Let E be an elliptic curve over Q and ` be an odd prime. Also, let K be a number field and assume that E has a semi-stable reduction at `. Under certain assumptions, we prove the vanishing of the Galois cohomology group H1(Gal(K(E[`i])/K), E[`i]) for all i ≥ 1. When K is an imaginary quadratic field with the usual Heegner assumption, this vanishing theorem enables us to extend a result of Kolyv...

In this study, transparent conducting nanocrystalline ZnO:Ga (GZO) films were deposited by dc magnetron sputtering at room temperature on polymers (and glass for comparison). Electrical resistivities of 8.8 × 10-4 and 2.2 × 10-3 Ω cm were obtained for films deposited on glass and polymers, respectively. The crack onset strain (COS) and the cohesive strength of the coatings were investigated by ...

This Article is brought to you for free and open access by the Electrical & Computer Engineering at ODU Digital Commons. It has been accepted for inclusion in Electrical & Computer Engineering Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Repository Citation Marsillac, S.; Khatri, H.; Aryal, K.; and Colli...

We give an elementary proof of the Mazur-TateTeitelbaum conjecture for elliptic curves by using Kato’s element. 2000 Mathematics Subject Classification: 11F85, 11G05, 11G07, 11G40, 11S40.

In this paper, we study the relation between the cohomology of Coxeter groups and their parabolic subgroups of nite order. Let W be a Coxeter group and k a commutative ring with identity. We investigate the natural map : H (W; k) ! lim:inv: H (W F ; k), where W F runs all parabolic subgroups of nite order, and prove that the kernel and the cokernel of consist of nilpotent elements. This general...

The problem of estimating the number of imaginary quadratic fields whose ideal class group has an element of order ` ≥ 2 is classical in number theory. Analogous questions for quadratic twists of elliptic curves have been the focus of recent interest. Whereas works of Stewart and Top [St-T], and of Gouvêa and Mazur [G-M] address the nontriviality of MordellWeil groups, less is known about the n...

An investigation is performed into the optical, electrical, and microstructural properties of Ti-Ga-doped ZnO films deposited on polyimide (PI) flexible substrates and then annealed at temperatures of 300 °C, 400 °C, and 450 °C, respectively. The X-ray diffraction (XRD) analysis results show that all of the films have a strong (002) Ga doped ZnO (GZO) preferential orientation. As the annealing ...