共查询到20条相似文献,搜索用时 156 毫秒
1.
首先通过集代数得到了Stone代数的表示定理,然后证明了每一个Stone代数均嵌入到某个集合X上的一个Stone映射类S中. 相似文献
2.
一个BCK-代数叫做关联的,如果它满足 (1).x*(y*x)=x K.Is’eki[2]证明了满足(1)的BCI-代数是一个BCK-代数。于是为了引入关联BCI-代数概念,先给出关联BCK-代数的等价条件。本文将不加说明地引用[1]中的记号和结论。 相似文献
3.
本文讨论了单BCI-代数。证明了一个BCI-代数是单的当且仅当它的子代数都是单的;给出了单p-半单BCI-代数的一种表示式;证明了一个p-半单BCI-代数是单的当且仅当它的阶是素数;这样得到了一批(无限多个)单BCI-代数;证明了商BCK-代数X/A是单的当且仅当A是X的极大理想。 相似文献
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5.
《数学的实践与认识》2017,(23)
首先,在FI代数X上以全体MP滤子之集为基建立了一个拓扑空间(X,F_(MP)).给出了拓扑空间(X,F_(MP))中集合A的导集、闭包和内部的计算公式.其次,考察了(X,X_(MP))的若干拓扑性质.最后,研究了乘积FI代数的乘积MP滤子拓扑. 相似文献
6.
Fuzzy蕴涵代数的MP滤子 总被引:6,自引:3,他引:6
给出了Fuzzy蕴涵代数(简称FI代数)上的MP滤子的等价刻画和由非空子集生成的MP滤子的表示定理; 探讨了FI代数的MP滤子与偏序滤子之间的关系; 证明了一个FI代数上全体MP滤子之集在集合包含序下构成一个分配连续(代数)格,从而构成一个Frame. 相似文献
7.
可换BCH-代数 总被引:1,自引:1,他引:0
李金龙 《数学的实践与认识》2014,(23)
引入了可换BCH-代数的概念,给出了可换BCH-代数的两个充要条件.对偏序可换BCH-代数进行了讨论,给出了偏序BCH-代数是可换的两个充要条件.证明了偏序可换BCH-代数的每个分支是一个下半格,局部有界偏序可换BCH-代数的每个分支是一个格. 相似文献
8.
研究元素个数不超过6的真伪BCK-代数的计数问题.首先,证明了在元素个数不超过3的偏序集上不存在真伪BCK-代数.其次,引入NP-型偏序集(不存在真伪BCK-代数的含重大元的偏序集)、偏序集的层、次余原子等概念,证明了在一个层数n≤3的NP-型偏序集上添加孤立余原子(或孤立次余原子或上邻元的个数n≥3的极小次余原子)后得到的偏序集也是NP-型偏序集,由此得到26种NP-型偏序集(元素个数n≤6).最后,借助Matlab软件编程计算得出所有非同构的元素个数不超过6的真伪BCK-代数,其中元素个数为4的真伪BCK-代数2个,元素个数为5的真伪BCK-代数34个,元素个数为6的真伪BCK-代数631个. 相似文献
9.
DR0代数:由De Morgan代数导出的正则剩余格 总被引:3,自引:0,他引:3
首先讨论了De Morgan代数与剩余格的关系,并引入强De Morgan代数的概念,讨论了它的基本性质.随后,将著名的R0蕴涵拓广到De Morgan代数上,称为广义R0蕴涵;证明了添加广义凰蕴涵和相应 算子后的De Morgan代数L成为剩余格的充要条件是L为强De Morgan代数,并由此引入D‰代数的概念.接着,研究了DR0代数与‰代数的关系,证明了以下结论:Boole代数是DR0代数;全序DR0代数和全序R0代数等价;DR0代数是R0代数当且仅当它满足预线性条件;无中点的DR0代数是BL代数当且仅当它是Boole代数.最后,举例说明了非D兄D代数的RD代数、以及非R0代数的DR0代数都是存在的. 相似文献
10.
通过对MV代数和Lukasiewicz命题演算系统的研究,我们对MV代数的定义进行了简化,并讨论了MV代数和其它代数之间的关系。主要结果是:(1)从蕴涵角度出发,给出了MV代数的两种简化定义;(2)提出了弱格蕴涵代数的概念,并证明了它与BR0代数等价;(3)证明了弱格蕴涵代数是正则Fuzzy蕴涵代数。 相似文献
11.
Cui Xi & Guoxing JI 《数学研究通讯:英文版》2015,31(1):89-96
Let $\mathcal{B}(\mathcal{H})$ be the $C^∗$-algebra of all bounded linear operators on a complex
Hilbert space $\mathcal{H}$. It is proved that an additive surjective map $φ$ on $\mathcal{B}(\mathcal{H})$ preserving
the star partial order in both directions if and only if one of the following assertions
holds. (1) There exist a nonzero complex number $α$ and two unitary operators $\boldsymbol{U}$and$\boldsymbol{V}$ on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$. (2)
There exist a nonzero $α$ and two anti-unitary operators$\boldsymbol{U}$and$\boldsymbol{V}$on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$ or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$. 相似文献
12.
This paper deals with the optimal transportation for generalized Lagrangian L = L(x, u, t), and considers the following cost function: c(x, y) = inf x(0)=x x(1)=y u∈U∫_0~1 L(x(s), u(x(s), s), s)ds, where U is a control set, and x satisfies the ordinary equation x(s) = f(x(s), u(x(s), s)).It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation:V_t(t, x) + sup u∈UV_x(t, x), f(x, u(x(t), t), t)-L(x(t), u(x(t), t), t) = 0,V(0, x) = Φ0(x). 相似文献
13.
On Initial-boundary-value Problems for a Class of Systems of Quasi-linear Evolution Equations 下载免费PDF全文
Cheng Yan 《偏微分方程(英文版)》1994,7(4)
In this paper the initial-boundary-value problems for pseudo-hyperbolic system of quasi-linear equations: {(-1)^Mu_{tt} + A(x, t, U, V)u_x^{2M}_{tt} = B(x, t, U, V)u_x^{2M}_{t} + C(x, t, U, V)u_x^{2M} + f(x, t, U, V) u_x^k(0,t) = ψ_{0k}(t), \quad u_x^k(l,t) = ψ_{lk}(t), \quad k = 0,1,…,M - 1 -u(x,0) = φ_0(x), \quad u_t(x,0) = φ_1(x) is studied, where U = (u_1, u_x,…,u_x^{2M - 1}) V = (u_t, u_{xt},…,u_x^{2M - 1_t}), A, B, C are m × m matrices, u, f, ψ_{0k}, ψ_{1k}, ψ_0, ψ_1 are m-dimensional vector functions. The existence and uniqueness of the generalized solution (in H² (0, T; H^{2M} (0, 1))) of the problems are proved. 相似文献
14.
V. L. Girko 《Journal of Mathematical Sciences》1993,63(5):604-607
For the functions f(a), f L2, where a is a m-dimensional vector expectation of the vector , we derive the equation
相似文献
15.
In this paper, we give some characterizations of almost completely regular spaces and c-semistratifiable spaces(CSS) by semi-continuous functions. We mainly show that:(1)Let X be a space. Then the following statements are equivalent:(i) X is almost completely regular.(ii) Every two disjoint subsets of X, one of which is compact and the other is regular closed, are completely separated.(iii) If g, h : X → I, g is compact-like, h is normal lower semicontinuous, and g ≤ h, then there exists a continuous function f : X → I such that g ≤ f ≤ h;and(2) Let X be a space. Then the following statements are equivalent:(a) X is CSS;(b) There is an operator U assigning to a decreasing sequence of compact sets(Fj)j∈N,a decreasing sequence of open sets(U(n,(Fj)))n∈N such that(b1) Fn■U(n,(Fj)) for each n ∈ N;(b2)∩n∈NU(n,(Fj)) =∩n∈NFn;(b3) Given two decreasing sequences of compact sets(Fj)j∈N and(Ej)j∈N such that Fn■Enfor each n ∈ N, then U(n,(Fj))■U(n,(Ej)) for each n ∈ N;(c) There is an operator Φ : LCL(X, I) → USC(X, I) such that, for any h ∈ LCL(X, I),0 Φ(h) h, and 0 Φ(h)(x) h(x) whenever h(x) 0. 相似文献
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设X(t)(t∈R )是一个d维非退化扩散过程.本文得到了比原有结果更一般的非退化扩散过程极性的充分条件,证明了对任意u∈Rd,紧集E(0, ∞),有若d=1,则对任意紧集F(?)R, 若d≥2,则对任意紧集E ∈(0, ∞), 其中B(Rd)为Rd上的Borel σ-代数,dim和Dim分别表示Hausdorff维数和Packing 维数. 相似文献
18.
The purpose of this paper is to give characterizations for uniform exponential dichotomy of evolution families on the real
line. We consider a general class of Banach function spaces denoted
and we prove that if
with
and the pair
is admissible for an evolution family
then
is uniformly exponentially dichotomic. By an example we show that the admissibility of the pair
for an evolution family is not a sufficient condition for uniform exponential dichotomy. As applications, we deduce necessary
and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pairs
and
with
相似文献
19.
In this note we define a new topology on C(X),the set of all real-valued continuous functions on a Tychonoff space X.The new topology on C(X) is the topology having subbase open sets of both kinds:[f,C,ε[={g E C(X):|f(x)-g(x)| ε for every x∈C} and[U,r]~-={g∈C(X):g~(-1)(r)∩U≠φ},where f∈C(X),C∈KC(X)={nonempty compact subsets of X},ε 0,while U is an open subset of X and r∈R.The space C(X) equipped with the new topology T_(kh) which is stated above is denoted by C_(kh)(X).Denote X_0={x∈X:x is an isolated point of X} and X_c={x∈X:x has a compact neighborhood in X}.We show that if X is a Tychonoff space such that X_0=X_c,then the following statements are equivalent:(1) X_0 is G_δ-dense in X;(2) C_(kh)(X) is regular;(3) C_(kh)(X) is Tychonoff;(4) C_(kh)(X) is a topological group.We also show that if X is a Tychonoff space such that X_0=X_c and C_(kh)(X) is regular space with countable pseudocharacter,then X is σ-compact.If X is a metrizable hemicompact countable space,then C_(kh)(X) is first countable. 相似文献
20.
Xiao Erjian 《数学年刊B辑(英文版)》1993,14(4):497-506
The author defines, using jets, cohomology $H^p(\Lambda _{f,k-})$ for hypersurfaces, which are invariant under contact transformations. For isolated hypersurface singularities, it is proved that
$H^0(\Lambda _{f,k-})=O_{U,0}/f^{k+1}O_{U,0},$
$H^p(\Lambda _{f,k-})=0,1\leq p \leq N-3 or p=N,$
$dimH^{N-2}(\Lambda _{f,k-})-dimH^{N-1}(\Lambda _{f,k-})=\[\left( {\begin{array}{*{20}{c}}
k \ N
\end{array}} \right)\dim {O_{U,0}}/(f,\frac{{\partial f}}{{\partial {x_1}}}, \cdots ,\frac{{\partial f}}{{\partial {x_N}}}){O_{U,0}}\] $
The algorithm of computation for H^{N-2} and H^{N-1} is given, and it is proved that $H^{N-1}=0$ when f is quasi-homogeneous. 相似文献
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