Search results for "group theory"
showing 10 items of 703 documents
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
2018
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.
Does "whole-word shape" play a role in visual word recognition?
2002
To analyze the impact of outline shape on visual word recognition, the visual pattern of the stimuli can be distorted by size alternation. Contrary to the predictions of models that rely on outline shape (Allen, Wallace, & Weber, 1995), the effect of size alternationwas greater for low-frequency words than for high-frequency words in a lexical decision task (Experiment 1). In Experiment 2, the effect of case type (lowercase vs. UPPERCASE) occurred for low-frequency words, but not for high-frequency words. The effect of neighborhood size was remarkably similar in the two experiments. The results can be readily explained in the framework of a resonance model (Grossberg & Stone, 1986), in whic…
Graphemic complexity and multiple print-to-sound associations in visual word recognition
2005
Max Planck Institute for Psycholinguistics, Nijmegen, The Netherlands It has recently been reported that words containing a multiletter grapheme are processed slower than are words composed of single-letter graphemes (Rastle & Coltheart, 1998; Rey, Jacobs, Schmidt-Weigand, & Ziegler, 1998). In the present study, using a perceptual identification task, we found in Experiment 1 that this graphemic complexity effect can be observed while controlling for multiple print-to-sound associations, indexed by regularity or consistency. In Experiment 2, we obtained cumulative effects of graphemic complexity and regularity. These effects were replicated in Experiment 3 in a naming task. Overall, these r…
Priming in word stem completion tasks: comparison with previous results in word fragment completion tasks
2015
This study investigates priming in an implicit Word Stem Completion (WSC) task. A total of 305 participants performed a WSC task in two phases (study and test). The test phase included 63 unique-solution stems and 63 multiple-solution stems. After confirming the presence of priming (mean = 0.22), analysis revealed that it was stronger in the case of multiple-solution stems, indicating that the stems were not a homogeneous group of stimuli. Thus, further analyses were performed only for the data of the unique-solution stems. The correlations between priming and a set of conceptual (familiarity, frequency of use, number of meanings) and non-conceptual (letters/blanks ratio and difficulty of c…
On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups
2002
Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the `Bestvina-Brady group', or `Artin kernel', Gamma_K. We show that Gamma_K has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i) the geometric dimension is 2, or (ii) the cohomological dimension is 2 and the geometric dimension is not known.
Whitney forms and their extensions
2021
Whitney forms are widely known as finite elements for differential forms. Whitney’s original definition yields first order functions on simplicial complexes, and a lot of research has been devoted to extending the definition to nonsimplicial cells and higher order functions. As a result, the term Whitney forms has become somewhat ambiguous in the literature. Our aim here is to clarify the concept of Whitney forms and explicitly explain their key properties. We discuss Whitney’s initial definition with more depth than usually, giving three equivalent ways to define Whitney forms. We give a comprehensive exposition of their main properties, including the proofs. Understanding of these propert…
Abelian Sylow subgroups in a finite group, II
2015
Abstract Let p ≠ 3 , 5 be a prime. We prove that Sylow p-subgroups of a finite group G are abelian if and only if the class sizes of the p-elements of G are all coprime to p. This gives a solution to a problem posed by R. Brauer in 1956 (for p ≠ 3 , 5 ).
ON SYLOW NORMALIZERS OF FINITE GROUPS
2013
[EN] The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent Hall subgroups for given sets of primes are exactly the subgroup- closed saturated formations satisfying the following property: a group belongs to the class if and only if its Sylow normalizers do so. The paper analyzes the extension of this research to the universe of all finite groups.
On second minimal subgroups of Sylow subgroups of finite groups
2011
A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids its chief factors. Partial cover and avoidance property has turned out to be very useful to clear up the group structure. In this paper, finite groups in which the second minimal subgroups of their Sylow p-subgroups, p a fixed prime, are partial CAP-subgroups are completely classified.
The average number of Sylow subgroups of a finite group
2013
We prove that if the average Sylow number (ignoring the Sylow numbers that are one) of a finite group G is ⩽7, then G is solvable.