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Let F be any field of prime characteristic p and let q be a power of p. We assume that F contains the finite field of order q. A q -polynomial L over F is an element of the polynomial ring F [ x ] with the property that all exponents are a power of q. We assume that the coefficient of the x term of L is nonzero. We investigate the Galois group G of L over F , under the assumption that L (x) / x is irreducible in F [ x ]. It is well known that if L has q -degree n , its roots are an n -dimensional vector space over the field of order q and G acts linearly on this space. Our main theorem is the following. We consider a monic q -polynomial L whose q -degree is a prime, r , say, with L (x) / x irreducible over F. Assuming that the coefficient of the x term of L is (− 1) r , we show that the Galois group of L over F must be the special linear group S L (r , q) of degree r over the field of order q when q > 2. We also prove a projective version for the projective special linear group P S L (r , q) , and we present the analysis when q = 2. [ABSTRACT FROM AUTHOR]

A method for forming a carbon nanotube (CNT) reinforced copper (Cu) composite by an electrodeposition process has been developed. Nanoscale diamond particles were introduced as a dispersing agent to prevent aggregation of carbon nanotubes while performing electrodeposition, or what is commonly referred to as electroplating. The technique involves co-deposition of Cu and CNTs in an electroplating process that uses both direct current and a sequence of forward and reverse pulses. Reverse pulse times were varied in order to examine parameters for dispersion of carbon nanotubes in the resultant composite material. Electrical resistivity, surface morphology, and composite structure were investigated using a probe station, scanning electron microscopy, and x-ray diffraction, respectively. Experimental results show carbon nanotubes can be dispersed uniformly in a Cu/CNT composite due to the role played by the nanodiamond particles in CNT de-aggregation. Direct current electrodeposition yields high deposition rates while reverse pulse electrodeposition is a slower process although necessary for providing a higher percentage of CNTs integrated into the composite. [ABSTRACT FROM AUTHOR]

Abstract: We give a construction of cocyclic Butson–Hadamard matrices from bilinear forms over finite Frobenius rings, which generalizes previous constructions. We then prove a classification result, showing that the resulting matrices depend only on the additive group of the underlying module of the form. [Copyright &y& Elsevier]

Diamond nanoparticles occupy a special niche among nanomaterials due to their combination of outstanding mechanical performance, chemical resistance, biocompatibility, and unique optical and electronic properties. In this review a brief survey of the different classes of nanodiamond particles based on synthesis method and associated structural features is provided. Then major structural features of ND particles (size, shape, crystallographic core, surface chemistry, internal defects / dopants, and presence of sp 2 carbon) are discussed as well as their connection with ND properties and related applications. In conclusion current opportunities in the fields of production and processing of nanodiamond particles and the outlook for the future of the field are critically discussed. [ABSTRACT FROM AUTHOR]

Abstract: Let be a field and let denote the space of matrices over . We investigate properties of a subspace of of dimension in which each non-zero element of has rank at least and enumerate the number of elements of a given rank in when is finite. We also provide an upper bound for the dimension of a constant rank subspace of when is finite and give non-trivial examples to show that our bound is optimal in some cases. We include a similar a bound for the maximum dimension of a constant rank subspace of skew-symmetric matrices over a finite field. [Copyright &y& Elsevier]

Abstract: We study PN and APN functions over the integers modulo . We give some construction techniques based on Costas arrays, which allow us to construct APN permutations on where is a prime. Although PN permutations do not exist, one set of our functions is very close to being a set of PN permutations. [Copyright &y& Elsevier]

Recent advancements in high temperature rapid thermal annealing (RTA) of irradiated diamond particles has made possible the production of the particles with fluorescence based on complexes of nitrogen and vacancies in a broad range of colors: blue, green, red/NIR as well as their mixtures, depending on the temperature and irradiation fluence. Still, the production of fluorescent diamond particles suffers from fluorescence inhomogeneity among particles. The goal of the current study is improvement of the fluorescence uniformity among the treated particles. Experiments were performed using as-grown 40 μm in diameter type Ib synthetic diamond particulate assuming that nitrogen uniformity among the as-grown particles should be higher versus milled ones used in previous studies. Particles were irradiated under mild conditions with 1 MeV electrons to a fluence 3 × 1018 e/cm2 without overheating during irradiation which resulted in relatively uniform green fluorescence among particles treated via RTA at temperatures corresponding to H3 centers formation. [ABSTRACT FROM AUTHOR]