Subsets of finite groups exhibiting additive regularity

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In particular, we show that any sum set must exhibit higher-order regularity and that an abelian sum set is necessarily a reversible difference set. We next develop several general construction techniques under the hypothesis that the over-riding group contains a normal subgroup of order 2. Finally, by exploiting properties of dihedral groups and Frobenius groups, several infinite classes of sum sets and partial sum sets are introduced

On the evaluation of a class of Weil sums in characteristic 2

Abstract. We consider a class of Weil sums involving polynomials of a par-ticular shape. In all cases, explicit evaluations are obtained. 1

Level of adherence to prescribed exercise in spondyloarthritis and factors affecting this adherence: a systematic review

Adherence is a primary determinant of the effectiveness of any intervention. Exercise is considered essential in the management of spondyloarthritis (SpA); however, the overall adherence to exercise programmes and factors affecting adherence are unknown. The aim of this systematic review was to examine measures of, and factors influencing adherence to, prescribed exercise programmes in people with SpA. A search was performed in August 2018 using five data bases; the Cochrane library, CINAHL, EMBASE, MEDLINE, and Web of Science Collections. Inclusion criteria were: studies with adults (> 18 years) with SpA, with a prescribed exercise intervention or educational programme with the aim of increasing exercise participation. Article quality was independently assessed by two assessors. Extracted descriptive data included: populations, interventions, measures of adherence and factors affecting adherence. Percentage adherence rates to prescribed exercises were calculated if not reported. Nine studies were included with a total of 658 participants, 95% of participants had a diagnosis of ankylosing spondylitis. Interventions and measurement of adherence varied, making comparisons difficult. Rates of adherence ranged from 51.4 to 95%. Single studies identified; adherence improved following educational programmes, and higher disease severity and longer diagnostic delays were associated with higher adherence. Conflicting evidence was found as to whether supervision of exercise improved adherence. Three consecutive studies demonstrated adherence reduced over time. Adherence to prescribed exercise in SpA was poorly reported and predominately for people with AS. The levels of adherence and factors affecting prescribed exercise in SpA remain unclear. Future research should measure adherence across a longer time period and investigate possible factors which may influence adherence

A result on polynomials derived via graph theory

We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that some trinomials over finite fields have the same number of roots

In vivo and in vitro models of demyelinating diseases. V. Comparison of the assembly of mouse hepatitis virus, strain JHM, in two murine cell lines.

The developmental sequence of a neurotropic strain (JHM) of mouse hepatitis virus was examined by transmission electron microscopy and immunocytology. The nucleoprotein core of this coronavirus, which contains RNA of positive polarity and is helical in configuration, becomes incorporated into enveloped particles in the same manner as the nucleocapsids of the orthomyxo- and paramyxoviruses. However, JHM virus is assembled intracellularly by budding at surfaces of smooth membranous vacuoles. A comparison of JHM virus replication in L2 and 17Cl-1 cell lines revealed that L2 cells undergo more rapid cytopathology and cease virus production much sooner than 17Cl-l cells. In L2 cells the accumulation of core material appears to continue after the abrupt cessation of virus assembly. This is evident by the massive cytoplasmic accumulation of structure resembling nucleocapsids, which react with hybridoma antibody to the nucleocapsid antigen as demonstrated by the immunoperoxidase procedure. The current findings are consistent with our previously published demonstration, using cells of neural and other deviation, of the fundamental role of the host cell type in regulating the replication and expression of coronaviruses

The Thermal Environment of the Fiber Glass Dome for the New Solar Telescope at Big Bear Solar Observatory

The New Solar Telescope (NST) is a 1.6-meter off-axis Gregory-type telescope with an equatorial mount and an open optical support structure. To mitigate the temperature fluctuations along the exposed optical path, the effects of local/dome-related seeing have to be minimized. To accomplish this, NST will be housed in a 5/8-sphere fiberglass dome that is outfitted with 14 active vents evenly spaced around its perimeter. The 14 vents house louvers that open and close independently of one another to regulate and direct the passage of air through the dome. In January 2006, 16 thermal probes were installed throughout the dome and the temperature distribution was measured. The measurements confirmed the existence of a strong thermal gradient on the order of 5 degree Celsius inside the dome. In December 2006, a second set of temperature measurements were made using different louver configurations. In this study, we present the results of these measurements along with their integration into the thermal control system (ThCS) and the overall telescope control system (TCS).Comment: 12 pages, 11 figures, submitted to SPIE Optics+Photonics, San Diego, U.S.A., 26-30 August 2007, Conference: Solar Physics and Space Weather Instrumentation II, Proceedings of SPIE Volume 6689, Paper #2

Bounds on the differential uniformity of the Wan-Lidl polynomials

We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order $3\bmod 4$, irrespective of the field size. Computational results are also given

Extending abelian groups to rings

For any abelian group G and any function f : G &rarr; G we define a commutative binary operation or `multiplication\u27 on G in terms of f. We give necessary and sufficient conditions on f for G to extend to a commutative ring with the new multiplication. In the case where G is an elementary abelian p-group of odd order, we classify those functions which extend G to a ring and show, under an equivalence relation we call weak isomorphism, that there are precisely six distinct classes of rings constructed using this method with additive group the elementary abelian p-group of odd order p2. <br /

Prostate cancer radiotherapy: potential applications of metal nanoparticles for imaging and therapy

Prostate cancer (CaP) is the most commonly diagnosed cancer in males. There have been dramatic technical advances in radiotherapy delivery, enabling higher doses of radiotherapy to primary cancer, involved lymph nodes and oligometastases with acceptable normal tissue toxicity. Despite this, many patients relapse following primary radical therapy, and novel treatment approaches are required. Metal nanoparticles are agents that promise to improve diagnostic imaging and image-guided radiotherapy and to selectively enhance radiotherapy effectiveness in CaP. We summarize current radiotherapy treatment approaches for CaP and consider pre-clinical and clinical evidence for metal nanoparticles in this condition