An N=8 Superaffine Malcev Algebra and Its N=8 Sugawara

A supersymmetric affinization of the algebra of octonions is introduced. It satisfies a super-Malcev property and is N=8 supersymmetric. Its Sugawara construction recovers, in a special limit, the non-associative N=8 superalgebra of Englert et al. This paper extends to supersymmetry the results obtained by Osipov in the bosonic case.Comment: 10 pages, LaTe

Normal ordering and boundary conditions in open bosonic strings

Boundary conditions play a non trivial role in string theory. For instance the rich structure of D-branes is generated by choosing appropriate combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an antisymmetric background is present at the string end-points (corresponding to mixed boundary conditions) space time becomes non-commutative there. We show here how to build up normal ordered products for bosonic string position operators that satisfy both equations of motion and open string boundary conditions at quantum level. We also calculate the equal time commutator of these normal ordered products in the presence of antisymmetric tensor background.Comment: 7 pages no figures, References adde

G\"odel-type Spacetimes in Induced Matter Gravity Theory

A five-dimensional (5D) generalized G\"odel-type manifolds are examined in the light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by three essential parameters $k$, $m^2$ and $\omega$: identical triads $(k, m^2, \omega)$ correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian generalized G\"odel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that the generalized G\"odel-type 5D manifolds admit maximal group of isometry $G_r$ with $r=7$, $r=9$ or $r=15$ depending on the essential parameters $k$, $m^2$ and $\omega$. The breakdown of causality in all these classes of homogeneous G\"odel-type manifolds are also examined. It is found that in three out of the six irreducible classes the causality can be violated. The unique generalized G\"odel-type solution of the induced matter (IM) field equations is found. The question as to whether the induced matter version of general relativity is an effective therapy for these type of causal anomalies of general relativity is also discussed in connection with a recent article by Romero, Tavakol and Zalaletdinov.Comment: 19 pages, Latex, no figures. To Appear in J.Math.Phys.(1999

Division Algebras and Extended N=2,4,8 SuperKdVs

The first example of an N=8 supersymmetric extension of the KdV equation is here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It corresponds to the unique N=8 solution based on a generalized hamiltonian dynamics with (generalized) Poisson brackets given by the Non-associative N=8 Superconformal Algebra. The complete list of inequivalent classes of parametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associative N=8 SCA" is also furnished. Furthermore, a fundamental domain characterizing the class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" is given.Comment: 14 pages, LaTe

Central extensions, classical non-equivariant maps and residual symmetries

The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps. Further, the notion of "residual symmetry" for theories formulated in given non-vanishing EM backgrounds is introduced. It is pointed out that this is a Lie-algebraic, model-independent, concept.Comment: 8 pages, LaTex. Talk given at the International Conference "Renormalization Group and Anomalies in Gravitation and Cosmology", Ouro Preto, Brazil, March 2003. To appear in the Proceeding

A class of surfaces with planar lines of curvature

En este articulo estudiamos superficies parametrizadas por líneas de curvatura. Obtenemos una caracterización de una clase de superficies con líneas de curvatura planas, esta caracterización depende de ciertas funciones holomorfas. Presentamos una clase de superficies con dos familias de líneas de curvatura planas, esta clase incluye las superficies de Dupin. También damos algunos ejemplos explícitos.In this paper we study surfaces parameterized by lines of curvature. We obtain a characterization of a class of surfaces with planar lines of curvature, this characterization depend on certain holomorphic function. We present a class of surfaces with two family of planar lines of curvature, this class of surfaces includes the Dupin surfaces. Also, we give explicit examples

A shared database of underground utility lines for 3D mapping and GIS applications

For the purpose of facility management it is very important to have detailed and up-to-date databases of underground utility lines, but such data are not always available with adequate accuracy. Hence, the need of collecting and organizing suitable information on underground services is a fundamental issue when dealing with urban data. Besides, by analyzing the process of designing and laying new underground infrastructures it is possible to implement an efficient and cost-effective approach to integrate and update existing maps by exploiting the surveying required for the installation of new facilities. It is also important to underline that collecting all the data in a unique integrated database (and GIS) gives the possibility to share (at least at a local level) the cartographic and thematic information for an optimal management of underground networks. In this paper, a database (DB) model for archiving the underground lines data is presented. The structure of the DB has been designed by following the standard methodology for the modelling of a relational DB, going through successive phases and originating the external, conceptual and logical model. Finally, preliminary tests have been carried on for parts of the DB to verify quality parameters

A Self-Organized Method for Computing the Epidemic Threshold in Computer Networks

In many cases, tainted information in a computer network can spread in a way similar to an epidemics in the human world. On the other had, information processing paths are often redundant, so a single infection occurrence can be easily "reabsorbed". Randomly checking the information with a central server is equivalent to lowering the infection probability but with a certain cost (for instance processing time), so it is important to quickly evaluate the epidemic threshold for each node. We present a method for getting such information without resorting to repeated simulations. As for human epidemics, the local information about the infection level (risk perception) can be an important factor, and we show that our method can be applied to this case, too. Finally, when the process to be monitored is more complex and includes "disruptive interference", one has to use actual simulations, which however can be carried out "in parallel" for many possible infection probabilities

On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule

We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for supergroups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest non-trivial example is given by the N=2 SQM with a real $(1,2,1)$ multiplet and a cubic potential. The action is real. Depending on the overall sign ("Euclidean" or "Lorentzian") of the deformation, a Bender-Boettcher pseudo-hermitian hamiltonian is encountered when solving the equation of motion of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out.Comment: Final version to be published in Int. J. Mod. Phys. A; 20 page