Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry

We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of $SL(2,{\mathbb Z})$) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of an hyperbolic three-geometry associated with $q$-series in the computation of the string amplitudes.Comment: Revised version. References added, results remain unchanged. arXiv admin note: text overlap with arXiv:hep-th/0701156, arXiv:1105.4571, arXiv:1206.0664 by other author

The Transition to College Process in PR-CETP Scholars

This article describes a study about the experiences of a group of students during the transition from high school to college. The students are future teachers who evidenced a high level of academic achievement in high school and received merit scholarships from the Puerto Rico Collaborative for Excellence in Teacher Preparation (PR-CETP). Two groups of students were compared: those who sustained a high GPA during their freshman year, and those who did not and, therefore, no longer qualified for the scholarship. The study was carried out through focused interviews with eight students, from three universities, four of whom maintained the scholarship and four who did not. Findings indicate that the main problems encountered were academic and social, and that the students received support from their families during the entire process. Regarding formal support, they pointed out that they felt highly satisfied with the services provided by PR-CETP and the universities, but they also pointed out (particularly those who lost the scholarship) that they needed additional services from the universities. They suggested, for example, better tutoring, and social activities among the scholars. The interviewed students, in general, consider that they faced the transition successfully since most of them described their academic, emotional, and social status as satisfactory at the time of the interviews

The percentile residual life up to time t0: ordering and aging properties

Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied, and also an application in Reliability Theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t0 aging notion.Aging notion, Hazard rate, Mean residual life, Percentile residual life, Reliability, Stochastic ordering

Characterization of bathtub distributions via percentile residual life functions

In reliability theory and survival analysis, many set of data are generated by distributions with bathtub shaped hazard rate functions. Launer (1993) established several relations between the behaviour of the hazard rate function and the percentile residual life function. In particular, necessary conditions were given for a special type of bathtub distributions in terms of percentile residual life functions. The purpose of this paper is to complete the study initiated by Launer (1993) and to characterize (necessary and sufficient conditions) all types of bathtub distributions.Percentile residual life, Bathtub hazard rate, Aging notions,

Comparing quantile residual life functions by confidence bands

A quantile residual life function is the quantile of the remaining life of a surviving subject, as it varies with time. In this article we present a nonparametric method for constructing confidence bands for the difference of two quantile residual life functions. These bands provide evidence for two random variables ordering with respect to a quantile residual life order introduced in Franco-Pereira et al. (2010). A simulation study has been carried out in order to evaluate and illustrate the performance and the consistency of this new methodology. We also present applications to real data examples.Quantile residual life, Confidence bands

Casimir energy and the superconducting phase transition

We study the influence of Casimir energy on the critical field of a superconducting film, and we show that by this means it might be possible to directly measure, for the first time, the variation of Casimir energy that accompanies the superconducting transition. It is shown that this novel approach may also help clarifying the long-standing controversy on the contribution of TE zero modes to the Casimir energy in real materials.Comment: 12 pages, 5 figures. Talk given at 7th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT 05), Barcelona, Catalonia, Spain, 5-9 Sep 200

The decreasing percentile residual life aging notion

Earlier researchers have studied some aspects of the classes of distribution functions with decreasing ?-percentile residual life (DPRL(?)), 0Reliability theory, Hazard rate, Stochastic orders, Aging notions, Nonparametric estimation, Strongly uniform consistency

A lower bound for the number of components of the moduli schemes of stable rank 2 vector bundles on projective 3-folds

Fix a smooth projective 3-fold X, c1, H ∈ Pic(X) with H ample, and d ∈ Z. Assume the existence of integers a, b with a ≠ 0 such that ac1 is numerically equivalent to bH. Let M(X, 2, c1, d, H) be the moduli scheme of H-stable rank 2 vector bundles, E, on X with c1(E) = c1 and c2(E) · H = d. Let m(X, 2, c1, d, H) be the number of its irreducible components. Then lim supd→ ∞m(X, 2, c1, d, H) = +∞