We develop an algorithm for computing numerical evidence for a conjecture whose validity is predicted by the requirement that the Equivariant Tamagawa Number conjectures for Tate motives as formulated by Burns and Flach are compatible with the functional equation of Artin Ä-series. The algorithm includes methods for the computation of Fitting ideals and projective lattices over the integral gro...

We have performed nonlinear transport measurements as a function of a perpendicular magnetic field in a semiconductor Aharonov-Bohm ring connected to two leads. While the voltage-symmetric part of the conductance is symmetric in the magnetic field, the voltage-antisymmetric part of the conductance is not symmetric. These symmetry relations are compatible with the scattering theory for nonlinear...

SpikeNet is an image-processing system that uses very large-scale networks of asynchronously -ring neurons. The latest version allows very e0cient object identi-cation in real-time using a video input, and although this speci-c implementation is designed to run on standard computer hardware, there are a number of clear implications for computational neuroscience. Speci-cally, SpikeNet demonstra...

[2.2]Paracyclophanes, incorporating functional groups in the aliphatic bridges, suitable for elimination to give [2.2]paracyclophanedienes, are synthesized through a novel approach. It relies on a double Pummerer rearrangement on dithiacyclophane precursors, followed by ring contraction through a photochemical sulfur extrusion, and it is compatible with aryl moieties possessing very different e...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

Let D be a division ring, T be a variable over D, σ be an endomorphism of D, δ be a σ-derivation on D and R = D[T ;σ, δ] the left skew polynomial ring over D. We show that the set (V alν(R), ) of σ-compatible real valuations which extend to R a fixed proper real valuation ν on D has a natural structure of parameterized complete non-metric tree, where is the partial order given by μ μ̃ if and onl...

We investigate the athermal characteristics of silicon waveguides clad with TiO(2) designed for 1.3 µm wavelength operation. Using CMOS-compatible fabrication processes, we realize and experimentally demonstrate silicon photonic ring resonators with resonant wavelengths that vary by less than 6 pm/°C at 1.3 µm. The measured ring resonance wavelengths across the 20-50°C temperature range show ne...