Applications of Metric Coinduction

Metric coinduction is a form of coinduction that can be used to establish properties of objects constructed as a limit of finite approximations. One can prove a coinduction step showing that some property is preserved by one step of the approximation process, then automatically infer by the coinduction principle that the property holds of the limit object. This can often be used to avoid complicated analytic arguments involving limits and convergence, replacing them with simpler algebraic arguments. This paper examines the application of this principle in a variety of areas, including infinite streams, Markov chains, Markov decision processes, and non-well-founded sets. These results point to the usefulness of coinduction as a general proof technique

Decreasing Caregiver Stress

Stress is both critical and personal experience and has significant effects on caregivers’ physical, mental, and social well-being. The nature of caregiving and the responsibility to work and serve individuals at their illness conditions are very personal encounters that often result in adverse effects on the health and well-being of caregivers (Frederick, 2016). A decrease in stress experience can lead to the satisfaction of caregiver roles and improvement of patient’s quality of life (Choi, Jisun & Boyle, Diane, 2013; Yada, Nagata, & Inagaki, 2014). This scholarly project determined that evidence-based stress management interventions have decreased the perceived stress in caregivers. The scholarly project identified low levels of stress among research participants, and how evidence-based interventions decreased caregiver stress by increasing their knowledge and awareness of evidence-based stress management interventions. The results of this scholarly project agree with the literature that caregiver stress experience can be decreased through the implementation of evidence-based stress management interventions (Blom, Zarit, Groot Zwaaftink, Cuijpers, & Pot, 2013). It is significant to implement evidence-based stress management interventions to decrease perceived stress among caregivers

The Case for a Cooperative Studio Classroom: Teaching Petrology in a Different Way

NOTE: This file size is large, 16.52 mb. This article describes one educator's attempts to modify his Petrology course, changing the lab-lecture format to one that emphasizes studio and cooperative learning. The goals of the changes are to improve student learning by covering a smaller number of topics in greater depth, deemphasize knowledge-based learning and emphasize development of higher order thinking skills (comprehension, application, analysis, synthesis, evaluation), and help students develop good habits of the mind and fundamental skills useful for lifelong learning. The reformatted course requires that students take more responsibility for their learning. Educational levels: Graduate or professional

A public code for general relativistic, polarised radiative transfer around spinning black holes

Ray tracing radiative transfer is a powerful method for comparing theoretical models of black hole accretion flows and jets with observations. We present a public code, grtrans, for carrying out such calculations in the Kerr metric, including the full treatment of polarised radiative transfer and parallel transport along geodesics. The code is written in Fortran 90 and efficiently parallelises with OpenMP, and the full code and several components have Python interfaces. We describe several tests which are used for verifiying the code, and we compare the results for polarised thin accretion disc and semi-analytic jet problems with those from the literature as examples of its use. Along the way, we provide accurate fitting functions for polarised synchrotron emission and transfer coefficients from thermal and power law distribution functions, and compare results from numerical integration and quadrature solutions of the polarised radiative transfer equations. We also show that all transfer coefficients can play an important role in predicted images and polarisation maps of the Galactic center black hole, Sgr A*, at submillimetre wavelengths.Comment: 22 pages, 12 figures, submitted to MNRAS. code available at: github.com/jadexter/grtran