Invariance of the parity conjecture for p-Selmer groups of elliptic curves in a D2pnD_{2p^n}-extension

In section 2, we show a $p$-parity result in a $D_{2p^{n}}$-extension of number fields $L/K$ ($p\geq 5$) for the twist $1\oplus \eta \oplus \tau$: W(E/K,1\oplus \eta \oplus \tau)=(-1)^{}, where $E$ is an elliptic curve over $K,$ $\eta$ and $\tau$ are respectively the quadratic character and an irreductible representation of degree 2 of $Gal(L/K)=D_{2p^{n}},$ and $X_{p}(E/L)$ is the $p$-Selmer group. The main novelty is that we use a congruence result between $$-factors (due to Deligne) for the determination of local root numbers in bad cases (places of additive reduction above 2 and 3). We also give applications to the $p$-parity conjecture (using the machinery of the Dokchitser brothers).Comment: 19 page

Engineering Education Periodicals and Proceedings: Increasing Awareness of and Access to the Literature

In the vast realm, of engineering literature there is a set of publications that is often unknown and certainly underutilized: engineering education periodicals and proceedings. These publications can easily be overlooked by engineering faculty, researchers, students, librarians or information professionals, and others who may not be fully aware of their existence or content. There has been a need for a definitive list of such publications for some time. This paper presents an initial list of these hems as the first step to make them more accessible to those in engineering education who may need them. The next step wil1 be to create a descriptive database of these items, briefly detailing their content, stating who publishes them, indicating what indexes or databases they are indexed or 'abstracted in and showing if they are available electronical1y. A, print-out of such a database could serve as an annotated bibliography, a finding guide, and as a checklist of engineering education periodicals and conference proceedings. Such a print-out could then be published by ASEE in its Guide to the Literature series or as an additional conference paper. As a result, the engineering education literature of ASEE and other organizations or publishers could be more easily identified and utilized by those who create it and by those who would benefit the most from it, namely engineering educators

Eigenmode-based capacitance calculations with applications in passivation layer design

The design of high-speed metallic interconnects such as microstrips requires the correct characterization of both the conductors and the surrounding dielectric environment, in order to accurately predict their propagation characteristics. A fast boundary integral equation approach is obtained by modeling all materials as equivalent surface charge densities in free space. The capacitive behavior of a finite dielectric environment can then be determined by means of a transformation matrix, relating these charge densities to the boundary value of the electric potential. In this paper, a new calculation method is presented for the important case that the dielectric environment is composed of homogeneous rectangles. The method, based on a surface charge expansion in terms of the Robin eigenfunctions of the considered rectangles, is not only more efficient than traditional methods, but is also more accurate, as shown in some numerical experiments. As an application, the design and behavior of a microstrip passivation layer is treated in some detail

Partial compact quantum groups

Compact quantum groups of face type, as introduced by Hayashi, form a class of compact quantum groupoids with a classical, finite set of objects. Using the notions of a weak multiplier bialgebra and weak multiplier Hopf algebra (resp. due to B{\"o}hm--G\'{o}mez-Torrecillas--L\'{o}pez-Centella and Van Daele-Wang), we generalize Hayashi's definition to allow for an infinite set of objects, and call the resulting objects partial compact quantum groups. We prove a Tannaka-Kre$\breve{\textrm{\i}}$n-Woronowicz reconstruction result for such partial compact quantum groups using the notion of a partial fusion C$^*$-category. As examples, we consider the dynamical quantum $SU(2)$-groups from the point of view of partial compact quantum groups.Comment: 56 page

Construction and applications of the Dirichlet-to-Neumann operator in transmission line modeling

The Dirichlet-to-Neumann (DIN) operator is a useful tool in the characterization of interconnect structures. in. combination with the Method of Moments; it con. be used for the calculation, of the per-unit length transmission line parameters of multi-conductor Or to directly determine the interval impedance of conductors. This paper presents a new and fast calculation method for the DIN boundary operator in the important case of rectangular structures, based on the superposition of parallel-plate waveguide modes. Especially for its non-differential form, some numerical issues need to be addressed. It is further explained how the DtN operator can be determined for composite geometries. The theory is illustrated with some numerical examples

A geometric approach to Mathon maximal arcs

In 1969 Denniston gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of isomorphism classes of Mathon maximal arcs of degree 8 in PG(2,2^h), h prime.Comment: 20 page