Distributional Borel Summability of Odd Anharmonic Oscillators

It is proved that the divergent Rayleigh-Schrodinger perturbation expansions for the eigenvalues of any odd anharmonic oscillator are Borel summable in the distributional sense to the resonances naturally associated with the system

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Convergence Radii for Eigenvalues of Tri--diagonal Matrices

Consider a family of infinite tri--diagonal matrices of the form $L+ zB,$ where the matrix $L$ is diagonal with entries $L_{kk}= k^2,$ and the matrix $B$ is off--diagonal, with nonzero entries $B_{k,{k+1}}=B_{{k+1},k}= k^\alpha, 0 \leq \alpha < 2.$ The spectrum of $L+ zB$ is discrete. For small $|z|$ the $n$-th eigenvalue $E_n (z), E_n (0) = n^2,$ is a well--defined analytic function. Let $R_n$ be the convergence radius of its Taylor's series about $z= 0.$ It is proved that $$ R_n \leq C(\alpha) n^{2-\alpha} \quad \text{if} 0 \leq \alpha <11/6.$

Bender-Wu Formula and the Stark Effect in Hydrogen

We discuss a close connection between the formula of Banks, Bender, and Wu for the asymptotics of the Rayleigh-Schrödinger coefficients of the two-dimensional rotationally symmetric anharmonic oscillator and the behavior of resonances of the hydrogen Stark problem in two regimes: small field (Oppenheimer's formula) and large field (where we obtain the new results arg E → −π/3, ∣E∣ ∼α[F(lnF)^(2/3) for F, the electric field strength, going to infinity). We also announce a rigorous proof of Bender-Wu-type formulas

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

First Multicharged Ion Irradiation Results from the CUEBIT Facility at Clemson University

A new electron beam ion trap (EBIT) based ion source and beamline were recently commissioned at Clemson University to produce decelerated beams of multi- to highly-charged ions for surface and materials physics research. This user facility is the first installation of a DREEBIT-designedsuperconducting trap and ion source (EBIS-SC) in the U.S. and includes custom-designed target preparation and irradiation setups. An overview of the source, beamline, and other facilities as well as results from first measurements on irradiated targets are discussed here. Results include extracted charge state distributions and first data on a series of irradiated metal-oxide-semiconductor (MOS) device targets. For the MOS devices, we show that voltage-dependent capacitance can serve as a record of theelectronic component of ion stopping power for an irradiated, encapsulated oxide target

Application of inverse weighting analysis to assess the association of youth perceptions with the age of initiation of tobacco products

IntroductionTo examine if perceptions of harmfulness and addictiveness of hookah and cigarettes impact the age of initiation of hookah and cigarettes, respectively, among US youth. Youth (12-17 years old) users and never users of hookah and cigarettes during their first wave of PATH participation were analyzed by each tobacco product (TP) independently. The effect of perceptions of (i) harmfulness and (ii) addictiveness at the first wave of PATH participation on the age of initiation of ever use of hookah was estimated using interval-censoring Cox proportional hazards models.MethodsUsers and never users of hookah at their first wave of PATH participation were balanced by multiplying the sampling weight and the 100 balance repeated replicate weights with the inverse probability weight (IPW). The IPW was based on the probability of being a user in their first wave of PATH participation. A Fay’s factor of 0.3 was included for variance estimation. Crude hazard ratios (HR) and 95% confidence intervals (CIs) are reported. A similar process was repeated for cigarettes.ResultsCompared to youth who perceived each TP as “a lot of harm”, youth who reported perceived “some harm” had younger ages of initiation of these tobacco products, HR: 2.53 (95% CI: 2.87-4.34) for hookah and HR: 2.35 (95% CI: 2.10-2.62) for cigarettes. Similarly, youth who perceived each TP as “no/little harm” had an earlier age of initiation of these TPs compared to those who perceived them as “a lot of harm”, with an HR: 2.23 (95% CI: 1.82, 2.71) for hookah and an HR: 1.85 (95% CI: 1.72, 1.98) for cigarettes. Compared to youth who reported each TP as “somewhat/very likely” as their perception of addictiveness, youth who reported “neither likely nor unlikely” and “very/somewhat unlikely” as their perception of addictiveness of hookah had an older age of initiation, with an HR: 0.75 (95% CI: 0.67-0.83) and an HR: 0.55 (95% CI: 0.47, 0.63) respectively.DiscussionPerceptions of the harmfulness and addictiveness of these tobacco products (TPs) should be addressed in education campaigns for youth to prevent early ages of initiation of cigarettes and hookah

Importance of clinical measures of ischemia in the prognosis of patients with documented coronary artery disease

AbstractTo examine the value of clinical measures of ischemia for stratifying prognosis, 5,886 consecutive patients who had symptomatic significant (≥75% stenosis) coronary artery disease were studied. Using the Cox regression model in a randomly selected half of the patients, the prognostically independent clinical variables were weighted and arranged into a simple angina score: angina score = angina course × (1 + daily angina frequency) + ST-T changes, where angina course was equal to 3 if unstable or variant angina was present, 2 if the patient's angina was progressive with nocturnal episodes, 1 if it was progressive without nocturnal symptoms and 0 if it was stable; 6 points were added for the presence of “ischemic” ST-T changes. This angina score was then validated in an independent patient sample.The score was a more powerful predictor of prognosis than was any individual anginal descriptor. Furthermore, the angina score added significant independent prognostic information to the patient's age, sex, coronary anatomy and left ventricular function. Patients with three vessel disease and a normal ventricle (n = 1,233) had a 2 year infarction-free survival rate of 90% with an angina score of 0 and a 68% survival rate with an angina score ≥9. With an ejection fraction <50% and three vessel disease (n = 1,116), the corresponding infarction-free survival figures were 76 and 56%. Thus, a careful summarization of clinical markers of ischemia in the form of an angina score can provide a powerful prognostic tool and may aid clinicians in identifying high risk patients who are candidates for aggressive therapeutic interventions

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Clinical judgement and therapeutic decision making

AbstractClinical decision making is under increased scrutiny due to concerns about the cost and quality of medical care. Variability in physician decision making is common, in part because of deficiencies in the knowledge base, but also due to the difference in physicians' approaches to clinical problem solving. Evaluation of patient prognosis is a critical factor in the selection of therapy, and careful attention to methodology is essential to provide reliable information.Randomized controlled clinical trials provide the most solid basis for the establishment of broad therapeutic principles. Because randomized studies cannot be performed to address every question, observational studies will continue to play a complementary role in the evaluation of therapy. Randomized studies in progress, meta analyses of existing data, and increased use of administrative and collaborative clinical data bases will improve the knowledge base for decision making in the future