On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

The supernova remnant CTB 37B and its associated magnetar CXOU J171405.7-381031: evidence for a magnetar-driven remnant

We discuss the association between the candidate magnetar CXOU J171405.7-381031 and the supernova remnant CTB 37B. The recent detection of the period derivative of the object allowed an estimation of a young characteristic age of only similar to 1000 yr. This value is too small to be compatible even with the minimum radius of the remnant being >= 10 pc, the value corresponding to the lower limit of the estimated distance of 10.2 +/- 3.5 kpc, unless the true distance happens to be even smaller than the lower limit. We argue that a consistent scenario for the remnant`s origin, in which the latter is powered by the energy injected by a young magnetar, is indeed more accurate to explain the young age, and demonstrates its non-standard (i.e. magnetar-driven) nature.

The Occurrence of the Plantaris Muscle and its Muscle-Tendon Relationship in Adult Human Cadavers

Twenty legs from adult male cadavers were examined to analyze the anatomical relationships between the component parts of the plantaris muscle. This muscle was present in all of the cadavers and it was found that the length of the muscle in relation to its belly was approximately three times greater than in relation to the tendon.

On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall`s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index. (C) 2008 Elsevier Inc. All rights reserved.

Dimethylthallium(III) complexes with picolinic acid and its hydroxyl derivatives

The reaction of dimethylthallium(III) hydroxide with picolinic acid (Hpic), 3-hydroxypicolinic acid (H(2)3hpic) and 6-hydroxypicolinic acid (H(2)6hpic) in an aqueous/methanol mixture afforded the complexes [TlMe(2)(pic)] (1), [TlMe(2)(H3hpic)] (2) and [TlMe(2)(H6hpic)] (3), respectively. Complex 3`, [NaTlMe(2)(6hpic)(2)](n), was obtained as a minor product from a methanolic solution of 3. Compounds 1-3 were characterized by IR and Raman spectroscopy and, in the cases of 1, 2 and Y, by single-crystal X-ray diffraction. Complex 3` is the first example of an H6hpic(-) heterobimetallic compound to be isolated. The (1)H and (13)C NMR spectra of 1 and 2 are also discussed. (c) 2008 Elsevier Ltd. All rights reserved.