Saint Mary's School

A branch of mathematical analysis called complex analysis studies the functions of complex numbers. It is also sometimes referred to as the theory of functions of a complex variable. Complex analysis has been used extensively in mathematics, physics, and engineering over the years, particularly in the areas of algebraic geometry, fluid dynamics, quantum mechanics, and other related fields. It dates back to the 16th century, when Italian mathematicians Girolamo Cardano and Raphael Bombelli first noticed complex numbers while attempting to solve a particular algebra, and was later developed by Cauchy and Riemann in the 19th century. The development of complex numbers has a lengthy history. Mathematicians have advanced the discipline of mathematics significantly after thousands of years of development. During this time, mathematicians also found a great deal of previously unknown mathematical information and proved formulae and phenomena that had previously been impossible to verify. And it covers complex numbers as well as some of the mathematics related to them. In this paper, the complete discovery of complex numbers from cubic equation to topology of complex numbers is detailedly revealed.

We report the detection of a rapid occultation event in the nearby Seyfert galaxy NGC 6814, simultaneously captured in a transient light curve and spectral variability. The intensity and hardness ratio curves capture distinct ingress and egress periods that are symmetric in duration. Independent of the selected continuum model, the changes can be simply described by varying the fraction of the central engine that is covered by transiting obscuring gas. Together, the spectral and timing analyses self-consistently reveal the properties of the obscuring gas, its location to be in the broad line region (BLR), and the size of the X-ray source to be ~25 rg . Our results demonstrate that obscuration close to massive black holes can shape their appearance, and can be harnessed to measure the active region that surrounds the event horizon.

This paper makes the case for the importance of an empathetic approach to understanding dyslexia, in educational establishments, especially in Higher Education. An awareness of the implications that having dyslexia and how this affects both study skills (concentration, organisation, revision and so forth) and presentation skills (completion of assignments within academic language and structures and without grammar, punctation and spelling errors) is accentuated in this article.This research employs meta-ethnography, the Critical Appraisal Skills Programme (CASP) and a grounded theory overlay to thematic critical analysis. In so doing, UK literature of both quantitative and qualitative format was examined through specifying inclusion criteria and using a filtering approach.The justification for this work is to challenge any institutional or individual indirect discriminatory practice towards students with dyslexia.Conclusions indicate the need for enhanced institutional understanding of dyslexia and associated provision for individual dyslexic learners within Higher Education in its entirety. For example, access to digitalised resources, individual tutorials, assistive technology and adjusted expectations in marking criteria (as not to penalise for issues concomitant with dyslexia).

Parental involvement increases K-12 student interest in STEM careers; however, when parents lack confidence in STEM content, or language and cultural barriers exist, parental engagement decreases. The Teacher Enrichment Initiatives (TEI) collects annual teacher feedback regarding the level of parental involvement with students during science nights, which laid the foundation for teachers to develop a science night training. Using qualitative methods, this single-case study follows elementary teachers who participated in the TEI science night training as they implement a Science Night program at a majority-minority elementary school. Data were gathered by TEI staff during the inaugural and third year of the Science Night program showing an increase in attendance from 700 (2016) to 800 (2018) and an increase in parental engagement with their student in STEM-related activities from 46% (2016) to 62% (2018). The data and follow-up summary were used by the case study school teachers to write and secure grants to support an annual Science Night program. This case study suggests Science Nights can be a mechanism to promote parental engagement with their student in hands-on STEM activities. Further, this case study suggests teacher feedback and inclusion in developing a science night model is central to successful implementation of a science night program.

We examine a 200 ks XMM-Newton observation of the narrow-line Seyfert 1 galaxy Mrk 493. The active galaxy was half as bright as in a previous 2003 snapshot observation and the current lower flux enables a study of the putative reflection component in detail. We determine the characteristics of the 2015 X-ray continuum by first analyzing the short-term variability using model-independent techniques. We then continue with a time-resolve analysis including spectral fitting and modelling the fractional variability. We determine that the variability arises from changes in the amount of primary flux striking the accretion disk, which induces changes in the ionization parameter and flux of the blurred reflection component. The observations seem consistent with the picture that the primary source is of roughly constant brightness and that variations arise from changes in the degree of light bending happening in the vicinity of the supermassive black hole.

Jessi Streib, The Power of the Past: Understanding Cross-Class Marriages. Oxford University Press (2015), 290 pages, $24.95 (paperback).

As nanotechnology is emerging, (1) there is a strong need for well-educated nanoscale systems engineers by industry, and (2) research and education efforts are also called to overcome numerous nanoscale systems issues. This paper is to identify necessary teaching elements for nanotechnology and to propose a way to teach nanotechnology by introducing emerging technologies: Crossbar-based Nano-Architecture and Carbon Nanotube FETs. By investigating read-out scheme of the crossbar memory architectures with students, a set of teaching items have been identified for undergraduate nanotechnology curriculum. The simulation of the student shows that the CNTFET-based crossbar memory achieves improvements in both sensing voltages on/off ratio and noise margin compared to the molecular memory implementation.

In March 2009 the well-studied quasar, PG 0844+349, was discovered with Swift to be in an X-ray weak state. A follow-up XMM-Newton observation several weeks later generated a good quality spectrum of the source, showing substantial curvature and spectral hardening. In combination with archival data at two previous epochs when the source was in a bright state, we examine the long-term spectral and timing properties of PG 0844+349 spanning nearly ten years and a factor of ten in brightness. Partial covering and blurred reflection models are compared to the data at each flux state while attempting to maintain consistency between the various epochs. In terms of the blurred reflection model, PG 0844+349 is in a reflection dominated state during the 2009 X-ray weak observations, which can be understood in terms of light bending. Moreover, the light bending scenario can also account for the short-term (i.e. ~1000s) spectral variability in the source. Other models cannot be decisively ruled out, but we note distinguishing features of the models that can be explored for in higher signal-to-noise data from current and future observatories.

Many popular hands‐on science activities, as traditionally implemented, fail to support inquiry‐based science instruction, because the activities direct teachers to terminate lessons prematurely. This paper presents a model describing one approach for extending seemingly limited hands‐on activities into full‐inquiry science lessons. The strategy involves (a) discrepant events to engage students in direct inquiry; (b) teacher‐supported brainstorming activities to facilitate students in planning investigations; (c) effective written job performance aids to provide structure and support; (d) requirements that students provide a product of their research, which usually includes a class presentation and a graph; and (e) class discussion and writing activities to facilitate students in reflecting on their activities and learning. The paper presents the model as a tool for facilitating science teachers' efforts to understand and implement the type of powerful, effective, and manageable inquiry‐based science instruction called for in the National Science Education Standards.