Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

How Entrepreneurs Become Skilled Cultural Operators

Cultural entrepreneurship and symbolic management perspectives portray entrepreneurs as skilled cultural operators and often assume them to be capable from the outset to purposefully use ‘cultural resources' in order to motivate resource-holding audiences to support their new ventures. We problematize this premise and develop a model of how entrepreneurs become skilful cultural operators and develop the cultural competences necessary for creating and growing their ventures. The model is grounded in a case study of an entrepreneur who set up shop and sought to acquire resources in a culturally unfamiliar setting. Our model proposes that two adaptive sensemaking processes - approval-driven sensemaking and autonomy-driven sensemaking - jointly facilitate the gradual development of cultural competences. These processes jointly enable entrepreneurs to gain cultural awareness and calibrate their symbolic enactments. Specifically, while approval-driven sensemaking facilitates recognizing cultural resources to symbolically couple a venture's identity claims more tightly with the cultural frames of targeted audiences and gain legitimate distinctiveness, autonomy-driven sensemaking enables recognizing cultural constraints and more effective symbolic decoupling to shield the venture from constraining cultural frames and defend the venture's autonomy and resources. We conclude the paper with a discussion of the theoretical implications of our study for cultural entrepreneurship and symbolic management research.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Alkenone UK37 measured in the upper water column at pump stations CariacoTrench, Peru and Vertex

A series of long-chain (C37, C38, C39), primarily di and tri-unsaturated methyl and ethyl ketones, first identified in sediments from Walvis Ridge off West Africa and from Black Sea (de Leeuw et al., 1979), has been found in marine sediments throughout the world (Brassell et al., 1986 doi:10.1038/320129a0). The marine coccolithophorid Emiliania huxleyi and members of the class Prymnesiophyceae are now the recognized sources of these compounds (Volkman et al., 1979; Marlowe, et al., 1984). Experiments with laboratory cultures of algae showed the degree of unsaturation in the ketone seris biosynthesized depends on growth temperature (Brassell et al., 1986; Marlowe, 1984), a physiological respons observed for classical membrane lipids (vanDeenen et al., 1972). Brassell and co-workers (Brassell et al., 198; Brassell et al., 1986b) thus proposed that systematic fluctuations in the unsaturation of these alkenones noted down-core in sediments from the Kane Gap region of the north-east tropical Atlantic Ocean and correlated with glacial-interglacial cycles provide an organic geochemical measure of past sea-surface water temperatures. Using laboratory cultures of E. huxleyi, we have calibrated changes in the unsaturation pattern of the long-chain ketone series versus growth temperature. The calibration curve is linear and accurtely predicts unsuturation patterns observed in natural particulate materials collected from oceanic waters of known temperature. We present evidence supporting the proposed paleotemperature hypothesis (Brassell et al., 1986, Brassel et al., 1986b) and suggesting absolute 'sea-surface temperatures' for a given oceanic location can be estimated from an analysis of long-chain ketone compositions preserved in glacial and interglacial horizons of deep-sea sediment cores.

What motivates female operators to enter the garment industry in Pakistan in the post-MFA period?

Pakistan's knitwear exports had been struggling since the quota phase-out until 2009. A particular feature of Pakistan's garment industry is that hiring more male sewing operators at piece rates. Recently, a few surviving knitwear factories have adopted a strategy of shifting from male piece-rate operators to salaried female operators. In Pakistan, female participation in general workforce is very limited and hiring salaried female operators requires management effort and expertise. However, even in the factories with such management skills, household factors prevent females from working outside because Pakistani culture disrespects women working in factories. Our survey reveals that financial motives compel female household members to work outside their homes and that female operators contribute substantially to their households' finances.

A new DSATUR-based algorithm for exact vertex coloring

This paper describes a new exact algorithm PASS for the vertex coloring problem based on the well known DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate vertex to color, breaking ties by maximum degree w.r.t. uncolored vertices. Later Sewell introduced a new tiebreaking strategy, which evaluated available colors for each vertex explicitly. PASS differs from Sewell in that it restricts its application to a particular set of vertices. Overall performance is improved when the new strategy is applied selectively instead of at every step. The paper also reports systematic experiments over 1500 random graphs and a subset of the DIMACS color benchmark.

Asymptotically Toeplitz Hessenberg Operators and the Rieman mapping

In a recent work the authors have established a relation between the limits of the elements of the diagonals of the Hessenberg matrix D associated with a regular measure, whenever those limits exist, and the coe?cients of the Laurent series expansion of the Riemann mapping ?(z) of the support supp(?), when this is a Jordan arc or a connected nite union of Jordan arcs in the complex plane C. We extend here this result using asymptotic Toeplitz operator properties of the Hessenberg matriz.

Coronary Artery Tracking in 3D Cardiac CT Images Using Local Morphological Reconstruction Operators

Automatic segmentation and tracking of the coronary artery tree from Cardiac Multislice-CT images is an important goal to improve the diagnosis and treatment of coronary artery disease. This paper presents a semi-automatic algorithm (one input point per vessel) based on morphological grayscale local reconstructions in 3D images devoted to the extraction of the coronary artery tree. The algorithm has been evaluated in the framework of the Coronary Artery Tracking Challenge 2008 [1], obtaining consistent results in overlapping measurements (a mean of 70% of the vessel well tracked). Poor results in accuracy measurements suggest that future work should refine the centerline extraction. The algorithm can be efficiently implemented and its general strategy can be easily extrapolated to a completely automated centerline extraction or to a user interactive vessel extraction

Solving the minimum vertex floodlight problem with hybrid metaheuristics

In this paper we propose four approximation algorithms (metaheuristic based), for the Minimum Vertex Floodlight Set problem. Urrutia et al. [9] solved the combinatorial problem, although it is strongly believed that the algorithmic problem is NP-hard. We conclude that, on average, the minimum number of vertex floodlights needed to illuminate a orthogonal polygon with n vertices is n/4,29.

Spatio-temporal filtering with morphological operators for robust cell migration estimation in "in-vivo" images

The understanding of the embryogenesis in living systems requires reliable quantitative analysis of the cell migration throughout all the stages of development. This is a major challenge of the "in-toto" reconstruction based on different modalities of "in-vivo" imaging techniques -spatio-temporal resolution and image artifacts and noise. Several methods for cell tracking are available, but expensive manual interaction -time and human resources- is always required to enforce coherence. Because of this limitation it is necessary to restrict the experiments or assume an uncontrolled error rate. Is it possible to obtain automated reliable measurements of migration? can we provide a seed for biologists to complete cell lineages efficiently? We propose a filtering technique that considers trajectories as spatio-temporal connected structures that prunes out those that might introduce noise and false positives by using multi-dimensional morphological operators.

Aircraft flight trajectory deviation in the standard instrument departures. Operators penalties.

In the recent years many problems are emerging due to the aircraft noise on the airport surrounding areas. The solution to this problem is not easy considering that the neighbourhood asks for the reduction of the number of aircraft operations and the airlines ask for a growing demand in the number of operations in the major airports. So the airport and regulatory authorities try to get a solution imposing a fine to the aircraft which its actual trajectory differs from the nominal one more than a lateral deviation. But, which is the value of this deviation?. The current situation is that many operators have to pay a lot of money for exceeding a deviation which has been established without operational criteria. This paper presents the results of a research program which is being carried out by the authors which aims to determine the "delta" deviation to be used for this purpose. In addition it is proposed a customized method per SID and per airport to be used for determining the maximum allowed lateral deviation by which if the aircraft is within it, then none fine will be imposed.