Generalized Reciprocals, Factors of Dickson Polynomials and Generalized Cyclotomic Polynomials over Finite Fields

We give new descriptions of the factors of Dickson polynomials over finite fields in terms of cyclotomic factors. To do this generalized reciprocal polynomials are introduced and characterized. We also study the factorization of generalized cyclotomic polynomials and their relationship to the factorization of Dickson polynomials

Pencils of Quadratic Forms over Finite Fields

A formula for the number of common zeros of a non-degenerate pencil of quadratic forms is given. This is applied to pencils which count binary strings with an even number of 1\u27s prescribed distances apart

Irreducible Polynomials over GF(2) with Three Prescribed Coefficients

For an odd positive integer n, we determine formulas for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of xn-1, xn-2 and xn-3 are specified in advance. Formulas for the number of elements in GF(2n) with the first three traces specified are also given

Sums of Gauss Sums and Weights of Irreducible Codes

We develop a matrix approach to compute a certain sum of Gauss sums which arises in the study of weights of irreducible codes. A lower bound on the minimum weight of certain irreducible codes is given

Explicit Factorizations of Cyclotomic and Dickson Polynomials over Finite Fields

We give, over a finite field Fq, explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3·2n, the Dickson polynomials of the first kind of order 3·2n and the Dickson polynomials of the second kind of order 3·2n  − 1

Factors of Dickson Polynomials over Finite Fields

We give new descriptions of the factors of Dickson polynomials over finite fields

Longitudinal Monitoring of SARS-CoV-2 IgM and IgG Seropositivity to Detect COVID-19.

BackgroundSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a novel beta-coronavirus that has recently emerged as the cause of the 2019 coronavirus pandemic (COVID-19). Polymerase chain reaction (PCR) based tests are optimal and recommended for the diagnosis of an acute SARS-CoV-2 infection. Serology tests for viral antibodies provide an important tool to diagnose previous exposure to the virus. Here we evaluate the analytical performance parameters of the Diazyme SARS-CoV-2 IgM/IgG serology assays and describe the kinetics of IgM and IgG seroconversion observed in patients with PCR-confirmed COVID-19 who were admitted to our hospital.MethodsWe validated the performance of the Diazyme assay in 235 presumed SARS-CoV-2 negative subjects to determine specificity. Subsequently, we evaluated the SARS-CoV-2 IgM and IgG seroconversion of 54 PCR-confirmed COVID-19 patients and determined sensitivity of the assay at three different timeframes.ResultSensitivity and specificity for detecting seropositivity at ≥15 days following a positive SARS-CoV-2 PCR result, was 100.0% and 98.7% when assaying for the panel of IgM and IgG. The median time to seropositivity observed for a reactive IgM and IgG result from the date of a positive PCR was 5 days (IQR: 2.75-9 days) and 4 days (IQR: 2.75-6.75 days), respectively.ConclusionsOur data demonstrate that the Diazyme IgM/IgG assays are suited for the purpose of detecting SARS-CoV-2 IgG and IgM in patients with suspected SARS-CoV-2 infections. For the first time, we report longitudinal data showing the evolution of seroconversion for both IgG and IgM in a cohort of acutely ill patients in the United States. We also demonstrate a low false positive rate in patients who were presumed to be disease free

Photometric and proper motion study of neglected open cluster NGC 2215

Optical UBVRI photometric measurements using the Faulkes Telescope North were taken in early 2011 and combined with 2MASS JHK$_s$ and WISE infrared photometry as well as UCAC4 proper motion data in order to estimate the main parameters of the galactic open cluster NGC 2215 of which large uncertainty exists in the current literature. Fitting a King model we estimate a core radius of 1.12$'\pm$0.04$'$ (0.24$\pm$0.01pc) and a limiting radius of $4.3'\pm$0.5$'$ (0.94$\pm$0.11pc) for the cluster. The results of isochrone fits indicates an age of $log(t)=8.85\pm0.10$ with a distance of $d=790\pm90$pc, a metallicity of $[Fe/H]=-0.40\pm0.10$ dex and a reddening of $E(B-V)=0.26\pm0.04$. A proportion of the work in this study was undertaken by Australian and Canadian upper secondary school students involved in the Space to Grow astronomy education project, and is the first scientific publication to have utilized our star cluster photometry curriculum materials.Comment: 10 pages, 9 Figures, 3 Table

High hole and electron mobilities using Strained Si/Strained Ge heterostructures

PMOS and NMOS mobility characteristics of the dual channel (strained Si/strained Ge) heterostructure have been reviewed. It is shown that the dual channel heterostructure can provide substantially enhanced mobilities for both electrons and holes. However, germanium interdiffusion from the germanium rich buried layer into the underlying buffer layer could potentially reduce the hole mobility enhancements.Singapore-MIT Alliance (SMA