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

New non-unitary representations in a Dirac hydrogen atom

New non-unitary representations of the SU(2) algebra are introduced for the case of the Dirac equation with a Coulomb potential; an extra phase, needed to close the algebra, is also introduced. The new representations does not require integer or half integer labels. The set of operators defined are used to span the complete space of bound state eigenstates of the problem thus solving it in an essentially algebraic way

Recurrence relation for relativistic atomic matrix elements

Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.Comment: 10 pages, no figure

Discovering the Fine-Scale Morphology of the Gulf of Cádiz: An Underwater Imaging Analysis

The dense and deep water flow that leaves the Mediterranean Sea to the Atlantic flows through the upper and middle slope of the Gulf of Cádiz as a powerful bottom stream that model sand interacts with bathymetry. The detailed analysis of underwater images,obtained with a photogrammetric sled in the central area of the upper and middle slope of the Gulf of Cádiz, together with multibeam bathymetry and oceanographic and sediment types data, has allowed conducting a detailed study of the seafloor microtopography and the predominant oceanographic dynamics in the study area. Different fine-scale spatial bedforms were identified, such as ripples, dunes, burrows, mounds, obstacle marks, rock bottoms, and low-roughness bottoms using underwater images. Besides, a geostatistical study of the different video transects studied was carried out and allowed us to differentiate three types of bottoms depending on the processes that affect their microtopography.En prens

Economic Feasibility of Passive Strate gies for Energy Efficient Envelopes of Mass-Built Housing in Hot -Dry Climate

The authors thank the Autonomous University of Baja California and the Master and Doctorate program in Architecture, Urbanism and Design (MyDAUD) for the support provided to carry out this study, the National Council of Science and Technology (CONACyT) for the scholarship provided for the completion of master’s degree studies, as well as the RUBA construction company.The building and construction industry represents 36% of the world’s final energy use and 39% of carbon emissions, while the residential sector is responsible for 22% of total energy consumption and 17% of carbon emissions. Therefore, energy consumption reduction measures are required by this sector, without affecting the living conditions of its occupants. In Baja California, Mexico, the more commonly used construction systems in mass-built housing are concrete block walls and cast in place insulated reinforced concrete roof deck. These systems negatively affect comfort conditions, especially in hot summer periods, and therefore increase energy consumption, particularly in areas with an hot-dry climate, such as Mexicali, Baja California. The objective of this article is to determine the cost-benefit of two passive design strategies applied in the housing envelope, which are thermal insulation and ventilated facade. A commercial model of mass-built housing was taken as a benchmark case. Building energy simulations were carried out with the Design Builder® program, whereby the performance of the house was evaluated without passive design strategies (benchmark case) and with applied strategies, that is, variations in thickness and position of the materials that make up the layers of the walls and roof. Additionally, the net present value (NPV) criterion was used to obtain the costs and benefits of the design strategies. The results show the differences in cooling demand, indoor operative temperature, and the total costs, in Mexican pesos, of the application of the strategies; the results show that there are significant energy savings, which contribute to reducing carbon emissions to the environment and provide economic savings for the user

Importancia del agua en la hidratación de la población española: documento FESNAD 2010

For any healthy individual, thirst is an appropriate sign to drink water, except for babies, sportsmen, and most of ill and elderly people. In these instances, it is convenient to schedule appropriate times to drink water since great demands and the physiological mechanisms that determine thirst in these situations may condition water unbalances with important consequences for health and the physical and intellectual performance. The human body has a number of mechanisms that allow keeping constant the water content by adjusting intakes and wastes. Water balance is determined by intake (consumed water, beverages, and water contained in foods) and wastes (urine, stools, the skin, and expired air from the lungs). Failure of these mechanisms and subsequent impairments in water balance may produce severe disarrangements that may threaten somebody's life. In the present document, we analyze the evidences regarding the factors conditioning water needs in the different life stages and physiological situations, as well as the consequences of water unbalance under different situations. A proper hydration may be achieved by feeding and the use of water and other liquids. Although water is the beverage by excellence and represents the ideal way of restoring the losses and get hydrated, we should be aware that, from the very beginning, we have sought other liquid sources with hydration properties. In the last decades we have increased the consumption of different beverages, with a proliferation of sugar-containing beverages. Since excessive sugar consumption has been related to obesity and other chronic conditions, it is evident that the use of these caloric beverages should be rationalized, especially in children. In this document all the considerations regarding hydration are presented and different recommendations are expose

Puberty in the Bronze Age: First application of a puberty estimation method to a prehistoric population

This is the peer reviewed version of the following article: Doe, Danielle M., et al. "Puberty in the Bronze Age: First application of a puberty estimation method to a prehistoric population". International Journal of Osteoarchaeology 29.6 (2019): 1091-1099, which has been published in final form at https://doi.org/10.1002/oa.2822. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsPuberty and adolescence represent a significant period of physical growth and maturation and a critical life stage in which children transition into adults within their societies. Numerous studies have observed a secular trend and have determined that puberty is now occurring earlier than in the past. This investigation represents the first application of a methodology for assessing the pubertal status of osteological remains to a prehistoric skeletal sample. Six Bronze Age adolescent skeletons from the Cerro de La Encantada archaeological site (Ciudad Real, Spain) were analysed. Prepubescence was observed at age 9 and the transition phase of the pubertal growth spurt at 15 years of age. These results were similar to those obtained from medieval, Industrial Revolution, and modern populations, both within and outside of the Iberian Peninsula. The similarity in the development of the Bronze Age adolescents to that of other past and contemporary populations suggests that the pubertal process has remained essentially unchanged across millennia until recent times. However, other interpretations, including the influence of a subpar developmental environment and potential methodological artefacts, are possible. Nevertheless, studies of this type provide important information about a crucial transitory period in human developmentThe Laboratorio de Poblaciones del Pasado (LAPP) has been supported by Projects HAR2016‐78036‐P, HAR2016‐74846‐P, HAR2017‐82755‐P, and HAR2017‐83004‐P (Spanish Government) and a grant (Ref. 38360) from the Leakey Foundatio