On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator

The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal form, also known as Jacobi matrix form. This Jacobi matrix structure involves a continued fraction representation for the inverse of the Green's matrix. The continued fraction can be transformed to a ratio of two $_{2}F_{1}$ hypergeometric functions. From this result we find an exact analytic formula for the matrix elements of the Green's operator of the Coulomb Hamiltonian.Comment: 8 page

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

Inter-rater reliability of the EPUAP pressure ulcer classification system using photographs

Background. Many classification systems for grading pressure ulcers are discussed in the literature. Correct identification and classification of a pressure ulcer is important for accurate reporting of the magnitude of the problem, and for timely prevention. The reliability of pressure ulcer classification systems has rarely been tested. Aims and objectives. The purpose of this paper is to examine the inter-rater reliability of classifying pressure ulcers according to the European Pressure Ulcer Advisory Panel classification system when using pressure ulcer photographs.Design. Survey was among pressure ulcer experts.Methods. Fifty-six photographs were presented to 44 pressure ulcer experts. The experts classified the lesions as normal skin, blanchable erythema, pressure ulcer (four grades) or incontinence lesion. Inter-rater reliability was calculated.Results. The multirater-Kappa for the entire group of experts was 0.80 (P < 0.001).Various groups of experts obtained comparable results. Differences in classifications are mainly limited to 1 degree of difference. Incontinence lesions are most often confused with grade 2 (blisters) and grade 3 pressure ulcers (superficial pressure ulcers).Conclusions. The inter-rater reliability of the European Pressure Ulcer Advisory Panel classification appears to be good for the assessment of photographs by experts. The difference between an incontinence lesion and a blister or a superficial pressure ulcer does not always seem clear.Relevance to clinical practice. The ability to determine correctly whether a lesion is a pressure ulcer lesion is important to assess the effectiveness of preventive measures. In addition, the ability to make a correct distinction between pressure ulcers and incontinence lesions is important as they require different preventive measures. A faulty classification leads to mistaken measures and negative results. Photographs can be used as a practice instrument to learn to discern pressure ulcers from incontinence lesions and to get to know the different grades of pressure ulcers. The Pressure Ulcer Classification software package has been developed to facilitate learning

Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries

We show that second-order superintegrable systems in two-dimensional and three-dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separation of variables, and demonstrate the increased insight into the structure of such problems provided by superintegrability. A principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable. Most past separation of variables treatments of QES problems via partial differential equations have only incorporated separability, not multiseparability. Also, we propose another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schrödinger equation can be expressed in terms of hypergeometric functions mFn and is QES if the Schrödinger equation admits polynomial solutions with coefficients necessarily satisfying a three-term or higher order of recurrence relations. In three dimensions we give an example of a system that is QES in one set of separable coordinates, but is not ES in any other separable coordinates. This example encompasses Ushveridze's tenth-order polynomial QES problem in one set of separable coordinates and also leads to a fourth-order polynomial QES problem in another separable coordinate set

Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\alpha$ particles.Comment: 7 pages, 4 ps figures, revised versio

Densities of States, Moments, and Maximally Broken Time-Reversal Symmetry

Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic limit point-wise in energy with increasing numbers of moments. In this work the moment problem is further constrained by minimal lifetimes or maximal breaking of time-reversal symmetry, to yield approximate densities of states with point-wise macroscopic limits. This is applied numerically to models with one and two finite bands with various singularities, as well as to a model with infinite band-width, and the results are compared with the maximum entropy approximation where possible.Comment: Accepted for publication in Physical Review

Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions

A three-body scattering process in the presence of Coulomb interaction can be decomposed formally into a two-body single channel, a two-body multichannel and a genuine three-body scattering. The corresponding integral equations are coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve them by applying the Coulomb-Sturmian separable expansion method. We present elastic scattering and reaction cross sections of the $e^++H$ system both below and above the $H(n=2)$ threshold. We found excellent agreements with previous calculations in most cases.Comment: 12 pages, 3 figure

Expression profile of the N-myc Downstream Regulated Gene 2 (NDRG2) in human cancers with focus on breast cancer

<p>Abstract</p> <p>Background</p> <p>Several studies have shown that <it>NDRG2 </it>mRNA is down-regulated or undetectable in various human cancers and cancer cell-lines. Although the function of <it>NDRG2 </it>is currently unknown, high <it>NDRG2 </it>expression correlates with improved prognosis in high-grade gliomas, gastric cancer and hepatocellular carcinomas. Furthermore, <it>in vitro </it>studies have revealed that over-expression of NDRG2 in cell-lines causes a significant reduction in their growth. The aim of this study was to examine levels of <it>NDRG2 </it>mRNA in several human cancers, with focus on breast cancer, by examining affected and normal tissue.</p> <p>Methods</p> <p>By labelling a human Cancer Profiling Array with a radioactive probe against <it>NDRG2</it>, we evaluated the level of <it>NDRG2 </it>mRNA in 154 paired normal and tumor samples encompassing 19 different human cancers. Furthermore, we used quantitative real-time RT-PCR to quantify the levels of <it>NDRG2 </it>and <it>MYC </it>mRNA in thyroid gland cancer and breast cancer, using a distinct set of normal and tumor samples.</p> <p>Results</p> <p>From the Cancer Profiling Array, we saw that the level of <it>NDRG2 </it>mRNA was reduced by at least 2-fold in almost a third of the tumor samples, compared to the normal counterpart, and we observed a marked decreased level in colon, cervix, thyroid gland and testis. However, a Benjamini-Hochberg correction showed that none of the tissues showed a significant reduction in <it>NDRG2 </it>mRNA expression in tumor tissue compared to normal tissue. Using quantitative RT-PCR, we observed a significant reduction in the level of <it>NDRG2 </it>mRNA in a distinct set of tumor samples from both thyroid gland cancer (p = 0.02) and breast cancer (p = 0.004), compared with normal tissue. <it>MYC </it>mRNA was not significantly altered in breast cancer or in thyroid gland cancer, compared with normal tissue. In thyroid gland, no correlation was found between <it>MYC </it>and <it>NDRG2 </it>mRNA levels, but in breast tissue we found a weakly significant correlation with a positive r-value in both normal and tumor tissues, suggesting that <it>MYC </it>and <it>NDRG2 </it>mRNA are regulated together.</p> <p>Conclusion</p> <p>Expression of <it>NDRG2 </it>mRNA is reduced in many different human cancers. Using quantitative RT-PCR, we have verified a reduction in thyroid cancer and shown, for the first time, that <it>NDRG2 </it>mRNA is statistically significantly down-regulated in breast cancer. Furthermore, our observations indicate that other tissues such as cervix and testis can have lower levels of <it>NDRG2 </it>mRNA in tumor tissue compared to normal tissue.</p