PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x real. We will give a complete characterization of three different classes of operators associated with the differential expression H: The class of all self-adjoint (Hermitian) operators, the class of all PT symmetric operators and the class of all P-self-adjoint operators. Surprisingly, some of the PT symmetric operators associated to this expression have no resolvent set

Photometric and spectroscopic variations of the Be star HD 112999

Be objects are stars of B spectral type showing lines of the Balmer series in emission. The presence of these lines is attributed to the existence of an extended envelope, disk type, around them. Some stars are observed in both the Be and normal B-type spectroscopic states and they are known as transient Be stars. In this paper we show the analysis carried out on a new possible transient Be star, labelled HD 112999, using spectroscopic optical observations and photometric data.Comment: 10 pages, 5 figures, accepted for publication in IBV

Rhodium metalloinsertor binding generates a lesion with selective cytotoxicity for mismatch repair-deficient cells

The DNA mismatch repair (MMR) pathway recognizes and repairs errors in base pairing and acts to maintain genome stability. Cancers that have lost MMR function are common and comprise an important clinical subtype that is resistant to many standard of care chemotherapeutics such as cisplatin. We have identified a family of rhodium metalloinsertors that bind DNA mismatches with high specificity and are preferentially cytotoxic to MMR-deficient cells. Here, we characterize the cellular mechanism of action of the most potent and selective complex in this family, [Rh(chrysi)(phen)(PPO)]^(2+) (Rh-PPO). We find that Rh-PPO binding induces a lesion that triggers the DNA damage response (DDR). DDR activation results in cell-cycle blockade and inhibition of DNA replication and transcription. Significantly, the lesion induced by Rh-PPO is not repaired in MMR-deficient cells, resulting in selective cytotoxicity. The Rh-PPO mechanism is reminiscent of DNA repair enzymes that displace mismatched bases, and is differentiated from other DNA-targeted chemotherapeutics such as cisplatin by its potency, cellular mechanism, and selectivity for MMR-deficient cells

Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

Self-reported clinical pharmacy service provision in Austria: an analysis of both the community and hospital pharmacy sector: a national study.

Background: With expansion of more advanced clinical roles for pharmacists we need to be mindful that the extent to which clinical pharmacy services (CPS) are implemented varies from one country to another. To date no comprehensive assessment of number and types of CPS provided by either community or hospital pharmacies in Austria exists. Objective: To analyse and describe the number and types of CPS provided in both community and hospital pharmacies, as well as the level of clinical pharmacy education of pharmacists across Austria. Setting: Austrian community and hospital pharmacies. Method: An electronic questionnaire to determine number and types of CPS provided was issued to all chief pharmacists at all community (n=1365) and hospital pharmacies (n=40) across Austria. Besides current and future CPS provision, education and training provision were determined. Main outcome measure: Extent of and attitude towards CPS in Austria. Results: Response rates to the surveys were 19.1% (n=261/1365) in community and 92.5% (n=37/40) in hospital pharmacies. 59.0% and 89.2% of community and hospital pharmacies, respectively, indicated that CPS provision has increased substantially in the past 10 years. 51.0% of community pharmacies reported to provide a medication review service, while 97.3% of hospitals provide a range of CPS. Only 18.0% of community pharmacies offer services other than medication review services at dispensing. Binary regressions show that provision of already established medication management is a predictor for the willingness of community pharmacists to extend the range of CPS (p [less than] 0.01), while completed training in the area of clinical pharmacy is not (p [greater than] 0.05). More hospital than community pharmacists have postgraduate education in clinical pharmacy (17.4% vs 6.5%). A desire to complete postgraduate education was shown by 28.3% of community and 14.7% of hospital pharmacists. Lack of time, inadequate remuneration, lack of resources and poor relationship between pharmacists and physicians were highlighted as barriers. Conclusion: Both community and hospital pharmacists show strong willingness to expand their CPS provision and will need continued support, such as improved legislative structures, more supportive resources and practice focused training opportunities, to further these services

Essential self-adjointness in one-loop quantum cosmology

The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which corrects section

Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators

We investigate the eigenvalues of perturbed spherical Schr\"odinger operators under the assumption that the perturbation $q(x)$ satisfies $x q(x) \in L^1(0,1)$. We show that the square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues up to an decaying error depending on the behavior of $q(x)$ near $x=0$. Furthermore, we provide sets of spectral data which uniquely determine $q(x)$.Comment: 14 page

Bound states in point-interaction star-graphs

We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a fixed spacing between the interaction sites. We prove that the essential spectrum of this system is the same as that of the infinite straight "polymer", but in addition there are isolated eigenvalues unless N=2 and the graph is a straight line. We also show that the system has many strongly bound states if at least one of the angles between the star arms is small enough. Examples of eigenfunctions and eigenvalues are computed numerically.Comment: 17 pages, LaTeX 2e with 9 eps figure

Green's function for a Schroedinger operator and some related summation formulas

Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem that arises in connection with integral equations. The new approach introduced in this paper may be useful for the construction of wider classes of generating function.Comment: 14 page