13,605 research outputs found
Voicing Transformations and a Linear Representation of Uniform Triadic Transformations (Preprint name)
Motivated by analytical methods in mathematical music theory, we determine the structure of the subgroup of generated by the three voicing reflections. We determine the centralizer of in both and the monoid of affine transformations, and recover a Lewinian duality for trichords containing a generator of . We present a variety of musical examples, including Wagner's hexatonic Grail motive and the diatonic falling fifths as cyclic orbits, an elaboration of our earlier work with Satyendra on Schoenberg, String Quartet in minor, op. 7, and an affine musical map of Joseph Schillinger. Finally, we observe, perhaps unexpectedly, that the retrograde inversion enchaining operation RICH (for arbitrary 3-tuples) belongs to the setwise stabilizer in of root position triads. This allows a more economical description of a passage in Webern, Concerto for Nine Instruments, op. 24 in terms of a morphism of group actions. Some of the proofs are located in the Supplementary Material file, so that this main article can focus on the applications
On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups
We show that, if there exists a realization of a Hopf algebra in a
-module algebra , then one can split their cross-product into the tensor
product algebra of itself with a subalgebra isomorphic to and commuting
with . This result applies in particular to the algebra underlying
inhomogeneous quantum groups like the Euclidean ones, which are obtained as
cross-products of the quantum Euclidean spaces with the quantum groups
of rotation of , for which it has no classical analog.Comment: Latex file, 27 pages. Final version to appear in J. Phys.
An aging evaluation of the bearing performances of glass fiber composite laminate in salt spray fog environment
The aim of the present paper is to assess the bearing performance evolution of pinned, glass-composite laminates due to environmental aging in salt-spray fog tests. Glass fibers/epoxy pinned laminates were exposed for up to 60 days in salt-spraying, foggy environmental conditions (according to ASTM B117 standard). In order to evaluate the relationship between mechanical failure mode and joint stability over increasing aging time, different single lap joints, measured by the changing hole diameter (D), laminate width (W) and hole free edge distance (E), were characterized at varying aging steps. Based on this approach, the property-structure relationship of glass-fibers/epoxy laminates was assessed under these critical environmental conditions. Furthermore, an experimental 2D failure map, clustering main failure modes in the plane E/D versus W/D ratios, was generated, and its cluster variation was analyzed at each degree of aging
Phase transition in conservative diffusive contact processes
We determine the phase diagrams of conservative diffusive contact processes
by means of numerical simulations. These models are versions of the ordinary
diffusive single-creation, pair-creation and triplet-creation contact processes
in which the particle number is conserved. The transition between the frozen
and active states was determined by studying the system in the subcritical
regime and the nature of the transition, whether continuous or first order, was
determined by looking at the fractal dimension of the critical cluster. For the
single-creation model the transition remains continuous for any diffusion rate.
For pair- and triplet-creation models, however, the transition becomes first
order for high enough diffusion rate. Our results indicate that in the limit of
infinite diffusion rate the jump in density equals 2/3 for the pair-creation
model and 5/6 for the triplet-creation model
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Value encoding in the globus pallidus: fMRI reveals an interaction effect between reward and dopamine drive
The external part of the globus pallidus (GPe) is a core nucleus of the basal ganglia (BG) whose activity is disrupted under conditions of low dopamine release, as in Parkinson's disease. Current models assume decreased dopamine release in the dorsal striatum results in deactivation of dorsal GPe, which in turn affects motor expression via a regulatory effect on other nuclei of the BG. However, recent studies in healthy and pathological animal models have reported neural dynamics that do not match with this view of the GPe as a relay in the BG circuit. Thus, the computational role of the GPe in the BG is still to be determined. We previously proposed a neural model that revisits the functions of the nuclei of the BG, and this model predicts that GPe encodes values which are amplified under a condition of low striatal dopaminergic drive. To test this prediction, we used an fMRI paradigm involving a within-subject placebo-controlled design, using the dopamine antagonist risperidone, wherein healthy volunteers performed a motor selection and maintenance task under low and high reward conditions. ROI-based fMRI analysis revealed an interaction between reward and dopamine drive manipulations, with increased BOLD activity in GPe in a high compared to low reward condition, and under risperidone compared to placebo. These results confirm the core prediction of our computational model, and provide a new perspective on neural dynamics in the BG and their effects on motor selection and cognitive disorders
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Realization and efficiency evaluation of a micro-photocatalytic cell prototype for real-time blood oxygenation
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.A novel approach to blood oxygenation is presented. Microfluidic channels molded out of PDMS (using standard soft lithography techniques) work as photocatalytic cells, where the coupling of anatase titanium dioxide (TiO2) thin films and platinum electrodes, allow an electrically assisted photocatalytic reaction to produce dissolved oxygen gas from the water content of the flowing blood. The thin films were deposited onto quartz glass substrates at room temperature (300K) using reactive RF sputtering with a Ti metal target. The results of the current study, as a proof of concept, have shown that the device can generate oxygen at a rate of 4.06×10-3 mM O2/(cm2 min) and oxygenate venous blood to the oxygen saturation level of arterial blood
An objective representation of the Gaussian integers
A rig is a riNg without Negatives. We analyse the free rig on a generator x
subject to the equivalence x = 1 + x + x^2, showing that in it the non-constant
polynomials form a ring. This ring can be identified with the Gaussian
integers, which thus acquire objective meaning
Unbraiding the braided tensor product
We show that the braided tensor product algebra
of two module algebras of a quasitriangular Hopf algebra is
equal to the ordinary tensor product algebra of with a subalgebra of
isomorphic to , provided there exists a
realization of within . In other words, under this assumption we
construct a transformation of generators which `decouples' (i.e.
makes them commuting). We apply the theorem to the braided tensor product
algebras of two or more quantum group covariant quantum spaces, deformed
Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page
Inhomogeneous critical current in nanowire superconducting single-photon detectors
A superconducting thin film with uniform properties is the key to realize
nanowire superconducting single-photon detectors (SSPDs) with high performance
and high yield. To investigate the uniformity of NbN films, we introduce and
characterize simple detectors consisting of short nanowires with length ranging
from 100nm to 15{\mu}m. Our nanowires, contrary to meander SSPDs, allow probing
the homogeneity of NbN at the nanoscale. Experimental results, endorsed by a
microscopic model, show the strongly inhomogeneous nature of NbN films on the
sub-100nm scale.Comment: 10 pages, 4 figure
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