Eugenio M. Fedriani

A new method for classifying complex filiform Lie algebras

In this paper, we describe a new method to classify complex filiform Lie algebras based on the concept of isomorphism between Lie algebras. This method, which has the advantage of being applied to any dimension, gives the families of algebras in each dimension in an explicit way. In order to apply, only the corresponding structure theorem of complex filiform Lie algebras in each dimension is needed. As a consequence of our study, we also predict that the increase (in terms of quotiens) in the number of algebras families when passing from even dimension to odd dimension tends to 1 whereas it grows in a no finite way if passing from odd dimension to immediate even dimension.

Complex filiform Lie algebras of dimension 11

In this paper we give the explicit classification of complex filiform Lie algebras of dimension 11. To do this, we use a method previously obtained by us in an earlier paper, which is based on the concept of isomorphism between Lie algebras. At present, this explicit classification is not known, although Gomez, Jimenez and Khakimdjanov gave a list of these algebras in a non-explicit way, but in terms of cocycles. We find that there exist 188 families of complex filiform Lie algebras of dimension 11.

Design of an Efficient Algorithm to Determine a Near-Optimal Location of Parking Areas for Dangerous Goods in the European Road Transport Network

This paper deals with the problem of locating the minimal number of parking areas being necessary for dangerous goods in the European Road Transport Network. To obtain a near-optimal solution for this problem, we introduce the design of a new graph-based algorithm to locate parking areas in such a way that drivers can obey the regulations related to driving and resting times. This restriction is imposed to the problem as follows: each point in the European Road Transport Network has to be at a distance lower than 200 km from a parking area in the Network.

A complementary measure of heterogeneity on mathematical skills

Finding educational truths is an inherently multivariate problem. There are many factors affecting each student and their performances. Because of this, both measuring of skills and assessing students are always complex processes. This is a well-known problem, and a number of solutions have been proposed by specialists. One of its ramifications is that the variety of progress levels of students in the Mathematics classroom makes teaching more difficult. We think that a measure of the heterogeneity of the different student groups could be interesting in order to prepare some strategies to deal with these kinds of difficulties. The major aim of this study is to develop new tools, complementary to the statistical ones that are commonly used for these purposes, to study situations related to education (mainly to the detection of levels of mathematical education) in which several variables are involved. These tools are thought to simplify these educational analyses and, through a better comprehension of the topic, to improve our teaching. Several authors in our research group have developed some mathematical, theoretical tools, to deal with multidimensional phenomena, and have applied them to measure poverty and also to other business models. These tools are based on multidigraphs. In this article, we implement these tools using symbolic computational software and apply them to study a specific situation related to mathematical education.

DYNAMICS AND SPATIO-TEMPORAL VARIABILITY OF ENVIRONMENTAL FACTORS IN EASTERN AUSTRALIA USING FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS

This paper introduces a new technique in ecology to analyze spatial and temporal variability in environmental variables. By using simple statistics, we explore the relations between abiotic and biotic variables that influence animal distributions. However, spatial and temporal variability in rainfall, a key variable in ecological studies, can cause difficulties to any basic model including time evolution. The study was of a landscape scale (three million square kilometers in eastern Australia), mainly over the period of 1998–2004. We simultaneously considered qualitative spatial (soil and habitat types) and quantitative temporal (rainfall) variables in a Geographical Information System environment. In addition to some techniques commonly used in ecology, we applied a new method, Functional Principal Component Analysis, which proved to be very suitable for this case, as it explained more than 97% of the total variance of the rainfall data, providing us with substitute variables that are easier to manage and are even able to explain rainfall patterns. The main variable came from a habitat classification that showed strong correlations with rainfall values and soil types.

Survey Article: Consequences of some outerplanarity extensions

In this expository paper we revise some extensions of Kuratowski planarity criterion, providing a link between the embeddings of infinite graphs without accumulation points and the embeddings of finite graphs with some distinguished vertices in only one face. This link is valid for any surface and for some pseudosurfaces. On the one hand, we present some key ideas that are not easily accessible. On the other hand, we state the relevance of infinite, locally finite graphs in practice and suggest some ideas for future research.

Description of a Straightforward Strategy to Invest: An Experiment in the Spanish Stock Market

In this paper we reintroduce the topic of arbitrage, explaining an easy method to obtain reasonable results for every possible behavior in the stock market. It is based on purchases at low prices and sales at higher prices, and it is closely related to volatility. Obviously, our technique has its limitations, but we study the hypotheses needed to assure a good performance. Our aim is to contribute to the better understanding of the topic by the researchers, giving an idea of the way how algorithmic strategies work in practice. Finally, we exemplify and test the method through the use of a real data set from some shares of Madrid Stock Exchange, for the time period 1994-2011, and express some concluding remarks.

Outer-embeddability in certain pseudosurfaces arising from three spheres

In this paper we study graph embeddings in pseudosurfaces formed by three spheres sharing at most two points each pair, and in such a way that all vertices in the graph are in the same face. Our results and examples show that the behaviour of outer embeddings in these pseudosurfaces is rather different from embeddings on the pseudosurfaces considered in the literature so far.