Using Graphing Calculators to Integrate Mathematics and Science

The computational, graphing, statistical and programming capabilities of today’s graphing calculators make it possible for teachers and students to explore aspects of functions and investigate real-world situations in ways that were previously inaccessible because of computational constraints. Many of the features of graphing calculators can be used to integrate topics from mathematics and science. Here we provide a few illustrations of activities that use the graphing, parametric graphing, regression, and recursion features of graphing calculators to study mathematics in science contexts

Lightweight LCP Construction for Very Large Collections of Strings

The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several applications, especially in biological contexts. Nowadays, the input data for many problems are big collections of strings, for instance the data coming from "next-generation" DNA sequencing (NGS) technologies. In this paper we present the first lightweight algorithm (called extLCP) for the simultaneous computation of the longest common prefix array and the Burrows-Wheeler transform of a very large collection of strings having any length. The computation is realized by performing disk data accesses only via sequential scans, and the total disk space usage never needs more than twice the output size, excluding the disk space required for the input. Moreover, extLCP allows to compute also the suffix array of the strings of the collection, without any other further data structure is needed. Finally, we test our algorithm on real data and compare our results with another tool capable to work in external memory on large collections of strings.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The final version of this manuscript is in press in Journal of Discrete Algorithm

Application of ERTS-1 data to the protection and management of New Jersey's coastal environment

ERTS-1 imagery is being used by the New Jersey Department of Environmental Protection (NJDEP) to develop information products that will assist the state in optimally managing its coastal resources and in allocating funds. Interviews with NJDEP personnel have identified significant problem areas in the coastal zone, and the types of remote sensor derived information products that can be used in real-time decision making. Initial analyses of imagery from several successive ERTS-1 orbits have shown the extent, predominant drift, and dispersion characteristics of waste disposal in coastal New Jersey waters. Imagery (MSS Bands 4 and 5) for several orbits, shows that New-York Harbor tidal discharge extending as far south as Long Branch, New Jersey

Local behavior of p-harmonic Green's functions in metric spaces

We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincar\'e inequality

The Sub-Eddington Boundary for the Quasar Mass–Luminosity Plane: A Theoretical Perspective

By exploring more than sixty thousand quasars from the Sloan Digital Sky Survey Data Release 5, Steinhardt & Elvis discovered a sub-Eddington boundary and a redshift-dependent drop-off at higher black hole mass, possible clues to the growth history of massive black holes. Our contribution to this special issue of Universe amounts to an application of a model for black hole accretion and jet formation to these observations. For illustrativepurposes,we include~100,000 data points from the Sloan Digital Sky Survey Data Release 7 where the sub-Eddington boundary is also visible andpropose a theoretical picture that explains these features. By appealing to thin disk theory and both the lower accretion efficiency and the time evolution of jetted quasars compared to non-jetted quasars in our “gap paradigm”, we explain two features of the sub-Eddington boundary. First, we show that a drop-off on the quasar mass-luminosity plane for larger black hole mass occurs at allredshifts. But the fraction of jetted quasars is directly related to the merger function in thisparadigm, which means the jetted quasar fraction drops with decrease in redshift, which allows us to explain a second feature of the sub-Eddington boundary, namely a redshift dependence of the slope of the quasar mass-luminosity boundary at high black hole mass stemming from a change in radiative efficiency with time. We are able to reproduce the mass dependence of, as well as the oscillating behavior in, the slope of the sub-Eddington boundary as a function of time. The basic physical idea involves retrograde accretion occurring only for a subset of the more massive black holes,which implies that most spinning black holes in our model are prograde accretors.In short, this paper amounts to a qualitative overview of how a sub-Eddington boundary naturally emerges in the gap paradigm