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.

Monotone Methods for Distorted Economies

No abstract available.

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.

Maximal exercise hemodynamics and risk of mortality in apparently healthy men and women

The use of exercise electrocardiography (ECG) to detect latent coronary heart disease (CHD) is discouraged in apparently healthy populations because of low sensitivity. These recommendations however, are based on the efficacy of evaluation of ischemia (ST segment changes) with little regard for other measures of cardiac function that are available during exertion. The purpose of this investigation was to determine the association of maximal exercise hemodynamic responses with risk of mortality due to all-causes, cardiovascular disease (CVD), and coronary heart disease (CHD) in apparently healthy individuals. Study participants were 20,387 men (mean age = 42.2 years) and 6,234 women (mean age = 41.9 years) patients of a preventive medicine center in Dallas, TX examined between 1971 and 1989. During an average of 8.1 years of follow-up, there were 348 deaths in men and 66 deaths in women. In men, age-adjusted all-cause death rates (per 10,000 person years) across quartiles of maximal systolic blood pressure (SBP) (low to high) were: 18.2, 16.2, 23.8, and 24.6 (p for trend $<$0.001). Corresponding rates for maximal heart rate were: 28.9, 15.9, 18.4, and 15.1 (p trend $<$0.001). After adjustment for confounding variables including age, resting systolic pressure, serum cholesterol and glucose, body mass index, smoking status, physical fitness and family history of CVD, risks (and 95% confidence interval (CI)) of all-cause mortality for quartiles of maximal SBP, relative to the lowest quartile, were: 0.96 (0.70-1.33), 1.36 (1.01-1.85), and 1.37 (0.98-1.92) for quartiles 2-4 respectively. Similar risks for maximal heart rate were: 0.61 (0.44-0.85), 0.69 (0.51-0.93), and 0.60 (0.41-0.87). No associations were noted between maximal exercise rate-pressure product mortality. Similar results were seen for risk of CVD and CHD death. In women, similar trends in age-adjusted all-cause and CVD death rates across maximal SBP and heart rate categories were observed. Sensitivity of the exercise test in predicting mortality was enhanced when ECG results were evaluated together with maximal exercise SBP or heart rate with a concomitant decrease in specificity. Positive predictive values were not improved. The efficacy of the exercise test in predicting mortality in apparently healthy men and women was not enhanced by using maximal exercise hemodynamic responses. These results suggest that an exaggerated systolic blood pressure or an attenuated heart rate response to maximal exercise are risk factors for mortality in apparently healthy individuals. ^