Search results for "Abstract data type"
showing 10 items of 1140 documents
The set of conjugacy class sizes of a finite group does not determine its solvability
2014
Abstract We find a pair of groups, one solvable and the other non-solvable, with the same set of conjugacy class sizes.
Maximal subgroups and formations
1989
Abstract We define, in each finite group G , some subgroups of Frattini-type in relation with a saturated formation and with a set of primes and study their properties, especially their influence in the structure of G .
Nilpotent and perfect groups with the same set of character degrees
2014
We find a pair of finite groups, one nilpotent and the other perfect, with the same set of character degrees.
Attracting sets in a deterministic discrete traffic model
2001
The fundamental diagram of the Nagel-Schreckenberg traffic model is derived analytically for the deterministic case using methods and concepts from nonlinear dynamics. It is shown that the possible states of the long-term behaviour form a globally attractive subset which can be well characterized. This attractive set of states is composed of coexisting attractors. The attractor concept is applied to a slow-to-start extension of the model. For this example it is shown that the attractive set consists of coexisting attractors with different macroscopic properties, that can be determined analytically.
Reducing Local Alphabet Size in Recognizable Picture Languages
2021
A recognizable picture language is defined as the projection of a local picture language defined by a set of two-by-two tiles, i.e. by a strictly-locally-testable (SLT) language of order 2. The family of recognizable picture languages is also defined, using larger k by k tiles, \(k>2\), by the projection of the corresponding SLT language. A basic measure of the descriptive complexity of a picture language is given by the size of the SLT alphabet using two-by-two tiles, more precisely by the so-called alphabetic ratio of sizes: SLT-alphabet/picture-alphabet. We study how the alphabetic ratio changes moving from two to larger tile sizes, and we obtain the following result: any recognizable pi…
On WQO Property for Different Quasi Orderings of the Set of Permutations
2013
The property of certain sets being well quasi ordered (WQO) has several useful applications in computer science – it can be used to prove the existence of efficient algorithms and also in certain cases to prove that a specific algorithm terminates.
Algebraic Structures of Rough Sets
1994
This paper deals with some algebraic and set-theoretical properties of rough sets. Our considerations are based on the original conception of rough sets formulated by Pawlak [4, 5]. Let U be any fixed non-empty set traditionally called the universe and let R be an equivalence relation on U. The pair A = (U, R) is called the approximation space. We will call the equivalence classes of the relation R the elementary sets. We denote the family of elementary sets by U/R. We assume that the empty set is also an elementary set. Every union of elementary sets will be called a composed set. We denote the family of composed sets by ComR. We can characterize each set X ⊆ U using the composed sets [5].
Words and Patterns
2002
In this paper some new ideas, problems and results on patterns are proposed. In particular, motivated by questions concerning avoidability, we first study the set of binary patterns that can occur in one infinite binary word, comparing it with the set of factors of the word. This suggests a classification of infinite words in terms of the "difference" between the set of its patterns and the set of its factors. The fact that each factor in an infinite word can give rise to several distinct patterns leads to study the set of patterns of a single finite word. This set, endowed with a natural order relation, defines a poset: we investigate the relationships between the structure of such a poset…
On a projective representation of chain geometries
1984
We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GrasmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the “1-distance lines’, 1=1,..., r, which are in 1–1-correspondence to the so-called “generalized reguli of type (r, 1)”.
Spectral properties of correlation matrices for some hierarchically nested factor models
2007
We show that spectral methods, such as Principal Component Analysis and Random Matrix Theory, are unable to reveal the hierarchical (or nested) structure of a set of mutivariate data. We consider the method introduced in M. Tumminello et al., EPL 78, 30006 (2007) to associate a hierarchical factor model with a set of data by making use of clustering algorithms. This is done by proving the existence of a bijective correspondence between a hierarchical tree and a factor model.