Significance of Speech Communication in Human Needs Systems

The article presents the description of a complex syntactic whole as the main unit of written communication in the aspect of the efficiency of its use in the texts of the book of functional styles. Special attention is paid to invariant matrices of complex syntactic whole, as the external forms of complex syntactic whole form stable multiple of the identity, and the analysis forms of complex syntactic whole allows to speak about given regularities of production / perception, which is impossible within the scope of a shape.

Complex syntactic whole as a linguistic text unit

A complex syntactic whole is one of the linguistic units that function in the text. The article discusses structural and semantic indicators that realize indivisibility of expression and content planes, as well as discreteness and specific reproducibility. Special attention is paid to invariant matrices of the external form of a complex syntactic unit, which contribute to the spatial-temporal separateness of a complex syntactic whole in a text and allow to reveal the patterns of its production / perception. The term base of the article is based on the original author's glossary of the research topic.

Improved algorithms for computing the greatest right and left invariant Boolean matrices and their application

We define right and left invariant matrices as Boolean matrices that are solutions to certain systems of matrix equations and inequalities over additively idempotent semirings. We provide improved algorithms for computing the greatest right and left invariant equivalence and quasi-order matrices. The improvements are based on the usage of the well-known partition refinement technique. Afterwards, we present the application of right invariant matrices in the determinization of weighted automata over additively idempotent, commutative and zero-divisor free semirings. In particular, we provide improvements of the well-known determinization method of weighted automata over tropical semirings given by Mohri [Computational Linguistics 23 (2) (1997) 269-311].

Units of Written Communication: Complex Syntactic Integer

The article presents the description of a complex syntactic whole as the main unit of written communication in the aspect of the efficiency of its use in the texts of the book of functional styles. Special attention is paid to invariant matrices of complex syntactic whole, as the external forms of complex syntactic whole form stable multiple of the identity, and the analysis forms of complex syntactic whole allows to speak about given regularities of production / perception, which is impossible within the scope of a shape.

Cartan invariant matrices for finite monoids

International audience Let $M$ be a finite monoid. In this paper we describe how the Cartan invariant matrix of the monoid algebra of $M$ over a field $\mathbb{K}$ of characteristic zero can be expressed using characters and some simple combinatorial statistic. In particular, it can be computed efficiently from the composition factors of the left and right class modules of $M$. When $M$ is aperiodic, this approach works in any characteristic, and generalizes to $\mathbb{K}$ a principal ideal domain like $\mathbb{Z}$. When $M$ is $\mathcal{R}$-trivial, we retrieve the formerly known purely combinatorial description of the Cartan matrix. Soit $M$ un monoïde fini. Dans cet article, nous exprimons la matrice des invariants de Cartan de l'algèbre de $M$ sur un corps $\mathbb{K}$ de caractéristique zéro à l'aide de caractères et d'une statistique combinatoire simple. En particulier, elle peut être calculée efficacement à partir des facteurs de compositions des modules de classes à gauche et à droite de $M$. Lorsque $M$ est apériodique, cette approche se généralise à toute caractéristique et aux anneaux principaux comme $\mathbb{Z}$. Lorsque $M$ est $\mathcal{R}$-trivial, nous retrouvons la description combinatoire de la matrice de Cartan précédemment connue.