Julio P. Lafuente

On complemented nonabelian chief factors of a finite group

The number of chief factors which are complemented in a finite groupG may not be the same in two chief series ofG, despite what occurs with the number of frattini chief factors or of chief factors which are complemented by a maximal subgroup ofG. In this paper we determine the possible changes on that number. These changes can only occur in a certain type of nonabelian chief factors. All groups considered in this paper are assumed to be finite.

Error Probabilities for Bounded Distance Decoding

Decoding errors can be seen from the point of view of the receiver or the transmitter. This naturally leads to different functions for the decoding error probability. We study their behaviour and the relation between these two functions. Though both functions are equally good when used to compare two codes with respect to decoding errors only one of them reflects in general the properties such a function should have. This is not the function one usually considers in the literature when studying decoding errors. Both functions coincide only if the underlying code is perfect. The investigations in this paper can be seen as a continuation of earlier work of MacWilliams (see chap. 16.1 in [2]).

Edge Detection Based on Ordered Directionally Monotone Functions

We present an image edge detection algorithm that is based on the concept of ordered directionally monotone functions, which permit our proposal to consider the direction of the edges at each pixel and perform accordingly. The results of this method are presented to the EUSFLAT 2017 Competition on Edge Detection.

Strengthened Ordered Directional and Other Generalizations of Monotonicity for Aggregation Functions.

A tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss strengthened ordered directional monotonicity, its relation to other types of monotonicity, such as directional and ordered directional monotonicity and the main properties of the class of functions that are strengthened ordered directionally monotone. We also study some construction methods for such functions and provide a characterization of usual monotonicity in terms of these notions of monotonicity.

Strengthened ordered directionally monotone functions. Links between the different notions of monotonicity

Abstract In this work, we propose a new notion of monotonicity: strengthened ordered directional monotonicity. This generalization of monotonicity is based on directional monotonicity and ordered directional monotonicity, two recent weaker forms of monotonicity. We discuss the relation between those different notions of monotonicity from a theoretical point of view. Additionally, along with the introduction of two families of functions and a study of their connection to the considered monotonicity notions, we define an operation between functions that generalizes the Choquet integral and the Łukasiewicz implication.

Some properties and construction methods for ordered directionally monotone functions

In this work we propose a new generalization of the notion of monotonicity, the so-called ordered directionally monotonicity. With this new notion, the direction of increasingness or decreasingness at a given point depends on that specific point, so that it is not the same for every value on the domain of the considered function.

EXTENSIONS OF IRREDUCIBLE -MODULES

where V and U are irreducible KG-modules and their centralizers in G. Note that the intersection of all centralizers of the above extensions for a fixed U is equal to CGðPGðUÞ=PGðUÞJÞ, where PGðUÞ, is the projective cover of the KG-module U and J 1⁄4 JðKÞG is the Jacobson radical of KG. Well known results on the centralizers in G of the set of composition factors of PGðUÞ or CGðPGðUÞ=PGðUÞJÞ, are due to Brauer, Michler, Willems VII §14) and Pahlings.1⁄214 Our main motivations are the fundamental results of Gaschütz for K 1⁄4 Fp and p-soluble groups VII , and the fact that ð Þ FpðCGðUÞÞ CGðPGðUÞ=PGðUÞJÞ FpðGÞ \ CGðUÞ; COMMUNICATIONS IN ALGEBRA Vol. 30, No. 8, pp. 3935–3951, 2002