(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves

Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We then determine when both Delta and Delta^* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.Comment: 16 pages, some minor change

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

Nottingham Health Profile and Short-Form 36 Health Survey questionnaires in patients with chronic lower limb ischemia: Before and after revascularization

AbstractObjective: The purpose of this study was to compare the usefulness of the Nottingham Health Profile (NHP) and the Short-Form 36 Health Survey (SF-36) as general outcome measures after vascular intervention for lower limb ischemia with respect to patients' quality of life, on the basis of validity, reliability, and responsiveness analyses. Patients and Methods: Eighty patients, 40 with claudication and 40 with critical ischemia, were assessed before and one month after revascularization by using comparable domains of the NHP and the SF-36 questionnaires. Results: The SF-36 scores were less skewed and were distributed more homogeneously than the NHP scores. Discriminate validity results showed that NHP was better than SF-36 in discriminating among levels of ischemia with respect to pain and physical mobility. For both questionnaires, the reliability standards were satisfactory in most respects. The NHP was more responsive than the SF-36 in detecting within-patient changes. All of the NHP domains not zero at baseline were improved significantly one month after hemodynamically successful revascularization for patients with claudication, whereas patients with critical ischemia showed significant abatement of pain and improvements in physical mobility and social isolation. The SF-36 scores indicated a significant decrease in bodily pain and improvements in physical functioning and vitality for patients with claudication, and decrease in bodily pain and improvement in physical functioning for patients with critical ischemia. Conclusions: The findings indicated that both NHP and SF-36 were reliable. The SF-36 scores were less skewed than the NHP scores, whereas NHP discriminated better among levels of ischemia and was more responsive in detecting quality-of-life changes over time than SF-36 in these particular patients. (J Vasc Surg 2002;36:310-7.

The application of parameter sensitivity analysis methods to inverse simulation models

Knowledge of the sensitivity of inverse solutions to variation of parameters of a model can be very useful in making engineering design decisions. This paper describes how parameter sensitivity analysis can be carried out for inverse simulations generated through approximate transfer function inversion methods and also by the use of feedback principles. Emphasis is placed on the use of sensitivity models and the paper includes examples and a case study involving a model of an underwater vehicle. It is shown that the use of sensitivity models can provide physical understanding of inverse simulation solutions that is not directly available using parameter sensitivity analysis methods that involve parameter perturbations and response differencing

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

State transition of a non-Ohmic damping system in a corrugated plane

Anomalous transport of a particle subjected to non-Ohmic damping of the power $\delta$ in a tilted periodic potential is investigated via Monte Carlo simulation of generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locking state and the running state. Under the surrounding of sub-Ohmic damping ($0<\delta<1$), the particle should transfer into a running state from a locking state only when local minima of the potential vanish; hence the particle occurs a synchronization oscillation in its mean displacement and mean square displacement (MSD). In particular, the two motion modes are allowed to coexist in the case of super-Ohmic damping ($1<\delta<2$) for moderate driving forces, namely, where exists double centers in the velocity distribution. This induces the particle having faster diffusion, i.e., its MSD reads $= 2D^{(\delta)}_{eff} t^{\delta_{eff}}$. Our result shows that the effective power index $\delta_{\textmd{eff}}$ can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture effect of the two motion modes also leads to a breakdown of hysteresis loop of the mobility.Comment: 7 pages,7 figure

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