Represented Value Sets for Integral Binary Quadratic Forms and Lattices

A characterization is given for the integral binary quadratic forms for which the set of represented values is closed under products. It is also proved that for an integral binary quadratic lattice over the ring of integers of a global field, the product of three values represented by the form is again a value represented by the form. This generalizes the trigroup property discovered by V. Arnold for the case of integral binary quadratic forms

Multiplicative Properties of Integral Binary Quadratic Forms

In this paper, the integral binary quadratic forms for which the set of represented values is closed under k-fold products, for even positive integers k, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under k-fold products can always be expressed by a k-linear mapping from (Z2)k to Z2. In the case k = 2, this resolves a conjecture of Aicardi and Timorin

Are universities responding to the needs of students from refugee backgrounds?

Although many Australian universities have been proactive in responding to students' diverse needs through orientation and support programs, very little is known about programs needed for the successful transition of students from refugee backgrounds into tertiary study. Facilitating the early engagement of students with their studies and campus life is linked to greater student satisfaction, improved retention rates and better educational outcomes. One of the challenges that academics face is the paucity of research on the learning styles and academic needs of African and Middle Eastern students from refugee backgrounds.This paper reports on a needs analysis undertaken with a group of students from refugee backgrounds in Victoria and Western Australia, using in-depth interviews and focus group discussions. Participants reported that current support systems and programs are inadequate or non-existent and that many feel disadvantaged compared to Australian-born and international students. The article concludes with recommendations on how universities can better respond to the needs of students from refugee backgrounds

Metro System of Local Government (A Survey)

Growth of many American cities into vast metropolitan communities of suburban cities, towns and villages clustered about the central city is creating complex problems of local government. Duplication of services and costs is matched by artificial compartmentalization of adjacent areas, all developing with little or no overall plan or logic.Herein, four outstanding community leaders examine the problem in terms of the situation in the Ohio area of Cuyahoga County, around the core city of Cleveland. Extracts from four speeches are set forth here, all delivered at a recent luncheon of the Cleveland-Marshall Alumni Association

Atomic layer deposition of titanium nitride for quantum circuits

Superconducting thin films with high intrinsic kinetic inductance are of great importance for photon detectors, achieving strong coupling in hybrid systems, and protected qubits. We report on the performance of titanium nitride resonators, patterned on thin films (9-110 nm) grown by atomic layer deposition, with sheet inductances of up to 234 pH/square. For films thicker than 14 nm, quality factors measured in the quantum regime range from 0.4 to 1.0 million and are likely limited by dielectric two-level systems. Additionally, we show characteristic impedances up to 28 kOhm, with no significant degradation of the internal quality factor as the impedance increases. These high impedances correspond to an increased single photon coupling strength of 24 times compared to a 50 Ohm resonator, transformative for hybrid quantum systems and quantum sensing.Comment: 10 pages, 8 figures including supplemental material