Abstract:
We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and that the integral forms are needed. They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold. In our construction of the Hodge dual of superforms they arise naturally. The compatibility between Hodge duality and supersymmetry is exploited and applied to several examples. We define the irreducible representations of supersymmetry in terms of integral and superforms in a new way which can be easily generalised to several models in different dimensions. The construction of supersymmetric actions based on the Hodge duality is presented and new supersymmetric actions with higher derivative terms are found. These terms are required by the invertibility of the Hodge operator.

Abstract:
Integral forms provide a natural and powerful tool for the construction of supergravity actions. They are generalizations of usual differential forms and are needed for a consistent theory of integration on supermanifolds. The group geometrical approach to supergravity and its variational principle are reformulated and clarified in this language. Central in our analysis is the Poincare' dual of a bosonic manifold embedded into a supermanifold. Finally, using integral forms we provide a proof of Gates' so-called "Ectoplasmic Integration Theorem", relating superfield actions to component actions.

Abstract:
We present a new construction for the Hodge operator for differential manifolds based on a Fourier (Berezin)-integral representation. We find a simple formula for the Hodge dual of the wedge product of differential forms, using the (Berezin)-convolution. The present analysis is easily extended to supergeometry and to non-commutative geometry.

Abstract:
We review the extraordinary fertility and proliferation in mathematics and physics of the concept of a surface with constant and negative Gaussian curvature. In his outstanding 1868 paper Beltrami discussed how non-Euclidean geometry is actually realized and displayed in a disk on the plane. This metric is intrinsically defined and definite but only if indefinite metrics are introduced it is possible to fully understand the structure of pseudospheres. In a 3D flat space R^3 the fundamental quadric is introduced, with the same signature as the metric of R^3; this leads to 3 kinds of surfaces with constant Gaussian curvature: the sphere, the single-sheet hyperboloid and the two-sheet hyperboloid; the last one is shown to be isomorphic to Beltrami's disk. The spacetime corresponding to the single-sheet case is de Sitter cosmological model, which, due to its symmetry, has an important role in cosmology. When two of the three fundamental quadrics are combined, a simple, yet deep, solution of Einstein-Maxwell equations corresponding to a uniform electromagnetic field is obtained with many applications in mathematical physics. One of them is a "no go" theorem: when one tries to frame a Riemannian four-dimensional manifold in a Kahlerian structure, it is found that, while this is generically possible with a definite signature, in spacetime only BR fulfills the requirement. The BR metric plays an important role in the exploration of new principles in fundamental physical theories; we briefly mention some examples related to the horizon of a black hole and the dilaton in string theory.

Abstract:
We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the geometry of superprojective spaces, we extend Donaldson's definition of balanced manifolds to supermanifolds and we derive the new conditions of a balanced supermanifold. We apply the construction to superpoints viewed as submanifolds of superprojective spaces. We conclude with a list of open issues and interesting problems that can be addressed in the present context.

Abstract:
We present a study on the integral forms and their Cech/de Rham cohomology. We analyze the problem from a general perspective of sheaf theory and we explore examples in superprojective manifolds. Integral forms are fundamental in the theory of integration in supermanifolds. One can define the integral forms introducing a new sheaf containing, among other objects, the new basic forms delta(dtheta) where the symbol delta has the usual formal properties of Dirac's delta distribution and acts on functions and forms as a Dirac measure. They satisfy in addition some new relations on the sheaf. It turns out that the enlarged sheaf of integral and "ordinary" superforms contains also forms of "negative degree" and, moreover, due to the additional relations introduced, its cohomology is, in a non trivial way, different from the usual superform cohomology.

Abstract:
We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential calculus on finite G is given for selfconsistency. Exterior derivative, exterior product, metric, Hodge dual, connections, torsion, curvature, and biinvariant integration can be defined algebraically. A projector decomposition of the braiding operator is found, and used in constructing the projector on the space of 2-forms. By means of the braiding operator and the metric a knot invariant is defined for any finite group.

Abstract:
a cultura popular analisada a partir da concep？？o dos folcloristas e dos membros do centro popular de cultura, colocando em cena os termos tradi？？o e transforma？？o, considerados antag？nicos por ambas as tendências e envolvidos pela quest？o nacional, amplamente discutida pelas ciências sociais durante todo o século xx

Abstract:
o trabalho descreve a ocorrência de diphyllobothrium mansoni (cestoda, diphyllobothridae) no intestino delgado de um exemplar de cerdocyon thous (mammalia, canidae), proveniente da regi？o de itatinga, estado de s？o paulo, brasil. este é o primeiro relato da presen？a desse cestódeo em c. thous.

Abstract:
the importance of studies with hematological, serum biochemistry and urinary values of crab-eating fox (cerdocyon thous) is based on the need for health care and maintenance of those populations. this paper has the objective to investigate hematological, serum biochemistry and urinary physiological parameters of the crab-eating fox, comparing gender and age differences. blood samples were collected in 2003 from 52 animals of different zoos in s？o paulo state, brazil; 7ml of blood was used to obtain a complete blood cell count (cbc) and the profile of the serum biochemistry. moreover, 5ml of urine were collected for analysis. there was no difference in values for male and female animals, as for the cbc and serum biochemistry. some hematological and serum biochemical parameters were influenced by age, showing significant differences. urinalysis results were just demonstrated in a descriptive form. the studied values were, rbc 4.35±0.73 x 106 /μl, wbc 7.72±3.66 x 103 /μl (predominance of segmented neutrophils), platelets 227.06±111.58 x 103 /μl, urea 43.06±14.28mg/dl and creatinine 1.03±0.24mg/dl. hematological, serum biochemistry and urinary values obtained in this study can be used as physiological values of the captive crab-eating fox. it is possible to conclude that wild species need their own reference values, differentiating animals in captivity from free-ranging animals.