Construction of class fields over cyclotomic fields

Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ let $k_\mu$ be the ray class field of $k=\mathbb{Q}(e^{2\pi i/\ell})$ modulo $2p^\mu$. We present certain class fields $K_\mu$ of $k$ such that $k_\mu\leq K_\mu\leq k_{\mu+1}$, and find the degree of $K_\mu/k_\mu$ explicitly. And we also construct, in the sense of Hilbert, primitive generators of the field $K_\mu$ over $k_\mu$ by using Shimura's reciprocity law and special values of theta constants

Ray class fields generated by torsion points of certain elliptic curves

We first normalize the derivative Weierstrass $\wp'$-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind $\eta$-function. And, by making use of this normalization of $\wp'$ we associate certain elliptic curve to a given imaginary quadratic field $K$ and then generate an infinite family of ray class fields over $K$ by adjoining to $K$ torsion points of such elliptic curve. We further construct some ray class invariants of imaginary quadratic fields by utilizing singular values of the normalization of $\wp'$, as the $y$-coordinate in the Weierstrass equation of this elliptic curve, which would be a partial result for the Lang-Schertz conjecture of constructing ray class fields over $K$ by means of the Siegel-Ramachandra invariant

The Role of Aesthetic Interaction in Sound Experience

Department of Creative Design EngineeringIn this paper, I examined how Aesthetic Interaction, which plays an important role in HCI, affects the evaluation of human emotion and product image when applied to products that provide an auditory experience. For this, I used a Research through Design approach and built a prototype with three elements of ???Aesthetic Interaction???. This could be measured through a self-emotion report, 29SD. The Friedman test also showed statistically significant results. These results suggest that in designing products that can provide an auditory experience, we can apply aesthetic interaction to the emotions and images that designers intentionally project.clos

Au-SN Flip-Chip Solder Bump for Microelectronic and Optoelectronic Applications

As an alternative to the time-consuming solder pre-forms and pastes currently used, a co-electroplating method of eutectic Au-Sn alloy was used in this study. Using a co-electroplating process, it was possible to plate the Au-Sn solder directly onto a wafer at or near the eutectic composition from a single solution. Two distinct phases, Au5Sn and AuSn, were deposited at a composition of 30at.%Sn. The Au-Sn flip-chip joints were formed at 300 and 400 degrees without using any flux. In the case where the samples were reflowed at 300 degrees, only an (Au,Ni)3Sn2 IMC layer formed at the interface between the Au-Sn solder and Ni UBM. On the other hand, two IMC layers, (Au,Ni)3Sn2 and (Au,Ni)3Sn, were found at the interfaces of the samples reflowed at 400 degrees. As the reflow time increased, the thickness of the (Au,Ni)3Sn2 and (Au,Ni)3Sn IMC layers formed at the interface increased and the eutectic lamellae in the bulk solder coarsened.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions