On compatibility between isogenies and polarisations of abelian varieties

We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show that certain questions about polarised isogenies can be reduced to questions about unpolarised isogenies or vice versa. Our main theorem concerns abelian varieties B which are isogenous to a fixed abelian variety A. It establishes the existence of a polarised isogeny A to B whose degree is polynomially bounded in n, if there exist both an unpolarised isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As a further result, we prove that given any two principally polarised abelian varieties related by an unpolarised isogeny, there exists a polarised isogeny between their fourth powers. The proofs of both theorems involve calculations in the endomorphism algebras of the abelian varieties, using the Albert classification of these endomorphism algebras and the classification of Hermitian forms over division algebras

A near Fourier-transform limited optical parametric oscillator/amplifier system as a pulsed source for high resolution spectroscopy

© Copyright 2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.We use optical heterodyne and nonlinear-optical spectroscopic techniques to measure the near Fourier-transform limited output from a narrowband tunable injection-seeded, pulsed optical parametric oscillator/amplifier system that has a controllable frequency chirp of <10 MHzK.G.H. Baldwin, M. Kono, Y. He, R. T. White, B. J. Or

Serviceability of non-prismatic concrete beams: Combined-interaction method

Interest in the shape optimisation of concrete members is increasing alongside the availability of fabric formwork as a relatively simple technique to cast non-prismatic concrete structures. Research has shown that up 40% of concrete can be saved when shape optimised concrete beams are cast in fabric forms. However, optimisation results in members with non-uniform cross-sections and the resulting beam is less stiff than an equivalent strength prismatic beam. Serviceability, rather than strength, may govern the design of such members and therefore understanding the serviceability behaviour (deflection and cracking) of shape optimised concrete members becomes is a critical design consideration. There are many methods which can be used to evaluate serviceability behaviour of reinforced concrete beams, including the full-interaction method, which assumes no slip between the reinforcement and the surrounding concrete, and the partial-interaction method which accounts for slip. The full-interaction method is based on a smeared crack approach and so is unsuited for the prediction of cracking behaviour. The partial-interaction method, on the other hand, assumes that cracks form through bond-stress transfer only. In the case of non-prismatic concrete beams, the cracking capacity varies along the member. Therefore, cracking can occur over extended regions (full and partial bond interaction regions) and so it can be argued that neither of these models is fully suitable for the prediction of deflections and cracking of shape-optimised concrete beams. In this paper, a novel combined-interaction method is, for the first time, presented to predict the serviceability behaviour of non-prismatic concrete beams by simulating both full and partial bond interactions at different cracked and uncracked regions along the length of the member. In order to validate this approach, two non-prismatic simply supported beams were cast and tested. The test results for deflections, crack widths and crack spacings were in good agreement with the predicted results

Extreme value distributions for weakly correlated fitnesses in block model

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random variables drawn from a common parent distribution. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.Comment: Expanded, added reference

Structural and electrical transport properties of superconducting Au{0.7}In{0.3} films: A random array of superconductor-normal metal-superconductor (SNS) Josephson junctions

The structural and superconducting properties of Au{0.7}In{0.3} films, grown by interdiffusion of alternating Au and In layers, have been studied. The films were found to consist of a uniform solid solution of Au{0.9}In{0.1}, with excess In precipitated in the form of In-rich grains of various Au-In phases (with distinct atomic compositions), including intermetallic compounds. As the temperature was lowered, these individual grains became superconducting at a particular transition temperature (Tc), determined primarily by the atomic composition of the grain, before a fully superconducting state of zero resistance was established. From the observed onset Tc, it was inferred that up to three different superconducting phases could have formed in these Au{0.7}In{0.3} films, all of which were embedded in a uniform Au{0.9}In{0.1} matrix. Among these phases, the Tc of a particular one, 0.8 K, is higher than any previously reported for the Au-In system. The electrical transport properties were studied down to low temperatures. The transport results were found to be well correlated with those of the structural studies. The present work suggests that Au{0.7}In{0.3} can be modeled as a random array of superconductor-normal metal-superconductor (SNS) Josephson junctions. The effect of disorder and the nature of the superconducting transition in these Au{0.7}In{0.3} films are discussed.Comment: 8 text pages, 10 figures in one separate PDF file, submitted to PR

Patterns of Interaction Among Local Public Health Officials and the Adoption of Recommended Practices

The network that local health officials use to communicate about professional issues contains two groups of LHDs that are influential for either their ability to spread information or to innovate. Both groups are more likely to conduct community health assessments and develop health improvement plans. Since these activities are fundamental aspects of accreditation and health reform, the findings may present an early indication that these initiatives are having an effect on the public health system

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review

Unitization of route knowledge

There are many theories that explain how route knowledge is acquired. We examined here if the sequence of elements that are part of a route can become integrated into a single unit, to the extent that the processing of individual transitions may only be relevant in the context of this entire unit. In Experiments 1 and 2, participants learned a route for ten blocks. Subsequently, at test they were intermittently exposed to the same training route along with a novel route which contained partial overlap with the original training route. Results show that the very same stimulus, appearing in the very same location, requiring the very same response (e.g., left turn), was responded to significantly faster in the context of the original training route than in the novel route. In Experiment 3 we employed a modified paradigm containing landmarks, two matched routes which were both substantially longer and contained a greater degree of overlap than the routes in Experiments 1 and 2. Results were replicated, namely, the same overlapping route segment, common to both routes, was performed significantly slower when appearing in the context of a novel than the original route. Furthermore, the difference between the overlapping segments was similar to the difference observed for the non-overlapping segments, i.e., an old route segment in the context of a novel route was processed as if it were an entirely novel segment. We discuss the results in relation to binding, chunking and transfer effects, as well as potential practical implications

The N = 16 spherical shell closure in 24O

The unbound excited states of the neutron drip-line isotope 24O have been investigated via the 24O(p,p')23O+n reaction in inverse kinematics at a beam energy of 62 MeV/nucleon. The decay energy spectrum of 24O* was reconstructed from the momenta of 23O and the neutron. The spin-parity of the first excited state, observed at Ex = 4.65 +/- 0.14 MeV, was determined to be Jpi = 2+ from the angular distribution of the cross section. Higher lying states were also observed. The quadrupole transition parameter beta2 of the 2+ state was deduced, for the first time, to be 0.15 +/- 0.04. The relatively high excitation energy and small beta2 value are indicative of the N = 16 shell closure in 24O.Comment: to be submitted to Physical Review Letter