The golden ratio in Schwarzschild-Kottler black holes

In this paper we show that the golden ratio is present in the Schwarzschild-Kottler metric. For null geodesics with maximal radial acceleration, the turning points of the orbits are in the golden ratio $\Phi = (\sqrt{5}-1)/2$. This is a general result which is independent of the value and sign of the cosmological constant $\Lambda$

Testing a dissipative kinetic k-essence model

In this work, we present a study of a purely kinetic k-essence model, characterized basically by a parameter $\alpha$ in presence of a bulk dissipative term, whose relationship between viscous pressure $\Pi$ and energy density $\rho$ of the background follows a polytropic type law $\Pi \propto \rho^{\lambda+1/2}$, where $\lambda$, in principle, is a parameter without restrictions. Analytical solutions for the energy density of the k-essence field are found in two specific cases: $\lambda=1/2$ and $\lambda=(1-\alpha)/2\alpha$, and then we show that these solutions posses the same functional form than the non-viscous counterpart. Finally, both approach are contrasted with observational data from type Ia supernova, and the most recent Hubble parameter measurements, and therefore, the best values for the parameters of the theory are founds.Comment: 9 pages, 5 figures, accepted in EPJ

Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat U(1) bundles over the configuration space manifold. In the case of Riemannian manifolds, these representations are also manifestly diffeomorphic covariant. The general discussion, illustrated by some simple examples in non relativistic quantum mechanics, is of particular relevance to systems whose configuration space is parametrised by curvilinear coordinates or is not simply connected, which thus include for instance the modular spaces of theories of non abelian gauge fields and gravity.Comment: 22 pages, no figures, plain LaTeX file; changes only in details of affiliation and financial suppor

From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

Communities Creating Healthy Environments to Combat Obesity: Preliminary Evaluation Findings From Two Case Studies

While there is growing faith in community organizing to influence policy as a way to improve the built environment and increase food or recreational equity, relatively little research is available examining the successes and challenges of community organizing in Latino communities attempting to reduce obesity. Using process and outcome evaluation data, we present preliminary findings from a study of two community-based organizations that are making efforts to increase access to physical activity and access to healthy foods in predominantly Latino areas. The organizations are part of Communities Creating Healthy Environments (CCHE), a national initiative of the Robert Wood Johnson Foundation (RWJF) to prevent childhood obesity. Both community-based organizations were able to achieve redistribution of public resources to advance their CCHE objectives. We discuss the study’s implications, including the need for public policy research around obesity that examines community organizing as an intervention

IMPLEMENTATION STATUS OF K12 SOCIAL STUDIES PROGRAM IN PHILIPPINE PUBLIC SCHOOLS

Curriculum implementation needs to be gauged regularly to ensure its effectiveness, efficiency and its relevance to the needs of the students and of the industry. This descriptive-survey research gauged the status of the Social Studies program under the K12 Curriculum for its first four years of implementation. A total of 30 Social Studies teachers and 5 school administrators from three national secondary schools in one division in Central Luzon, Philippines served as respondents of the study. Results revealed that a typical teacher is a female, 37.33 years old, teaching profession for 3.07 years, and a college graduate while a typical administrator is a female, 32.20 years old, serving for about 21.60 years, and a college graduate with MA units. The secondary teachers and school administrators assessed the status of implementation of the curriculum in selected public secondary schools as “moderately observed” in terms of resource variables (M=3.63), process variables (M=3.84) and contextual variables (3.93). Moreover, there is no significant difference between the assessment of the teachers and administrators on the status of the implementation of Social Studies program with regard to the three components. Further, there is no significant difference in the assessment of the teachers and administrators when respondents are grouped according to profile variables. A well-monitored implementation of the K12 Curriculum, specifically the Social Studies program, by stakeholders is recommended. Periodic assessment of the curriculum may also be done to ensure its alignment to the changing educational landscapes and to cope with the challenges of Education 4.0