Microcomputer laboratories in mathematics education

AbstractThis article discusses the mathematical-educational potential of a computational laboratory at the pre-calculus and co-calculus levels. The laboratory envisaged is based on a set of microcomputers, whose use plays a central role in the teaching process, with particular emphasis on algorithmization. A new role for the mathematics teacher and professor is layed out, augmenting the “chalk and talk” methods by active participation as a laboratory instructor. Following a brief description of the integration of such a laboratory into the mathematical education, seven appropriate subjects are discussed, including some new relevant elementary proofs and worked out examples. Emphasis is placed upon the mathematical-educational byproducts (such as error bounds, ill-conditioning, complexity, rate of convergence, etc.) accompanying the implementation of these seven modules. Special attention is given to the removal of “black box” procedures and to the construction of “numerical methods that work”. Extensions and generalizations to more advanced topics are indicated, especially where the results in our modules may serve as points of departure in that direction

A Mixed Solar Core, Solar Neutrinos and Helioseismology

We consider a wide class of solar models with mixed core. Most of these models can be excluded as the predicted sound speed profile is in sharp disagreement with helioseismic constraints. All the remaining models predict $^7$Be and/or $^7$B neutrino fluxes at least as large as those of SSMs. In conclusion, helioseismology shows that a mixed solar core cannot account for the neutrino deficit implied by the current solar neutrino experiments.Comment: 6 pages, RevTeX, plus 5 postscript figure

An Exercise in Forecasting Loop Current and Eddy Frontal Positions in the Gulf of Mexico

As part of a model-evaluation exercise to forecast Loop Current and Loop Current eddy frontal positions in the Gulf of Mexico, the Princeton Regional Ocean Forecast System (PROFS) is tested to forecast 14 4-week periods Aug/25/99- Sep/20/00, during which a powerful eddy, Eddy Juggernaut (Eddy-J) separated from the Loop Current and propagated southwestward. To initialize each forecast, PROFS assimilates satellite sea surface height (SSH) anomaly and temperature (SST) by projecting them into subsurface density using a surface/subsurface correlation that is a function of the satellite SSH anomaly. The closest distances of the forecast fronts from seven fixed stations in the northern Gulf over a 4-week forecast horizon are then compared against frontal observations derived primarily from drifters. Model forecasts beat persistence and the major source of error is found to be due to the initial hindcast fields

The 10th International Workshop on Modeling the Ocean (IWMO 2018) in Santos, Brazil, June 25-28, 2018

The 10th International Workshop on Modeling the Ocean (IWMO 2018) was hosted by the University of Sao Paulo and held on June 25–28, 2018, at the beautiful coastal city of Santos, Brazil. This old city was founded by the Portuguese in the 1500s and is known for its world’s longest beach garden, the Coffee Museum and the Pele Museum (featuring the famous football player and a local hero). Since the inaugural IWMO meeting in Taiwan in 2009, meetings were held in Asia, Europe, North America, and Australia, but this was the first meeting to be held in South America. With the 10th anniversary of IWMO, we would like to acknowledge the foremost contribution and dedication of Prof. L.-Y. Oey who was one of the founding fathers of IWMO in 2009 (Oey et al. 2010a, b) and who led the organization for 10 successful years, before passing the leadership baton to a new generation of scientists. During this meeting, a special session was held to honor Professor Emeritus George L. Mellor for his pioneering contribution to ocean modeling, which started some 6 decades ago and continues today with his own contribution to this special issue (Mellor 2019). We would like thus to dedicate this special issue to Professor Mellor and his legacy

Loop Current Warming by Hurricane Wilma

Hurricanes mix and cool the upper ocean, as shown here in observations and modeling of the Caribbean Sea and the Gulf of Mexico during the passage of hurricane Wilma. Curiously, the upper ocean around the Loop Current warmed prior to Wilma\u27s entrance into the Gulf. The major cause was increased volume and heat transports through the Yucatan Channel produced by storm-induced convergences in the northwestern Caribbean Sea. Such oceanic variability may have important impacts on hurricane predictions

Evolution of low-mass metal-free stars including effects of diffusion and external pollution

We investigate the evolution of low-mass metal-free Population III stars. Emphasis is laid upon the question of internal and external sources for CNO-elements, which - if present in sufficient amounts in the hydrogen-burning regions - lead to a strong modification of the stars' evolutionary behavior. For the production of carbon due to nuclear processes inside the stars, we use an extended nuclear network, demonstrating that hot pp-chains do not suffice to produce enough carbon or are less effective than the triple3-alpha-process. As an external source of CNO-elements we test the efficiency of pollution by a nearby massive star combined with particle diffusion. For all cases investigated, the additional metals fail to reach nuclear burning regions before deep convection on the Red Giant Branch obliterates the previous evolution. The surface abundance history of the polluted Pop III stars is presented. The possibilities to discriminate between a Pop II and a polluted Pop III field star are also discussed.Comment: Accepted for publication in Ap

Severe Brain Injury, Disability, and the Law: Achieving Justice for a Marginalized Population

Thousands of persons with severe brain injury who are minimally conscious or locked in are wrongly treated as if they are unconscious. Such individuals are unable to advocate for themselves and are typically segregated from society in hospitals or nursing homes. As a result, they constitute a class of persons who often lack access to adequate medical care, rehabilitation, and assistive devices that could aid them in communication and recovery. While this problem is often approached from a medical or scientific point of view, here we frame it as a legal issue amenable to legal remedies. This Article comprehensively explores and analyzes sources of federal, state, and international human rights law that can be leveraged- both in traditional and novel ways-to improve the lives and protect the rights of persons with severe brain injury. We argue that state laws may be the most promising basis for legal action to ameliorate the clinical marginalization and societal neglect faced by persons with severe brain injury, and to promote their recovery and reintegration into their communities

Severe Brain Injury, Disability, and the Law: Achieving Justice for a Marginalized Population

Thousands of persons with severe brain injury who are minimally conscious or locked in are wrongly treated as if they are unconscious. Such individuals are unable to advocate for themselves and are typically segregated from society in hospitals or nursing homes. As a result, they constitute a class of persons who often lack access to adequate medical care, rehabilitation, and assistive devices that could aid them in communication and recovery. While this problem is often approached from a medical or scientific point of view, here we frame it as a legal issue amenable to legal remedies. This Article comprehensively explores and analyzes sources of federal, state, and international human rights law that can be leveraged- both in traditional and novel ways-to improve the lives and protect the rights of persons with severe brain injury. We argue that state laws may be the most promising basis for legal action to ameliorate the clinical marginalization and societal neglect faced by persons with severe brain injury, and to promote their recovery and reintegration into their communities

Numerical approaches to time evolution of complex quantum systems

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank-Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner-Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron-phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.Comment: 8 pages, 3 figure