布尔矩阵的指标格

本文首先构造了由一个布尔矩阵的特定行指标和列指标对所确定的指标格,然后刻画了指标格的同态像、直积和子格所对应的布尔矩阵的性质.     

可实现布尔矩阵与传递关系计数

传递关系的计数问题是一个开问题。本文建立了对称传递关系与可实现布尔矩阵的联系,并通过该联系,给出了对称传递关系的计数。     

布尔矩阵的指标格(英文)

本文介绍了布尔矩阵的指标格,并讨论了它的性质,得到了从布尔矩阵指标格到一个给定完备格的一个序嵌入映射存在的条件,回答了在什么条件下布尔矩阵的指标格是完全分配格的问题。     

布尔矩阵的指标格的性质

介绍了布尔矩阵的行零元、列零元和相容子矩阵的定义并讨论了它们的性质,给出了布尔矩阵的指标格分别为分配格、半分配格和半模格的等价条件.     

布尔矩阵平方根问题及其与图着色问题的关系

讨论了布尔矩阵平方根问题及其与图着色问题的关系.首先得到有平方根的布尔矩阵具有的一些性质;然后给出布尔矩阵存在平方根的一个充要条件;最后证明布尔矩阵的平方根问题可以转化为简单图的着色问题.     

格矩阵半群的Euler-Fermat公式

给出并证明格矩阵半群的Euler-Fermat公式:A(n-1)2 1 = A(n-1)2 1 [n], A ∈ Mn(L)其中L是任意的分配格,Mn(L)是L上所有n阶矩阵构成的半群.这是布尔矩阵半群的Euler-Fermat公式的一种推广.     

一种布尔矩阵传递核的计算算法

布尔矩阵的传递核一定存在且不一定唯一,但根据定义很难将其构造出来。本文首先根据传递布尔矩阵的性质,对于任意一个布尔矩阵,研究了一个包含于它的特殊传递布尔矩阵;然后给出了该特殊传递布尔矩阵是传递核的一个充要条件。最后,根据该充要条件,提出了一种计算一般布尔矩阵传递核的算法。     

一种求布尔矩阵传递闭包的基于自反矩阵构造的平方算法

首先,介绍布尔矩阵传递闭包的概念及计算问题;随后,分析布尔矩阵的传递闭包和由该布尔矩阵与单位矩阵取并所得到的自反矩阵的传递闭包之间的关系;最后,利用上述结果给出一种求解布尔矩阵传递闭包的基于自反矩阵构造的平方算法,并通过实例说明了其具体计算过程.     

布尔矩阵的可实现问题及其与色数问题的关系

讨论了布尔矩阵的可实现问题及其与色数问题的关系.首先给出布尔矩阵可实现的一些充要条件,讨论可实现布尔矩阵的性质,其次证明可实现布尔矩阵的容度等于该矩阵所生成的图的色数;简单图的邻接矩阵的对偶阵是可实现的,且其容度就是简单图的色数的一个上界.     

粗糙集的矩阵关系

将粗糙集中的集合转化为矩阵刻画,通过引入矩阵算子、类矩阵算子,借助截矩阵和关系矩阵,讨论了Paw lak粗糙集和变精度粗糙集中集合关系的矩阵计算及其所具有的一些基本性质.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Lengths of periods of continued fractions of square roots of integers

Empirical study of the period’s length T of the continued fractions of $\sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $T\leq C\sqrt{Q}\ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.