Chromatic dependence of first-order optical properties of the eye

Abstract: Many first-order optical properties depend on chromatic dispersion and, hence, on frequency of light. The purpose of this theoretical study is to investigate the dependence of first-order optical properties of model eyes on frequency. In this study we are purposefully not concerned with subjective measurements. Instead, definitions are obtained that are general for optical systems that have astigmatic and decentred elements, and then simplified for Gaussian systems. In linear optics the transference is a matrix that is a complete representation of the effects of the system on a ray traversing it. Almost all of the familiar optical properties of the system can be obtained from the transference. From the transference S we obtain the four fundamental properties namely dilation A, disjugacy B, divergence C and divarication D, submatrices of S. Transferences are symplectic and do not define a linear space. Linear spaces are amenable to statistical analyses and therefore a number of mappings to linear spaces are investigated, including the Cayley and logarithmic mappings to Hamiltonian space and the four characteristic matrices. In each case, the individual entries of the transform are studied for their dependence on frequency and then the chromatic dependence relationship between the entries is compared graphically.M.Phil. (Optometry

Public History in Australia

This article charts the peaks and troughs of public history inside and outside academia in Australia and the promise of the establishment of a new network of public historians in Australia and Aotearoa New Zealand. It reveals the value of Australian creative engagements with the past. It concludes by suggesting that networks and team-based work are vital for the successful practice of public history in Australasia and elsewhere. &nbsp

A Study of the New Zealand Mathematics Curriculum

Given the profound and uncritiqued changes that have been implemented in Aotearoa New Zealand education since the 1990s, this paper provides a critical commentary on the characterising features of the New Zealand mathematics' curriculum in the context of the first stage of a study. The emphasis is on the importance of research design that begins with an explicit, evidence-based hypothesis. To that end, we describe evidence that informs and identifies the study's hypothesised problem and causes. The study itself will show whether or not the hypothesis is justified; that is, is the absence of standardised prescribed content in New Zealand mathematics' curriculum the reason for the country's declining mathematics rankings? The study aims to increase understanding in the field of mathematics education by exploring the effects on New Zealand year 7 public school teachers' mathematics curriculum selection and design practices, teaching practices, and subsequently student achievement.Comment: Submitted to the New Zealand Journal of Educational Studies, 12 June 202

Australia, the healthiest nation: death, hospital and cost savings of the Preventative Health Taskforce target reductions for alcohol, 2007 to 2020

Background - The National Preventative Health Taskforce has set a 30% target reduction in the proportion of risky and high risk drinkers by 2020. This study estimated the potential saving in deaths, hospitalisations and associated economic cost savings to premature mortality and health of achieving the target. Method - Past national estimates of alcohol-attributable hospitalisations and deaths were used to forecast trends from 2007 to 2020. Estimated potential savings in deaths and hospitalisations were based on incremental decline in the prevalence of risky/high-risk drinking reaching a total of 30% by 2020 (about 2.3% per year). Associated economic costs of premature death were estimated using the Value of Statistical Life method (willingness to pay). Hospital costs were estimated from known trends in annual national costs for recent past years and taking inflation into account. Results - A 30% reduction in risky/high-risk drinkers would avoid an estimated 7,200 deaths and some 94,000 person-years-of-life lost due to premature death by 2020. The estimated benefit to the health sector would include 330,000 fewer hospitalisations and 1.5 million associated bed days. The net present value of these benefits is AUD 22.7 billion from deaths avoided and AUD 1.7 billion from fewer hospital separations totalling AUD 24.4 billion. Conclusion - The potential savings in premature deaths, health and associated financial costs of a 30% reduction in risky and high-risk drinking by 2020 across the Australian population are considerable

Chromatic properties of astigmatic eyes

Background: Chromatic differences in power, refractive compensation, position and magnification have been described in the literature for Gaussian eyes. Aim: This article explores these definitions and defines chromatic properties for eyes that have astigmatic and decentred or tilted elements. Setting: Linear optics. Methods: The optical model is linear optics and makes use of the ray transference T. Results: Results are presented as either 2 × 2 matrices or 2 × 1 vectors. The dependence of the chromatic properties on the position of an object and the limiting aperture is explored and results are presented as independent of, or dependent on, object and aperture position. Apertures undergo both longitudinal and transverse shifts in position. The results are general and apertures may include pupils or pinholes, either surgically inserted inside the eye or held in front of the eye. Numerical examples are provided for Le Grand’s four-surface eye and an arbitrary astigmatic heterocentric four-surface eye. Conclusion: Aperture-independent chromatic properties include chromatic difference in power and refractive compensation, both given as 2 × 2 matrices. Aperture-dependent chromatic properties are all dependent on longitudinal shifts in the plane of the limiting aperture. In addition, chromatic difference in position and inclination depend on both object and transverse aperture position. Chromatic difference in image size or angular spread depends on object position and is independent of transverse aperture position. These four aperture-dependent chromatic properties are given as 2 × 1 vectors. Chromatic magnifications are independent of object and transverse aperture position and are given as 2 × 2 matrices

Ready, Set, Match

As online education expands, cultivating a sense of belonging becomes increasingly complex, especially for students who may never set foot on a physical campus.  In this article, we explore the nuanced nature of fostering a sense of belonging and mattering among distance learners on our own campus, Indiana University (IU) East. To address these students’ unique needs, our English department organized three virtual events (the Alumni Career panel, the Faculty+Student Reading of creative work and the Celebration of Student Writing) utilizing Facebook Live, Zoom, and Pressbooks. Drawing on the concept of "belonging" as articulated by Strayhorn (2019), we examine the degree to which these virtual events fostered a sense of belonging and mattering, particularly through the concept of “matched pairs,” which emerged as a useful framework for creating personalized connections between faculty and students, a critical ingredient in both belonging and mattering. Both the Faculty+Student Reading and the Celebration of Student Writing worked to establish closer ties between participating faculty and student pairs, while the third event, the Alumni Career Panel, encouraged students to interact with alumni in a virtual “living room,” a relaxed online space (via Zoom) where they could learn about career paths. However, we also found that events like these cannot be viewed as “one-and-done” but rather must be part of a sustained program to enhance student connections. Acknowledging the time-intensive nature of planning and organizing such events, we caution against assumptions of seamless execution and underscore the need for purposeful planning, inclusive design, and flexibility to accommodate diverse student needs

The rise of female entrepreneurs:New evidence on gender differences in liquidity constraints

In this paper, we study the importance of liquidity constraints for entrepreneurial activity, using previously unexplored data from the UK. Using inheritances as an instrument, IV estimates reveal that single women drive the overall relationship between personal wealth and the propensity to start a new business. Defining business ownership rather than self-employment as the entrepreneurial outcome measure is also shown to be critical. Using self-employment leads to selection bias and underestimates the impact of personal wealth. The results imply that efforts aimed at relieving the liquidity constraints of single women could help further accelerate the recent rise of female entrepreneurship