rao model and Stewart model, are transformable mutually, and their water sensitive indices are approximately equivalent.

通过幂级数展开等代数变换发现，3种作物水分生产函数Jensen模型、Rao模型和Stewart模型可以近似相互转化，其各自水分敏感指数近似等价。

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.

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。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。