Loops and quasigroups: Aspects of current work and prospects for the future

summary:This paper gives a brief survey of certain recently developing aspects of the study of loops and quasigroups, focussing on some of the areas that appear to exhibit the best prospects for subsequent research and for applications both inside and outside mathematics

Lambda-rings of automorphisms

Abstract. The set of automorphisms of a single algebra forms a group under composition. This paper studies the full set of all automorphisms of all algebra structures in a given abstract class on a fixed finite set. A lambda-ring, known as the automorphism type ring, is associated with this full set of automorphisms, and its structure is described. For certain classes (such as the variety of lattices), the full set of automorphisms is represented up to conjugation in the symmetric group by the automorphisms of a single, so-called representative algebra. In this case, the automorphism type ring is a subring of the ring of class functions on the automorphism group of the representative algebra

A General Framework for Recursive Decompositions of Unitary Quantum Evolutions

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been proposed in the literature to express unitary operators as products of simple operators with properties relevant in entanglement dynamics. In this paper, using the concept of grading of a Lie algebra, we cast these decompositions in a unifying scheme and show how new recursive decompositions can be obtained. In particular, we propose a new recursive decomposition of the unitary operator on $N$ qubits, and we give a numerical example.Comment: 17 pages. To appear in J. Phys. A: Math. Theor. This article replaces our earlier preprint "A Recursive Decomposition of Unitary Operators on N Qubits." The current version provides a general method to generate recursive decompositions of unitary evolutions. Several decompositions obtained before are shown to be as a special case of this general procedur

Bilateral Vestibular Hypofunction in Neurosarcoidosis: A Case Report

We describe the case of a 59-year-old woman who presented with progressive bilateral vestibular hypofunction and who was found to have bilateral granulomatous mass lesions of the mesial temporal lobe. Initially, her condition stabilized neurologically with corticosteroids, but a diagnosis of neurosarcoidosis was delayed because of the unusual presentation and persistently normal chest imaging results and serum angiotensin-converting enzyme (ACE) levels. Approximately 1 year after her initial presentation, the patient died of complications of a myocardial infarction and pulmonary embolism. Sarcoidosis should be considered in the differential diagnosis of idiopathic bilateral vestibular hypofunction even if the chest imaging and serum ACE levels are normal, particularly when there is evidence of a multisystem process

An Interstellar Conduction Front Within a Wolf-Rayet Ring Nebula Observed with the GHRS

With the High Resolution Spectrograph aboard the Hubble Space Telescope we obtained high signal-to-noise (S/N > 200 - 600 per 17 km/s resolution element) spectra of narrow absorption lines toward the Wolf-Rayet star HD 50896. The ring nebula S308 that surrounds this star is thought to be caused by a pressure-driven bubble bounded by circumstellar gas (most likely from a red supergiant or luminous blue variable progenitor) pushed aside by a strong stellar wind. Our observation has shown for the first time that blueshifted (approximately 70 km/s relative to the star) absorption components of C IV and N V arise in a conduction front between the hot interior of the bubble and the cold shell of swept-up material. These lines set limits on models of the conduction front. Nitrogen in the shell appears to be overabundant by a factor ~10. The P Cygni profiles of N V and C IV are variable, possibly due to a suspected binary companion to HD 50896.Comment: 32 pages, Latex, to appear in the Astrophysical Journal, April, 199

A Comprehensive Economic Stimulus for our Failing Economy

This paper presents a comprehensive plan to fix the ailing American economy, through a five-step approach. First, the Federal Reserve must continue to broaden the scope of monetary policy, by purchasing and selling long-term securities. Manipulating expectations through FOMC statements is another tool at the Federal Reserve’s disposal. Secondly, the government must enact fiscal stimulus to stabilize the economy in the short and medium runs, through investment in infrastructure projects, green technology, fusion technology, and science education. Additionally, the new fiscal policy must tackle the mortgage meltdown, which is weighing down the entire economy. Third, the regulatory system must be changed to reduce the likelihood of another financial collapse, starting with the nationalization of the ratings agencies. Ratings should be updated faster, with a numeric grading system rather than the pre-existing letter grades. Fourth, our globalized economy insures that a coordinated globalized response is necessary to recover. Global cooperation to reduce inflation and avoid protectionist policies is vital. Finally, the American bailout policy must be made clear, only giving bailouts to companies that are sound but financially strapped and those that are too big to fail