(a) If p ramifies in Q(ζm), then p | m; the ramification index ep of the primes over p is φ(p) = (p− 1)pk−1 if p ‖ m. (b) The prime p is wildly ramified in Q(ζm) if and only if p | m. (c) If p m, then p is unramified. In the ring of integers Z[ζm] of Q(ζm), we obtain pOL = ∏gp i=1 pi. The primes pi have residue class degree fp = [Fp(ζm) : Fp], which (by looking at the Frobenius x 7→ x acting on...

Mussel adhesive proteins (MAPs) have received increased attention as potential biomedical and environmental friendly adhesives. However, practical application of MAPs has been severely limited by uneconomical extraction and unsuccessful genetic production. Developing new adhesives requires access to large quantities of material and demonstrations of bulk mechanical properties. Previously, the a...

A reverse k nearest neighbor (RkNN) query retrieves all the data points that have q as one of their k closest points. In recent years, considerable research has been conducted into monitoring reverse k nearest neighbor queries. In this paper, we study the problem of continuous reverse nearest neighbor queries where both the query object q and data objects are moving. Existing state-of-the-art t...

In this work, we describe a simple and efficient construction of a large subset S of Fp , where p is a prime, such that the set A(S) for any non-identity affine map A over Fp has small intersection with S . Such sets, called affine-evasive sets, were defined and constructed in [ADL14] as the central step in the construction of non-malleable codes against affine tampering over Fp , for a prime p...

Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in various fields. The simplest of such maps is the spherical proximity map which maps a point from the class of interest to a disk centered at the same point with ...

inverse transform of the subject FA map into standard space were combined in order to map the labelled white matter atlas into subject space, (B) regions associated with working memory identified on the atlas in the frontal (yellow), temporal (red) and parietal (green) lobes, (C) sagittal and axial projections of retained FT, FP and TP tracts for the 10 subjects in the middle-aged group overlai...

Context-awareness represents an important research domain in mobile computing by utilizing information about persons, places and objects anytime and anywhere. The highly dynamic contexts created by this paradigm raise questions how to efficiently determine alikeness and affinity between such contexts. Inspired by mechanisms from locationaware computing, we tackle the issue of contextual proximi...

Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed...