From Golden Spirals to Constant Slope Surfaces

In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bi-dimensional analogue of the generalized helices. Some pictures are drawn by using the parametric equations we found.Comment: 11 pages, 8 figure

Unbundling Faculty Roles In Online Distance Education Programs

Many colleges and universities are expanding their current online offerings and creating new programs to address growing enrollment.  Institutions often utilize online education as a method to serve more students while lowering instructional costs. While online education may be more cost effective in some situations, college decision makers need to consider the full range of cost implications associated with these online offerings. The unbundling of faculty roles in online distance education programs is one cost consideration which is often overlooked.  As the faculty role has become more distributed, so have the costs associated with providing instruction and instructional support. This paper reviews the hidden costs associated with the unbundling of the faculty role and presents a framework for calculating the true costs of the unbundled faculty role

Non-Riemannian Gravity and the Einstein-Proca System

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravit

Risk evaluations and condom use decisions of homeless youth: a multi-level qualitative investigation.

BackgroundHomeless youth are at higher risk for sexually transmitted infections and unwanted pregnancy than non-homeless youth. However, little is known about how they evaluate risk within the context of their sexual relationships. It is important to understand homeless youths' condom use decisions in light of their sexual relationships because condom use decisions are influenced by relationship dynamics in addition to individual attitudes and event circumstances. It is also important to understand how relationship level factors, sexual event circumstances, and individual characteristics compare and intersect.MethodsTo explore these issues, we conducted semi-structured interviews with 37 homeless youth in Los Angeles County in 2011 concerning their recent sexual relationships and analyzed the data using systematic methods of team-based qualitative data analysis.ResultsWe identified themes of risk-related evaluations and decisions at the relationship/partner, event, and individual level. We also identified three different risk profiles that emerged from analyzing how different levels of risk intersected across individual respondents. The three profiles included 1) Risk Takers, who consistently engage in risk and have low concern about consequences of risk behavior, 2) Risk Avoiders, who consistently show high concern about protection and consistently avoid risk, and 3) Risk Reactors, those who are inconsistent in their concerns about risk and protection and mainly take risks in reaction to relationship and event circumstances.ConclusionsInterventions targeting homeless youth should reflect multiple levels of risk behavior and evaluation in order to address the diversity of risk profiles. Relationship/partner-, event-, and individual-level factors are all important but have different levels of importance for different homeless youth. Interventions should be tailored to address the most important factor contributing to homeless youth reproductive needs

Isomorphism between Non-Riemannian gravity and Einstein-Proca-Weyl theories extended to a class of Scalar gravity theories

We extend the recently proved relation between certain models of Non-Riemannian gravitation and Einstein- Proca-Weyl theories to a class of Scalar gravity theories. This is used to present a Black-Hole Dilaton solution with non-Riemannian connection.Comment: 13 pages, tex file, accepted in Class. Quant. Gra

A note on the convergence of parametrised non-resonant invariant manifolds

Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds

Dark Matter Gravitational Interactions

We argue that the conjectured dark mater in the Universe may be endowed with a new kind of gravitational charge that couples to a short range gravitational interaction mediated by a massive vector field. A model is constructed that assimilates this concept into ideas of current inflationary cosmology. The model is also consistent with the observed behaviour of galactic rotation curves according to Newtonian dynamics. The essential idea is that stars composed of ordinary (as opposed to dark matter) experience Newtonian forces due to the presence of an all pervading background of massive gravitationally charged cold dark matter. The novel gravitational interactions are predicted to have a significant influence on pre-inflationary cosmology. The precise details depend on the nature of a gravitational Proca interaction and the description of matter. A gravitational Proca field configuration that gives rise to attractive forces between dark matter charges of like polarity exhibits homogeneous isotropic eternal cosmologies that are free of cosmological curvature singularities thus eliminating the horizon problem associated with the standard big-bang scenario. Such solutions do however admit dense hot pre-inflationary epochs each with a characteristic scale factor that may be correlated with the dark matter density in the current era of expansion. The model is based on a theory in which a modification of Einsteinian gravity at very short distances can be expressed in terms of the gradient of the Einstein metric and the torsion of a non-Riemannian connection on the bundle of linear frames over spacetime. Indeed we demonstrate that the genesis of the model resides in a remarkable simplification that occurs when one analyses the variational equations associated with a broad class of non-Riemannian actions.Comment: 40 pages, 4 Postscript figure