Analytically unramified one-dimensional semilocal rings and their value semigroups

AbstractIn a one-dimensional local ring R with finite integral closure each nonzerodivisor has a value in Nd, where d is the number of maximal ideals in the integral closure. The set of values constitutes a semigroup, the value semigroup of R. We investigate the connection between the value semigroup and the ring. There is a particularly close connection for some classes of rings, e.g. Gorenstein rings, Arf rings, and rings of small multiplicity. In many respects, the Arf rings and the Gorenstein rings turn out to be opposite extremes. We give applications to overrings, intersection numbers, and multiplicity sequences in the blow-up sequences studied by Lipman

A good leaf order on simplicial trees

Using the existence of a good leaf in every simplicial tree, we order the facets of a simplicial tree in order to find combinatorial information about the Betti numbers of its facet ideal. Applications include an Eliahou-Kervaire splitting of the ideal, as well as a refinement of a recursive formula of H\`a and Van Tuyl for computing the graded Betti numbers of simplicial trees.Comment: 17 pages, to appear; Connections Between Algebra and Geometry, Birkhauser volume (2013

Using the Uncharged Kerr Black Hole as a Gravitational Mirror

We extend the study of the possibility to use the Schwarzschild black hole as a gravitational mirror to the more general case of an uncharged Kerr black hole. We use the null geodesic equation in the equatorial plane to prove a theorem concerning the conditions the impact parameter has to satisfy if there shall exist boomerang photons. We derive an equation for these boomerang photons and an equation for the emission angle. Finally, the radial null geodesic equation is integrated numerically in order to illustrate boomerang photons.Comment: 11 pages Latex, 3 Postscript figures, uufiles to compres

Imaging a 1-electron InAs quantum dot in an InAs/InP nanowire

Nanowire heterostructures define high-quality few-electron quantum dots for nanoelectronics, spintronics and quantum information processing. We use a cooled scanning probe microscope (SPM) to image and control an InAs quantum dot in an InAs/InP nanowire, using the tip as a movable gate. Images of dot conductance vs. tip position at T = 4.2 K show concentric rings as electrons are added, starting with the first electron. The SPM can locate a dot along a nanowire and individually tune its charge, abilities that will be very useful for the control of coupled nanowire dots

Analyzing capacitance-voltage measurements of vertical wrapped-gated nanowires

The capacitance of arrays of vertical wrapped-gate InAs nanowires are analyzed. With the help of a Poisson-Schr"odinger solver, information about the doping density can be obtained directly. Further features in the measured capacitance-voltage characteristics can be attributed to the presence of surface states as well as the coexistence of electrons and holes in the wire. For both scenarios, quantitative estimates are provided. It is furthermore shown that the difference between the actual capacitance and the geometrical limit is quite large, and depends strongly on the nanowire material.Comment: 15 pages, 6 Figures included, to appear in Nanotechnolog

Real-time velocity optimization to minimize energy use in passenger vehicles

Energy use in internal combustion engine passenger vehicles contributes directly to CO 2 emissions and fuel consumption, as well as producing a number of air pollutants. Optimizing the vehicle velocity by utilising upcoming road information is an opportunity to minimize vehicle energy use without requiring mechanical design changes. Dynamic programming is capable of such an optimization task and is shown in simulation to produce fuel savings, on average 12%, compared to real driving data; however, in this paper it is also applied in real time on a Raspberry Pi, a low cost miniature computer, in situ in a vehicle. A test drive was undertaken with driver feedback being provided by a dynamic programming algorithm, and the results are compared to a simulated intelligent cruise control system that can follow the algorithm results precisely. An 8% reduction in fuel with no loss in time is reported compared to the test driver

Representation theory of super Yang-Mills algebras

We study in this article the representation theory of a family of super algebras, called the \emph{super Yang-Mills algebras}, by exploiting the Kirillov orbit method \textit{\`a la Dixmier} for nilpotent super Lie algebras. These super algebras are a generalization of the so-called \emph{Yang-Mills algebras}, introduced by A. Connes and M. Dubois-Violette in \cite{CD02}, but in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras \Cliff_{q}(k) \otimes A_{p}(k), for $p \geq 3$, or $p = 2$ and $q \geq 2$, appear as a quotient of all super Yang-Mills algebras, for $n \geq 3$ and $s \geq 1$. This provides thus a family of representations of the super Yang-Mills algebras

Feedback methods for inverse simulation of dynamic models for engineering systems applications

Inverse simulation is a form of inverse modelling in which computer simulation methods are used to find the time histories of input variables that, for a given model, match a set of required output responses. Conventional inverse simulation methods for dynamic models are computationally intensive and can present difficulties for high-speed applications. This paper includes a review of established methods of inverse simulation,giving some emphasis to iterative techniques that were first developed for aeronautical applications. It goes on to discuss the application of a different approach which is based on feedback principles. This feedback method is suitable for a wide range of linear and nonlinear dynamic models and involves two distinct stages. The first stage involves design of a feedback loop around the given simulation model and, in the second stage, that closed-loop system is used for inversion of the model. Issues of robustness within closed-loop systems used in inverse simulation are not significant as there are no plant uncertainties or external disturbances. Thus the process is simpler than that required for the development of a control system of equivalent complexity. Engineering applications of this feedback approach to inverse simulation are described through case studies that put particular emphasis on nonlinear and multi-input multi-output models

On the ubiquity of trivial torsion on elliptic curves

The purpose of this paper is to give a "down--to--earth" proof of the well--known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion

Numerical semigroups with large embedding dimension satisfy Wilf's conjecture

We give an affirmative answer to Wilf's conjecture for numerical semigroups satisfying 2 \nu \geq m, where \nu and m are respectively the embedding dimension and the multiplicity of a semigroup. The conjecture is also proved when m \leq 8 and when the semigroup is generated by a generalized arithmetic sequence.Comment: 13 page