Integration of positive constructible functions against Euler characteristic and dimension

Following recent work of R. Cluckers and F. Loeser [Fonctions constructible et integration motivic I, C. R. Math. Acad. Sci. Paris 339 (2004) 411 - 416] on motivic integration, we develop a direct image formalism for positive constructible functions in the globally subanalytic context. This formalism is generalized to arbitrary first-order logic models and is illustrated by several examples on the p-adics, on the Presburger structure and on o-minimal expansions of groups. Furthermore, within this formalism, we define the Radon transform and prove the corresponding inversion formula.Comment: To appear in Journal of Pure and Applied Algebra; 8 page

On the Stability of Black Holes at the LHC

The eventual production of mini black holes by proton-proton collisions at the LHC is predicted by theories with large extra dimensions resolvable at the Tev scale of energies. It is expected that these black holes evaporate shortly after its production as a consequence of the Hawking radiation. We show that for theories based on the ADS/CFT correspondence, the produced black holes may have an unstable horizon, which grows proportionally to the square of the distance to the collision point.Comment: 3 page

Mathematical Support to Braneworld Theory

The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold in a space of high dimension, the bulk, solution of Einstein's equations in high dimension. In this paper we approach the mathematical consistency of this theory with a new proof of the fundamental theorem of submanifolds for case of semi-Riemannian manifolds. This theorem consist an essential mathematical support for this new theory. We find the integrability conditions for the existence of space-time submanifolds in a pseudo-Euclidean space. Keywords: Submanifolds, Braneworld, Pseudo-Riemannian geometryComment: 10 page

Puerto Rican participation in work place health promotion programs in American organizations : the impact of three values.

The focus of this dissertation was to determine whether the values of Familism , Religion , and Personalization of Interpersonal Relations of Puerto Ricans were related to individuals\u27 participation in their work place health promotion programs. The study was conducted in six private corporations located in the Western New England area which had work place health promotion programs on-site. The sample population of the study consisted of 84 Puerto Ricans working at these organizations. This exploratory study did not deal with hypothesis testing. It set the basis for the formulation of hypothesis to be tested in future research endeavors. The instrument used in this study consisted of a (Likert-Type Scale) questionnaire, in English and Spanish versions, that combined demographic information and the three value clusters of familism, religion and interpersonal relations that were researched. The collected data were submitted to analysis using Statistical Packages for Social Sciences (SPSS). Results indicated that this Puerto Rican population was very young, with 98% falling between 18-to-45-years old. There were 40 females and 43 males, one case missing. The levels of education were low, with 66% having high school or less education; and 66% worked in manufacturing. Overall, there were no gender-based differences in the responses to the questions about values. All participants agreed that their health promotion program did not include activities for the family, and all thought it should do so. In addition, participants agreed that activities were not culturally sensitive, and all thought they should be, including the availability of written materials in Spanish. Responses to questions about religion and interpersonal relations, also showed a disapproval of the health promotion program, since it failed to pay attention to these values in the planning of activities; therefore, negatively influencing the participation of the subjects in the programs. This study was significant because it looked at cultural values as one of the underlying reasons for the lack of participation of Puerto Ricans in health promotion programs. Health promotion programs designers must be culturally sensitive when designing activities for Puerto Ricans, as well as for other special populations. Recommendations for health promotion program planners are offered as first-step solutions to the low participation problem

What is the topology of a Schwarzschild black hole?

We investigate the topology of Schwarzschild's black hole through the immersion of this space-time in spaces of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschild's black hole.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1102.446

On definably proper maps

In this paper we work in o-minimal structures with definable Skolem functions and show that a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is proper morphism in the category of definable spaces. We give several other characterizations of definably proper including one involving the existence of limits of definable types. We also prove the basic properties of definably proper maps and the invariance of definably proper in elementary extensions and o-minimal expansions