Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.Comment: 20 page

The effect of aminolevulinic acid photodynamic therapy on microcomedones and macrocomedones

Background: Photodynamic therapy (PDT) with aminolevulinic acid (ALA) has been shown to be an effective treatment for acne. However, the effect of ALA PDT on comedo formation has never been objectively evaluated. Cyanoacrylate follicular biopsy (CFB), a noninvasive procedure, has been proposed as the most reliable tool for studying follicular casts. Objective: To determine the possible effect of ALA and red light (550-700 nm) on macro- and microcomedones in acne patients. Patients and Methods: 10 patients with mild-to-moderate facial and/or chest/back acne resistant to conventional therapies received ALA PDT at 2-week intervals in 3 sessions. The severity of acne had been estimated by a system of points, the Global Acne Grading System. The patients underwent PDT utilizing ALA 10% (face) or 15% (back/chest) and red light (15 J/cm2 each session). CFBs were performed. Results: Four weeks after their last PDT session, the patients showed an average global score reduction of 50%. CFBs demonstrated a reduction in the total area, the average area and the density of macrocomedones. Conclusion: The results obtained in this study using CFB evaluation demonstrate that ALA PDT exerts an action on the comedogenic phase as well

Spin dependent point potentials in one and three dimensions

We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some ``generalized boundary conditions''. For every boundary condition we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi-component solvable models.Comment: 15 pages, some misprints corrected, one example added, some references modified or adde

On the spectrum of a bent chain graph

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theo

An evaluation of the capability of data conversion of impression creep test

High temperature power plant components are now working far beyond their operative designed life. Establishing their in-service material properties has become a matter of significant concern for power generation companies. Advantages for the assessment of creep material properties may come from miniature specimen creep testing techniques, like impression creep testing method, which can be treated as a quasistatic non-destructive technique and requires a small volume of material that can be scooped from in-service critical components, and can produce reliable secondary creep data. This paper presents an overview of impression creep testing method to highlight the capability in determining the minimum creep strain rate data by use of conversion relationships that relates uniaxial creep test data and impression creep test data. Stepped-load and stepped-temperature impression creep tests are also briefly described. Furthermore, the paper presents some new impression creep test data and their correlation with uniaxial data, obtained from P91, P92 and ½CrMoV steels at different stresses and temperatures. The presented data, in terms of creep strain rate against the reference uniaxial stress, are useful for calibration of impression creep testing technique and provide further comparative results for the evaluation of the reliability of the method in determining secondary creep properties

Collagen induction therapy for the treatment of upper lip wrinkles

Upper lip wrinkles are very common and impair the quality of life of many people due to their perceived unsightly appearance. Several options are available today for their treatment. A new therapeutic option, called collagen induction therapy (CIT), seems to be effective and safe for the treatment of upper lip wrinkles. The aim of this study is to demonstrate the efficacy and safety of CIT in the treatment of upper lip wrinkles. Ten female subjects, aged 50-65 years old, with upper lip wrinkles were enrolled. Each patient was treated with a specific tool in two sessions. Using a digital camera, photographs were taken of all the patients to evaluate the depth of the wrinkles and a silicon-print technique was used to obtain a microrelief impression of the wrinkles. Data of the cutaneous casts were analyzed by computerized image analysis. Analysis of the patients' photographs, supported by the sign test, and of the degree of irregularity of the surface microrelief, supported by Fast Fourier Transform and by wrinkle image processing, showed that, after only two sessions, the wrinkles' severity grade in most patients was greatly reduced. The present study confirms CIT as an effective and safe technique to improve upper lip wrinkles

Controlling a resonant transmission across the δ′\delta'-potential: the inverse problem

Recently, the non-zero transmission of a quantum particle through the one-dimensional singular potential given in the form of the derivative of Dirac's delta function, $\lambda \delta'(x)$, with $\lambda \in \R$, being a potential strength constant, has been discussed by several authors. The transmission occurs at certain discrete values of $\lambda$ forming a resonance set ${\lambda_n}_{n=1}^\infty$. For $\lambda \notin {\lambda_n}_{n=1}^\infty$ this potential has been shown to be a perfectly reflecting wall. However, this resonant transmission takes place only in the case when the regularization of the distribution $\delta'(x)$ is constructed in a specific way. Otherwise, the $\delta'$-potential is fully non-transparent. Moreover, when the transmission is non-zero, the structure of a resonant set depends on a regularizing sequence $\Delta'_\varepsilon(x)$ that tends to $\delta'(x)$ in the sense of distributions as $\varepsilon \to 0$. Therefore, from a practical point of view, it would be interesting to have an inverse solution, i.e. for a given $\bar{\lambda} \in \R$ to construct such a regularizing sequence $\Delta'_\varepsilon(x)$ that the $\delta'$-potential at this value is transparent. If such a procedure is possible, then this value $\bar{\lambda}$ has to belong to a corresponding resonance set. The present paper is devoted to solving this problem and, as a result, the family of regularizing sequences is constructed by tuning adjustable parameters in the equations that provide a resonance transmission across the $\delta'$-potential.Comment: 21 pages, 4 figures. Corrections to the published version added; http://iopscience.iop.org/1751-8121/44/37/37530

Role of subcutaneous abdominal fat on cardiac function and proinflammatory cytokines in premenopausal obese women

The role of surgically removing subcutaneous fat by abdominoplasty on circulating inflammatory markers and myocardial dysfunction, evaluated by myocardial performance index (MPI), were investigated. Twenty volunteers submitted to the abdominoplasty (abdominoplasty group), and other 28 women treated by hypocaloric diet (diet group) were evaluated. Echocardiographic parameters of MPI, circulating levels of tumor necrosis factor (TNF)-alpha and interleukin (IL)-6, were performed at baseline and 2 months later. Compared with nonobese women, obese women had increased concentrations of TNF-alpha (P < 0.01), IL-6 (P < 0.01), and higher MPI (P < 0.02), indicating ventricular dysfunction. Subcutaneous fat concentrations of TNF-alpha and IL-6 were related to MPI impairment. After 60 days, waist-to hip ratio was significantly reduced in the abdominoplasty group. Anthropometric changes were accompanied by a significant decline in plasma concentrations of TNF-alpha and IL-6 levels as well as by significant improvements of MPI in abdominoplasty group compared with diet group. Abdominoplasty may represent a safe method for ameliorating cardiac function in obese women

High flux cold Rubidium atomic beam for strongly coupled Cavity QED

This paper presents a setup capable of producing a high-flux continuous beam of cold rubidium atoms for cavity QED experiments in the regime of strong coupling. A 2 $D^+$ MOT, loaded by rubidium getters in a dry film coated vapor cell, fed a secondary moving-molasses MOT (MM-MOT) at a rate of 1.5 x $10^{10}$ atoms/sec. The MM-MOT provided a continuous beam with tunable velocity. This beam was then directed through the waist of a 280 $\mu$m cavity resulting in a Rabi splitting of more than +/- 10 MHz. The presence of sufficient number of atoms in the cavity mode also enabled splitting in the polarization perpendicular to the input. The cavity was in the strong coupling regime, with parameters (g, $\kappa$, $\gamma$)/2$\pi$ equal to (7, 3, 6)/ 2$\pi$ MHz.Comment: Journal pape

Resonances in Models of Spin Dependent Point Interactions

In dimension $d=1,2,3$ we define a family of two-channel Hamiltonians obtained as point perturbations of the generator of the free decoupled dynamics. Within the family we choose two Hamiltonians, $\hat H_0$ and \hat H_\ve, giving rise respectively to the unperturbed and to the perturbed evolution. The Hamiltonian $\hat H_0$ does not couple the channels and has an eigenvalue embedded in the continuous spectrum. The Hamiltonian \hat H_\ve is a small perturbation, in resolvent sense, of $\hat H_0$ and exhibits a small coupling between the channels. We take advantage of the complete solvability of our model to prove with simple arguments that the embedded eigenvalue of $\hat H_0$ shifts into a resonance for \hat H_\ve. In dimension three we analyze details of the time behavior of the projection onto the region of the spectrum close to the resonance.Comment: Changes in the proof of theorem 3, few misprints corrected, 21 page