Let IFq be a finite field of characteristic two and let φ be the Frobenius endomorphism of an elliptic curve. To find or improve efficient algorithms for scalar multiplication sP of point P in the elliptic curve cryptography, it is always an important subject. If IFq = IF2, Solinas [5] has developed an algorithm for computing the φ-NAF. In this note, we extend Solinas’ φ-NAF algorithm to IFq, w...

It may be well known in practice that high stress concentrations occur in fiberreinforced composites. There have been several works by analysis to estimate for the stresses between closed spaced fibers. However, the known results on stiff fibers have until now been restricted to the particular case of circular cross-sections. Thus, we extend the blow-up results on the stresses specialized only ...

Little is known of the course and distribution of blood vessels supplying and draining the hippozampus. Such information could be of value in designing and evaluating lesion and ablation experiments and may reflect spatial properties of neurons. This study mapped the distribution of major arteries and veins of the rat hippocampal formation. Arteries and veins of adult female Wistar rats anesthe...

We estimate the factors determining specialization of crop choice at the level of individual fields, distinguishing between the role of natural advantage (soil characteristics) and economies of density (scale economies achieved when farmers plant neighboring fields with the same crop). Using rich geographic data from North Dakota, including new data on crop choice collected by satellite, we est...

We demonstrate and investigate multiple localized ultrasonic manipulation functions in series in microfluidic chips. The manipulation functions are based on spatially separated and confined ultrasonic primary radiation force fields, obtained by local matching of the resonance condition of the microfluidic channel. The channel segments are remotely actuated by the use of frequency-specific exter...

A two-year study was conducted in South Carolina wheat (Triticum aestivum L. (Poales: Poaceae)) fields to describe spatial and temporal dynamics of stink bugs (Hemiptera: Pentatomidae), which were sampled weekly with sweep nets. In 2010, the main phytophagous stink bugs caught in a grid sampling plan across two fields were the brown stink bug, Euschistus servus (Say), the rice stink bug, Oebalu...