The transformation of irreducible tensor operators under spherical functions

The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the spherical coordinates of vector in the fixed and rotated coordinate systems are determined. A new way of calculation of the irreducible coupled tensor product matrix elements is suggested. As an example, the proposed technique is applied for the matrix element construction for two electrons in a field of a fixed nucleus.Comment: To appear in Int. J. Theor. Phy

Mathematical Aspects of Vacuum Energy on Quantum Graphs

We use quantum graphs as a model to study various mathematical aspects of the vacuum energy, such as convergence of periodic path expansions, consistency among different methods (trace formulae versus method of images) and the possible connection with the underlying classical dynamics. We derive an expansion for the vacuum energy in terms of periodic paths on the graph and prove its convergence and smooth dependence on the bond lengths of the graph. For an important special case of graphs with equal bond lengths, we derive a simpler explicit formula. The main results are derived using the trace formula. We also discuss an alternative approach using the method of images and prove that the results are consistent. This may have important consequences for other systems, since the method of images, unlike the trace formula, includes a sum over special ``bounce paths''. We succeed in showing that in our model bounce paths do not contribute to the vacuum energy. Finally, we discuss the proposed possible link between the magnitude of the vacuum energy and the type (chaotic vs. integrable) of the underlying classical dynamics. Within a random matrix model we calculate the variance of the vacuum energy over several ensembles and find evidence that the level repulsion leads to suppression of the vacuum energy.Comment: Fixed several typos, explain the use of random matrices in Section

N-body simulations of gravitational dynamics

We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development. We briefly touch upon the history of N-body simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu

Does bleeding affect patient‐reported outcome measures in patients with myelodysplasia or hematologic malignancies: a systematic review

Background Relatively minor bleeding (e.g., bruising and/or petechiae) may cause patient distress. This systematic review's objective was to assess whether bleeding affects health‐related quality of life (HRQoL) or illness perceptions or representations (IPs) in patients with hematologic malignancies or myelodysplasia (MDS). Study Design and Methods We searched, in full, 12 electronic databases (including CENTRAL, MEDLINE, and EMBASE) up to January 7, 2013, for eligible randomized controlled trials (RCTs), prospective cohort studies, and cross‐sectional studies. Results A total of 6247 studies were initially identified; 5945 studies were excluded on the basis of the abstract. A total of 302 full‐text articles were evaluated independently by two reviewers; of these, six studies within seven citations were eligible for inclusion. Two studies are still in progress, four studies within five citations were included in this review (one RCT, one prospective observational study, one interview study, and one Web‐based survey). None of the included studies were designed to assess the impact bleeding had on HRQoL or IPs. The Web‐based survey and observational study used two new patient‐reported outcome scales which specifically assessed patient distress or concern due to bleeding. The majority of patients within these two studies either did not experience bleeding or did not have severe thrombocytopenia. Conclusion There is insufficient evidence to demonstrate whether bleeding is a significant clinical problem that affects patients' HRQoL or IPs in either patients with MDS or patients with hematologic malignancies. Rigorously designed studies to assess the scale of this problem in both of these groups of patients are required

Neonatal levels of plasma thyroxine in male and female calves fed a colostrum or immunoglobulin diet or fasted for the first 28 hours of life

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Neonatal levels of plasma thyroxine in male and female calves fed a colostrum or immunoglobulin diet or fasted for the first 28 hours of life

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