A one line factoring algorithm

We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package

Class invariants from a new kind of Weber-like modular equation

A technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely `algebraic' method. They are obtained by means of specialising certain modular equations related to Weber's modular equations of `irrational type'. The technique works for certain eta quotients evaluated at points in an imaginary quadratic field with discriminant d1 (mod 8)

Bridging the Gap between the Interest Rate and Price Level Approaches in the AD-AS Model: The Role of the Loanable Funds Market

There are two generally accepted ways of plotting the aggregate demand (AD) and aggregate supply (AS) curves in the goods market. One puts the price level on the vertical axis (the P - y approach); the other plots the real interest rate on the vertical axis (the r - y approach). This paper develops the theoretical connections between these two approaches that permit one to tell a coherent dynamic story with the AD-AS model and also explores the conditions under which one approach or the other yields greater insight into the working of the model.Interest Rates; Interest; Price Level; Prices; Supply

Spectroscopic near-field imaging in the mid-infrared

This thesis focuses on two different approaches of beating the diffraction limit in the mid-infrared. One approach uses scattering-type scanning near-field optical microscopy (s-SNOM) to map the optical response of a sample surface with <10 nm resolution. By utilising the recent development of widely tuneable quantum cascade lasers (QCL), this work experimentally investigates two distinct applications. The first maps out the dispersion of plasmons in graphene to determine the local Fermi energy with high accuracy. In addition, novel plasmon focusing phenomena are presented at interfaces between single and bilayer graphene. The second experimental application uses infrared s-SNOM to image, for the first time, the ultrastructure inside individual human cells with ~8 nm resolution. Furthermore, nanoscale infrared spectroscopy is used to map out the location of a clinically relevant anti-cancer drug within a single cell without chemical labelling, for the first time. The final part of this thesis comprises a theoretical study of metamaterial superlenses, which allow for deeply sub-wavelength spatial resolution to be preserved. The insights gained here led to the development of a novel infrared superlens that is shown to improve the distance at which sub-diffraction limited (<λ/15) features are preserved by a factor of 25 over previous designs.Open Acces

Isolation and Onboarding: Gender Bias in Aviation Training Documents

There is a growing interest in male-dominated industries and the challenges women face finding their place within the workplace community. Yet, there seems to be little research on how training documents, generally created by technical communicators, may isolate and limit women who seek to pursue careers in these fields. Technical communication and gender scholars have examined women in the technical communication field and gender bias in male-dominated industries but have not yet examined gender stereotypes in training documents. Training documents are designed to provide written instructions and a reference guide for job functions, workplace rules, orientation, and company policies. This is sometimes the first opportunity for an employee to better understand the culture of the company and what it offers. Technical communicators, such as instructional designers, generally create the training material based on the goals of an organization with input from subject matter experts. This study examines FAA (Federal Aviation Administration) technical training documents, specifically focusing on manuals, handbooks, and guides found on the FAA website. The documents analyzed were published between the years of 1941 and 2017 and were all accessible on the FAA website at the time the documents were chosen. Factual and implied gender reference categories emerged from the data. A number of biased gender references were prevalent in documents created as recent as 2017. Gender bias was not only isolated to the role of the pilot but was also present in the description of other roles, including examples of professions outside the field of aviation. Qualitative analysis further revealed complex and frequently stereotypical portrayals of aviation roles and examples found in curriculum. The results highlight how technical writing functions as gender bias and serves as the basis for further investigative studies of gender bias in technical documents

Archive 2.0: Imagining the Michigan State University Israelite Samaritan Scroll Collection

This project will work with Michigan State University units and the A.B. Samaritan Institute in Holon, Israel to create using the latest in Web 2.0 technologies an accessible, useable and living archive for the Israelite Samaritan community in Holon and Nabulus as well as biblical scholars. To facilitate this work we will digitize over the next several years three 15th century Israelite Samaritan Pentateuch scrolls, and provide a unique suite of tools to help facilitate collaboration: social networking, tagging, social bookmarking, zoomify view, and multilingual support. The aim is to bring together two distinct groups of users - textual scholars and members of the Israelite Samaritan community - both of whom have a significant stake in the cultural and scholarly value of the Samaritan Archive, via an online environment in which they can view and interpret the Samaritan texts, interact with members of their respective communities, and interact with one another