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乘积集合

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Firstly, we analyze the deficiencies ofexisting ones, extend domains of fuzzy logical operators from the cap product withtwo sets to them with arbitrary (finite, enumerable, or non-enumerable) number ofsets to form two general mappings so as to conform them to the fuzzy conjunctionand infimum, and to fuzzy disjunction and supremum, respectively, and fuzzify theset inclusion of fuzzy sets. Similar to the classical adjunction, the concept of fuzzyadjunction is introduced.

首先分析了原有"模糊形态学"框架的缺陷,进而将模糊合取和模糊析取算子的定义域从两个集合的笛卡儿乘积推广到任意多个集合的笛卡儿乘积,形成两个一般的映射,使得模糊合取与下确界、模糊析取与上确界保持一致,以此将模糊集的包含关系一般化。

Motivated by the newψfunctional stability,we can establish some new kinds of stabilities which are different from the exponential stability.With the help of semimartingale convergence theorem,stochastic calculous,moment inequality,Burkholder-Davis-Gundy inequality,Gronwall inequality etc.,we find that the product ofψfunction and the solutions of neutral equations will approach a nonempty set if some specific conditions are satisfied.

我们应用半鞅收敛定理、随机微积分的相关知识以及矩不等式、Burkholder-Davis-Gundy不等式和Gronwall不等式等技巧,得到中立型随机泛函微分方程的解与特定的"ψ函数"的乘积在一定的条件下将趋向某非空集合这一结论,并建立了该中立型方程的随机LaSalle型定理。

The matrix =( xi, xjp having the e-th power of the greatest common P-divisorp of xi and xj as its-entry is called the e-th power GCD matrix on S. The matrix = having the e-th power of the least common P-multiple p of xi and xj as its-entry is called the e-th power LCM matrix on 5. We obtained the following results:(1) is nonsingular for any set S;(2) If S is an FC set, then the determined of has formula Det =Jpe(x1)...Jpe, where the function Jpe is the generalized Jordan totient function;(3) A formula of the inverse of is given when S is an FC set;(4) If S is an FC set, then |.

以_P的e次方为第i行j列元素的矩阵称为定义在S上的e次幂GCD矩阵,记为;以_P的e次方为第i行j列元素的矩阵称为S上的e次幂LCM矩阵,记为,我们得到了如下结果:①定义在集合S上的e次幂GCD矩阵是非奇异的;②若S是R上的FC集,则S上的e次幂GCD矩阵的行列式Det=J_p~e(x_1)J_P~e(x_2)…,J_p~e,其中J_p~e为R上的Jordan函数;③当S为FC集时,得到了的逆矩阵~-1的表达式;④证明了当S是FC集时,整除,即等于与R上另一个矩阵的乘积。

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