Ricci Collineations for Non-Degenerate, Diagonal and Spherically Symmetric Ricci Tensors

The expression of the vector field generator of a Ricci Collineation for diagonal, spherically symmetric and non-degenerate Ricci tensors is obtained. The resulting expressions show that the time and radial first derivatives of the components of the Ricci tensor can be used to classify the collineation, leading to 64 families. Some examples illustrate how to obtain the collineation vector

Youth Driven Engagement in the Homestay Program

Community-based tourism (CBT) is one of the tourist attracting ways involving local community which aims to develop and to enhance the era as well as to bring renewal to the local community. It includes the involvement of youth. CBT comes in various types and this study was conducted to find how CBT can create youth engagement in the homestay program. There were various factors that motivate youth to participate in homestay program. This study involved one case study of a qualitative study conducted in a district in Sabah, namely in Kundasang. In this study, Mersilou Homestay and Walai Tokou Homestay were chosen to be used as a place of study to review factors youth engagement in the homestay program. Data collection was through interviews in partial structures. Data were analyzed using NviVo 10 software and based on certain themes. The findings shown that there were several factors which drive engagement of youth in the homestay program in terms of interests, income, parental encouragement and comfort working in their own areas. In conclusion, the engagement of youth in the homestay program is based on the factors discovered in the study

Conformal Ricci collineations of static spherically symmetric spacetimes

Conformal Ricci collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating conformal Ricci collineations is found when the Ricci tensor is non-degenerate, in which case the number of independent conformal Ricci collineations is \emph{fifteen}; the maximum number for 4-dimensional manifolds. In the degenerate case it is found that the static spherically symmetric spacetimes always have an infinite number of conformal Ricci collineations. Some examples are provided which admit non-trivial conformal Ricci collineations, and perfect fluid source of the matter

Lie and Noether symmetries of geodesic equations and collineations

The Lie symmetries of the geodesic equations in a Riemannian space are computed in terms of the special projective group and its degenerates (affine vectors, homothetic vector and Killing vectors) of the metric. The Noether symmetries of the same equations are given in terms of the homothetic and the Killing vectors of the metric. It is shown that the geodesic equations in a Riemannian space admit three linear first integrals and two quadratic first integrals. We apply the results in the case of Einstein spaces, the Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each case the Lie and the Noether symmetries are computed explicitly together with the corresponding linear and quadratic first integrals.Comment: 19 page

Weighing the Milky Way

We describe an experiment to measure the mass of the Milky Way galaxy. The experiment is based on calculated light travel times along orthogonal directions in the Schwarzschild metric of the Galactic center. We show that the difference is proportional to the Galactic mass. We apply the result to light travel times in a 10cm Michelson type interferometer located on Earth. The mass of the Galactic center is shown to contribute 10^-6 to the flat space component of the metric. An experiment is proposed to measure the effect.Comment: 10 pages, 1 figur

Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of $\xi^a(x^b)$ is different from zero and (ii) two components of $\xi^a(x^b)$ are different from zero, for $a,b=1,2,3,4$, are presented. In subcase (i.b), which is $\xi^a= (0,\xi^2(x^a),0,0)$, some known solutions are found, and in subcase (i.d), which is $\xi^a =(0,0,0,\xi^4(x^a))$, choosing $S(t)=const.\times R(t)$, the Bianchi type II, VIII, and IX space-times is reduced to the Robertson-Walker metric.Comment: 12 Pages, LaTeX, 1 Table, no figure

Inflating Lorentzian Wormholes

It has been speculated that Lorentzian wormholes of the Morris- Thorne type might be allowed by the laws of physics at submicroscopic, e.g. Planck, scales and that a sufficiently advanced civilization might be able to enlarge them to classical size. The purpose of this paper is to explore the possibility that inflation might provide a natural mechanism for the enlargement of such wormholes to macroscopic size. A new classical metric is presented for a Lorentzian wormhole which is imbedded in a flat deSitter space. It is shown that the throat and proper length of the wormhole inflate. The resulting properties and stress-energy tensor associated with this metric are discussed.Comment: 24 pg

Cardiac acceleration as a marker of vagal withdrawal in heart rate control during exercise in humans

Objective: To investigate whether the time rate of change in heart rate i.e. cardiac acceleration, during aerobic exercise in human subjects could be used to differentiate vagal withdrawal from sympathetic stimulation.Methods: Fifteen male subjects exercised on a bicycle ergometer at 50 Watts (Step 1), then 100 Watts (Step 2), for 2 minutes each.Results: Heart rate (HR) was monitored from a resting value (mean +/- SD) of 80.3 +/- 12.9 to 113.8 +/- 13.6 beats min-1 in Step 1. In Step 2 exercise, HR increased from 113.8 +/- 13.6 to 145 +/- 20 beats min-1. At the initiation of Step 1, a rapid acceleration of HR was observed in the form of an overshoot response. In contrast to Step 1, a small overshoot response of cardiac acceleration was observed during Step 2. The difference between the mean cardiac acceleration at 10 seconds in Steps 1 and 2 was significant (2.40 +/- 0.19 and 0.71 +/- 0.12 beats min-1 sec-1, p \u3c 0.0001).CONCLUSION: The initial vagal withdrawal of exercise-induced tachycardia, as a frontline adaptive mechanism, can be indirectly identified from HR transients using cardiac acceleration as a new marker

Survey on Vision-based Path Prediction

Path prediction is a fundamental task for estimating how pedestrians or vehicles are going to move in a scene. Because path prediction as a task of computer vision uses video as input, various information used for prediction, such as the environment surrounding the target and the internal state of the target, need to be estimated from the video in addition to predicting paths. Many prediction approaches that include understanding the environment and the internal state have been proposed. In this survey, we systematically summarize methods of path prediction that take video as input and and extract features from the video. Moreover, we introduce datasets used to evaluate path prediction methods quantitatively.Comment: DAPI 201