Investigation into the performance of proximity coupled stacked patches

We investigate the parameters that control the impedance and radiation performance of proximity coupled stacked microstrip patch radiators. In particular we explore the relationship required between the dielectric layers to achieve broadband behavior and also how the dimensions of the stacked radiators and the relative location of the feed can influence the impedance response. Bandwidths in excess of 20% can be achieved with careful layer design. We also investigate the dielectric layer configurations required to achieve broadband impedance responses when higher dielectric constant feed material is used. This latter study is of particular importance when designing MMIC compatible printed antennas

Edge-fed patch antennas with reduced spurious radiation

In this paper, a technique to reduce the spurious feed radiation from edge-fed patch antennas by using a dual thickness substrate is presented. A thin microwave substrate is employed for the feed network, and then a transition is made to a thick substrate for the patch antenna element. The new feeding procedure allows the feed network and antenna elements to be optimized independently. Measured results on a single element prototype exhibit a reduction in the level of cross-polarized fields and decreased pattern distortion whilst preserving a reasonable impedance bandwidth. The technique is also proven to be beneficial in an array environment, as an extensive transmission line feed network is required. We present the theoretical and experimental results of a 1 x 8 edge-fed patch array that utilizes the dual thickness substrate configuration. Significant improvement in the radiation patterns and gain are observed for the new array compared to a standard edge-fed patch array

Some genus 3 curves with many points

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves

Tannakian approach to linear differential algebraic groups

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.Comment: 31 pages; corrected misprint

How do naloxone-based interventions work to reduce overdose deaths: a realist review

BACKGROUND: Naloxone-based interventions as part of health systems can reverse an opioid overdose. Previous systematic reviews have identified the effectiveness of naloxone; however, the role of context and mechanisms for its use has not been explored. This realist systematic review aims to identify a theory of how naloxone works based on the contexts and mechanisms that contribute to the success of the intervention for improved outcomes. METHODS: Pre-registered at PROSPERO, this realist review followed RAMESES standards of reporting. Keywords included 'naloxone' and ' opioid overdose'. All study designs were included. Data extraction using 55 relevant outputs based on realist logic produced evidence of two middle-range theories: Naloxone Bystander Intervention Theory and Skills Transfer Theory. RESULTS: Harm reduction and/or low threshold contexts provide a non-judgemental approach which support in-group norms of helping and empower the social identity of the trained and untrained bystander. This context also creates the conditions necessary for skills transfer and diffusion of the intervention into social networks. Stigma and negative attitudes held by first responders and stakeholders involved in the implementation process, such as police or GPs, can prohibit the bystander response by inducing fear in responding. This interferes with skills transfer, naloxone use and carriage of naloxone kits. CONCLUSIONS: The findings provide theoretically informed guidance regarding the harm reduction contexts that are essential for the successful implementation of naloxone-based interventions. Peer-to-peer models of training are helpful as it reinforces social identity and successful skills transfer between bystanders. Health systems may want to assess the prevalence of, and take steps to reduce opioid-related stigma with key stakeholders in contexts using a low threshold training approach to build an environment  to support positive naloxone outcomes. TRIAL REGISTRATION: PROSPERO 2019 CRD42019141003. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12954-022-00599-4

Gauss Sums and Quantum Mechanics

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.Comment: 14 pages, LaTe

Archaeal abundance in post-mortem ruminal digesta may help predict methane emissions from beef cattle

The Rowett Institute of Nutrition and Health and SRUC are funded by the Rural and Environment Science and Analytical Services Division (RESAS) of the Scottish Government. The project was supported by DEFRA and DA funded Agricultural Greenhouse Gas Inventory Research Platform. Our thanks are due to the excellent support staff at the SRUC Beef Research Centre, Edinburgh, also to Graham Horgan of BioSS, Aberdeen, for conducting multivariate analysis.Peer reviewedPublisher PD

Cubic Curves, Finite Geometry and Cryptography

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.Comment: This is a version of our article to appear in Acta Applicandae Mathematicae. In this version, we have corrected a sentence in the third paragraph. The final publication is available at springerlink.com at http://www.springerlink.com/content/xh85647871215644