JORDAN BIMODULES OVER THE SUPERALGEBRAS P(n) AND Q(n)

We extend the Jacobson's Coordinatization theorem to Jordan superalgebras. Using it we classify Jordan bimodules over superalgebras of types Q(n) and JP(n), n >= 3. Then we use the Tits-Kantor-Koecher construction and representation theory of Lie superalgebras to treat the remaining case Q(2).

COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

INTEGRABLE MODULES FOR AFFINE LIE SUPERALGEBRAS

Irreducible nonzero level modules with finite-dimensional weight spaces are discussed for nontwisted affine Lie superalgebras. A complete classification of such modules is obtained for superalgebras of type A(m, n)(boolean AND) and C(n)(boolean AND) using Mathieu's classification of cuspidal modules over simple Lie algebras. In other cases the classification problem is reduced to the classification of cuspidal modules over finite-dimensional cuspidal Lie superalgebras described by Dimitrov, Mathieu and Penkov. Based on these results a. complete classification of irreducible integrable (in the sense of Kac and Wakimoto) modules is obtained by showing that any such module is of highest weight, in which case the problem was solved by Kac and Wakimoto.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

GLOBALIZATION OF TWISTED PARTIAL ACTIONS

Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish a criteria for the existence of a globalization for a given twisted partial action of a group on A. If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corresponding to its globalization. For arbitrary unital rings the globalization problem is reduced to an extendibility property of the multipliers involved in the twisted partial action.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

AUSLANDER GENERATORS OF ITERATED TILTED ALGEBRAS

Let A be an iterated tilted algebra. We will construct an Auslander generator M in order to show that the representation dimension of A is three in case A is representation infinite.

Composition and screening of antifungal activity against Cladosporium sphaerospermum and Cladosporium cladosporioides of essential oils of leaves and fruits of Piper species

This study investigated the composition and antifungal activity against Cladosporium sphaerospermum and Cladosporium cladosporioides of essential oils of leaves of Piper cernuum, Piper diospyrifolium, Piper crassinervium, Piper solmsianum and Piper umbelata and fruits of P. cernuum and P. diospyrifolium. The essentials oils were analyzed by GC-MS and submitted of the antifungal activity tests. The essential oils of fruits from P. cernuum and leaves of P. crassinervium and P. solmsianum showed potential antifungal activity against C. sphaerospermum and C. cladosporioides. In addition, this is the first report of the composition of essential oils of fruits of P. cernuum and P. diospyrifolium.

Antimicrobial activity of Piper arboreum and Piper tuberculatum (Piperaceae) against opportunistic yeasts

In the scope of our ongoing research on bioactive agents from natural sources, 24 extracts and fractions obtained from Piper arboreum Aub. and Piper tuberculatum Jacq. ( Piperaceae) were screened for antifungal activity by using broth microdilution method. The current investigation reveals that P. arboreum extracts and fractions were more effective against Candida krusei and Candida parapsilosis than Cryptococcus neoformans. The growth of Candida albicans was weakly affected by all the tested extracts and fractions. The strongest effects were observed for hexane and ethyl acetate fractions from leaves of P. arboreum, with MIC values ( in mu g/ml) of 15.6 and 31.2 mu g/ml against C. krusei, respectively. Additionally, phytochemical investigation of the hexane fraction of P. arboreum leaves furnished 3 pyrrolidine amides; piperyline, 4,5-dihydropiperyline and tetrahydropiperyline, which could be responsible, at least in part for the observed antifungal activity. The most active compound, tetrahydropiperyline, displayed MIC values of 15.6 mu g/ml against C. krusei, C. parapsilosis and C. neoformans.

Intraspecific variability of dihydrochalcone, chromenes and benzoic acid derivatives in leaves of Piper aduncum L. (Piperaceae)

Chemical analysis carried out in leaves of 18 specimens of Piper aduncum L. (Piperaceae) occurring at Ripasa Reserve, Araraquara, SP, Brazil indicated two distinct populations when investigated over a period of 14 months (January 2000 to February 2001) and then submitted to cluster analysis. The two groups were characterized by accumulation of prenylated benzoic acids, chromenes and dihydrochalcone, respectively. A total of seven compounds were identified by HPLC analysis and compared with standards including two prenylated benzoic acid [aduncumene (1) and 3-(3'-7'-dimethyl-2'-6'-octadienyl)-4-methoxy-benzoic acid (5)], four chromenes [methyl 2,2-dimethyl-8-(3'-methyl-2'-butenyl)-2H-1-chromene-6-carboxylate (4), methyl 2,2-dimethyl-2H-1-chromene-6-carboxylate (2b), methyl 8-hydroxy-2,2-dimethyl-2H-1-chromene-6-carboxylate (3) and 2,2-dimethyl-2H-1-chromene-6-carboxylic acid (2a)] and one dihydrochalcone [2',6'-dihydroxy-4'-methoxy-dihydrochalcone (6)].

Study of Salmonella typhimurium mutagenicity assay of (E)-piplartine by the Ames test

Phytochemical studies carried out with Piperaceae species have shown great diversity of secondary metabolites among which are several displayed considerable biological activities. The species Piper tuberculatum has been intensively investigated and a series of amides have been described. For instance, (E)-piplartine showed significant cytotoxic activity against tumor cell lines, especially human leukemia cell lines; antifungal activity against Cladosporium species; trypanocidal activity and others. Considering the popular use of P. tuberculatum and the lack of pharmacological studies regarding this plant species, the mutagenic and antimutagenic effect of (E)-piplartine was evaluated by the Ames test, using the strains TA97a, TA98, TA100 and TA102 of Salmonella typhimurium. No mutagenic activity was observed for this compound.

The development of social tourism in Brazil

This article reflects on the origins and development of social tourism in Brazil, with particular reference to the socio-economic conditions in the country. It discusses the theoretical conceptualisation of social tourism and its implementations in the non-European context. The case study presented here is based on a secondary bibliographical research of existing definitions and an in-depth analysis of the political conditions that have framed its development. More particularly, this article will discuss public initiatives since the Labour Party gained power in Brazil in 2003. Apart from public sector involvement in social tourism, this article also examines the role of the third sector in provision. The example of Social Service of Commerce will be presented. This article will conclude by evaluating the phenomenon of social tourism in Brazil, highlighting where progress has been made and which are the key challenges that need to be overcome.

Organized Crime and Terrorism: From the Cells Towards Political Communication, A Case Study

During the first half of 2006 the city of Sao Paulo suffered three series of violent attacks against the security forces, civilians, and the government. The violent campaign also included a massive rebellion in prisons and culminated in the kidnapping of a journalist and the broadcast of a manifesto from the criminal organization PCC threatening the police and the government. Right after, the main device used to contain organized crime in the prisons was declared unconstitutional. This episode represents a prototypical example of the use of media-focused terrorism by organized crime for projection into the political communication arena.