Some properties of evolution algebras

The paper is devoted to the study of finite dimensional complex evolu- tion algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criteria of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent n−dimensional complex evolution algebras the possible maximal nilpotency index is 1 + 2n−1 . The criteria of planarity for finite graphs is formulated by means of evolution algebras defined by graphs.Junta de Andalucía FQM-14

Naturally Graded 2-Filiform Leibniz Algebras

The Leibniz algebras appear as a generalization of the Lie algebras [8]. The classification of naturally graded p-filiform Lie algebras is known [3], [4], [5], [9]. In this work we deal with the classification of 2-filiform Leibniz algebras. The study of p-filiform Leibniz non Lie algebras is solved for p = 0 (trivial) and p = 1 [1]. In this work we get the classification of naturally graded non Lie 2-filiform Leibniz algebras

On complex nilpotent Leibniz superalgebras of nilindex n+m

We present the description up to isomorphism of Leibniz superal- gebras with characteristic sequence (n|m1, . . . ,mk) and nilindex n+m, where m = m1 + · · · + mk, n and m (m 6= 0) are dimensions of even and odd parts, respectively.Junta de Andalucía FQM-14

Resprouting after experimental fire application and seed germination in Erica vagans

Resprouting after experimental fire treatments and the effect of light and heat on seed germination were studied in the evergreen shrub Erica vagans. Experimental fire application consisted of two levels of temperature and two levels of fire duration. The number of resprouts produced were counted after 4,9 and 12 months. Above-ground plant dry weight influenced plant survival, but not the number of resprouts produced. However, both temperature and duration of fire application showed significant effects on the number of resprouts produced. After low temperature and short application times E. vagans produced more resprouts, but did no differ from controls (plants clipped without fire treatment). Field observations showed that seedling establishment is rare both in control and burned areas. However, the seedlings were frequent in the cleared areas around experimentally burned stumps. To examine the effect of light and heat on seed germination two germination experiments were performed. Both light and heat application largely increased seed germination. Seeds heated from 80 °C to 100 °C increased their germination rates, but temperatures above that range strongly reduced the germination.Se estudió la capacidad de rebrote, después de la aplicación experimental de tratamientos de fuego, y la germinación del arbusto perennifolio Erica vagans. El fuego experimental consistió en dos niveles de temperatura y en dos niveles de tiempo de duración y se aplicó a tocones de matorrales previamente cortados. El número de rebrotes se contó después de 4,9 y 12 meses. El peso aéreo del matorral antes del experimento tuvo influencia en la supervivencia de la planta, pero no en el número de rebrotes producidos. No obstante, tanto la temperatura como el tiempo de aplicación del fuego mostraron efectos significativos sobre el número de rebrotes producidos. Los rebrotes producidos tras la aplicación de temperaturas bajas durante períodos breves fue el tratamiento que produjo mk rebrotes, pero no se diferenció de plantas control (matorral cortado pero no quemado). A pesar de que la germinación de semillas es rara en condiciones de campo, aparecieron muchas plántulas alrededor de los tocones quemados. Tanto la luz como la aplicación de tratamientos de calor, de 80°C a 100 °C, incrementaron las tasas de germinación

The derivations of some evolution algebras

In this work we investigate the derivations of n−dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero. The spaces of derivations for evolution algebras with matrices of rank n−1 are described.Junta de Andalucía FQM-14

On the description of Leibniz superalgebras of nilindex n+m

In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n1, . . . , nk|m) and nilindex n + m, where n = n1 + · · ·+nk, n and m (m 6= 0) are dimensions of even and odd parts, respectively. Such superalgebras with condition n1 ≥ n − 1 were classified in [4]–[5]. Here we prove that in the case n1 ≤ n − 2 the Leibniz superalgebras have nilindex less than n +m. Thus, we get the classification of Leibniz superalgebras with characteristic sequence (n1, . . . , nk|m) and nilindex n +m

Complex Nilpotent Leibniz Superalgebras with Nilindex Equal to Dimension

We present the description up to isomorphism of Leibniz superalgebras with the characteristic sequence equal to n m1 mk and nilindex n + m, where m = m1 + · · ·+mk, and n and m (m = 0) are the dimensions of the even and odd parts, respectively.Junta de Andalucía FQM14

Comparison of AESA and LAESA search algorithms using string and tree-edit-distances

Although the success rate of handwritten character recognition using a nearest neighbour technique together with edit distance is satisfactory, the exhaustive search is expensive. Some fast methods as AESA and LAESA have been proposed to find nearest neighbours in metric spaces. The average number of distances computed by these algorithms is very low and does not depend on the number of prototypes in the training set. In this paper, we compare the behaviour of these algorithms when string and tree-edit-distances are used.Work partially supported by the spanish CICYT TIC2000-1599-C02 and TIC2000-1703-CO3-02

Quasi-filiform Leibniz algebras of maximum length

The n-dimensional p-filiform Leibniz algebras of maximum length have already been studied with 0 p 2. For Lie algebras whose nilindex is equal to n − 2 there is only one characteristic sequence, (n − 2, 1, 1), while in Leibniz theory we obtain two possibilities: (n−2, 1, 1) and (n−2, 2). The first case (the 2-filiform case) is already known. The present paper deals with the second case, i.e., quasi-filiform non Lie Leibniz algebras of maximum length. Therefore this work completes the study of maximum length of Leibniz algebras with nilindex n − p with 0 p 2.Junta de Andalucía FQM-14

p-Filiform Leibniz algebras of maximum length

The descriptions (up to isomorphism) of naturally graded p-filiform Leibniz algebras and p-filiform (p 3) Leibniz algebras of maximum length are known. In this paper we study the gradation of maximum length for p-filiform Leibniz algebras. The present work aims at the classification of complex p-filiform (p 4) Leibniz algebras of maximum length