Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.Comment: 55 pages, 53 reference

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Differential Geometry of Quantum States, Observables and Evolution

The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the relevant geometrical structures and their associated algebraic properties are highlighted, and the Qubit example is thoroughly discussed.Comment: 20 pages, comments are welcome

A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Buprenorphine maintenance subjects are hyperalgesic and have no antinociceptive response to a very high morphine dose

Objective. Acute pain management in opioiddependent persons is complicated because of tolerance and opioid-induced hyperalgesia. Very high doses of morphine are ineffective in overcoming opioid-induced hyperalgesia and providing antinociception to methadone-maintained patients in an experimental setting. Whether the same occurs in buprenorphine-maintained subjects is unknown. Design. Randomized double-blind placebo-controlled. Subjects were tested on two occasions, at least five days apart, once with intravenous morphine and once with intravenous saline. Subjects were tested at about the time of putative trough plasma buprenorphine concentrations. Setting. Ambulatory. Subjects. Twelve buprenorphine-maintained subjects: once daily sublingual dose (range 5 2–22 mg); no dose change for 1.5–12 months. Ten healthy controls. Methods. Intravenous morphine bolus and infusions administered over two hours to achieve two separate pseudo-steady-state plasma concentrations one hour apart. Pain tolerance was assessed by application of nociceptive stimuli (cold pressor [seconds] and electrical stimulation [volts]). Ten blood samples were collected for assay of plasma morphine, buprenorphine, and norbuprenorphine concentrations until three hours after the end of the last infusion; pain tolerance and respiration rate were measured to coincide with blood sampling times. Results. Cold pressor responses (seconds): baseline: control 34 6 6 vs buprenorphine 17 6 2 (P 5 0.009); morphine infusion-end: control 52 6 11(P 5 0.04), buprenorphine 17 6 2 (P> 0.5); electrical stimulation responses (volts): baseline: control 65 6 6 vs buprenorphine 53 6 5 (P 5 0.13); infusion-end: control 74 6 5 (P 5 0.007), buprenorphine 53 6 5 (P> 0.98). Respiratory rate (breaths per minute): baseline: control 17 vs buprenorphine 14 (P 5 0.03); infusion-end: control 15 (P 5 0.09), buprenorphine 12 (P< 0.01). Infusion-end plasma morphine concentrations (ng/mL): control 23 6 1, buprenorphine 136 6 10. Conclusions. Buprenorphine subjects, compared with controls, were hyperalgesic (cold pressor test), did not experience antinociception, despite high plasma morphine concentrations, and experienced respiratory depression. Clinical implications are discussed.Peter Athanasos, Walter Ling, Felix Bochner, Jason M. White, and Andrew A. Somogy

Cross helicity and turbulent magnetic diffusivity in the solar convection zone

In a density-stratified turbulent medium the cross helicity is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations we find the cross helicity and the mean vertical magnetic field anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface exceeds the value of 1 Gauss km/s. Its sign is anti-correlated with that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.Comment: 9 pages, 2 figures, submitted to Solar Physic

Quality of life and symptom assessment in randomized clinical trials of bladder cancer: A systematic review

OBJECTIVES: Patient-reported outcomes (PRO) help patients, caretakers, clinicians, and policy makers make informed decisions regarding treatment effectiveness. Our objective was to assess the quality of PRO reporting and methodological strengths and weaknesses in randomized controlled trials (RCT) in bladder cancer.; METHODS: A systematic literature search of bladder cancer RCT published between January 2004 and March 2014 was performed. Relevant studies were evaluated using a predetermined extraction form that included trial demographics, clinical and PRO characteristics, and standards of PRO reporting based on recommendations of the International Society for Quality of Life Research.; RESULTS: In total, 9 RCTs enrolling 1,237 patients were evaluated. All studies were in patients with nonmetastatic disease. In 5 RCTs, a PRO was the primary end point. Most RCTs did not report the mode of administration of the PRO instrument or the methods of collecting data. No RCT addressed the statistical approaches for missing data.; CONCLUSIONS: We found that few RCTs in bladder cancer report PRO as an outcome. Efforts to expand PRO reporting to more RCTs and improve the quality of PRO reporting according to recognized standards are necessary for facilitating clinical decision making. Copyright 2015 Elsevier Inc. All rights reserved

A consideration of the challenges involved in supervising international masters students

This paper explores the challenges facing supervisors of international postgraduate students at the dissertation stage of the masters programme. The central problems of time pressure, language difficulties, a lack of critical analysis and a prevalence of personal problems among international students are discussed. This paper makes recommendations for the improvement of language and critical thinking skills, and questions the future policy of language requirements at HE for international Masters students

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ