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

Propensity-matched analysis of patient-reported outcomes for neoadjuvant chemotherapy prior to radical cystectomy

© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. Purpose: To evaluate patient-reported outcomes (PROs) for bladder cancer patients undergoing neoadjuvant chemotherapy (NAC) prior to radical cystectomy (RC) using longitudinal data and propensity-matched scoring analyses. Methods: 155 patients with muscle-invasive bladder cancer scheduled for RC completed the European Organization for Research and Treatment of Cancer questionnaires, EORTC QLQ-C30, EORTC QLQ-BLM30, Fear of Recurrence Scale, Mental Health Inventory and Satisfaction with Life Scale within 4 weeks of surgery. A propensity-matched analysis was performed comparing pre-surgery PROs among 101 patients who completed NAC versus 54 patients who did not receive NAC. We also compared PROs pre- and post-chemotherapy for 16 patients who had data available for both time points. Results: In propensity-matched analysis, NAC-treated patients reported better emotional and sexual function, mental health, urinary function and fewer financial concerns compared to those that did not receive NAC. Longitudinal analysis showed increases in fatigue, nausea and appetite loss following chemotherapy. Conclusion: Propensity-matched analysis did not demonstrate a negative effect of NAC on PRO. Several positive associations of NAC were found in the propensity-matched analysis, possibly due to other confounding differences between the two groups or actual clinical benefit. Longitudinal analysis of a small number of patients found small to modest detrimental effects from NAC similar to toxicities previously reported. Our preliminary findings, along with known survival and toxicity data, should be considered in decision-making for NAC

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

Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions

This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9, Trends in Mathematics, Birkh\"auser Basel, 201

THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS

We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of self-gravitating harmonic mappings.Comment: 18 pages, latex, no figure

Dominant Topologies in Euclidean Quantum Gravity

The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according on the sign of the cosmological constant. For $\Lambda>0$, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For $\Lambda<0$, on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the contribution of each individual manifold is strongly suppressed, the ``density of topologies'' grows fast enough to overwhelm this suppression. The value $\Lambda=0$ is thus a sort of boundary between phases in the sum over topologies. I discuss some implications for the cosmological constant problem and the Hartle-Hawking wave function.Comment: 14 pages, LaTeX. Minor additions (computability, relation to ``minimal volume'' in topology); error in eqn (3.5) corrected; references added. To appear in Class. Quant. Gra

Comparing Open Radical Cystectomy and Robot-assisted Laparoscopic Radical Cystectomy: A Randomized Clinical Trial

Background: Open radical cystectomy (ORC) and urinary diversion in patients with bladder cancer (BCa) are associated with significant perioperative complication risk. Objective: To compare perioperative complications between robot-assisted radical cystectomy (RARC) and ORC techniques. Design, setting, and participants: A prospective randomized controlled trial was conducted during 2010 and 2013 in BCa patients scheduled for definitive treatment by radical cystectomy (RC), pelvic lymph node dissection (PLND), and urinary diversion. Patients were randomized to ORC/PLND or RARC/PLND, both with open urinary diversion. Patients were followed for 90 d postoperatively. Intervention: Standard ORC or RARC with PLND; all urinary diversions were performed via an open approach. Outcome measurements and statistical analysis: Primary outcomes were overall 90-d grade 2-5 complications defined by a modified Clavien system. Secondary outcomes included comparison of high-grade complications, estimated blood loss, operative time, pathologic outcomes, 3-and 6-mo patient-reported quality-of-life (QOL) outcomes, and total operative room and inpatient costs. Differences in binary outcomes were assessed with the chi-square test, with differences in continuous outcomes assessed by analysis of covariance with randomization group as covariate and, for QOL end points, baseline score. Results and limitations: The trial enrolled 124 patients, of whom 118 were randomized and underwent RC/PLND. Sixty were randomized to RARC and 58 to ORC. At 90 d, grade 2-5 complications were observed in 62% and 66% of RARC and ORC patients, respectively (95% confidence interval for difference, -21% to -13%; p = 0.7). The similar rates of grade 2-5 complications at our mandated interim analysis met futility criteria; thus, early closure of the trial occurred. The RARC group had lower mean intraoperative blood loss (p = 0.027) but significantly longer operative time than the ORC group (p \u3c 0.001). Pathologic variables including positive surgical margins and lymph node yields were similar. Mean hospital stay was 8 d in both arms (standard deviation, 3 and 5 d, respectively; p = 0.5). Three-and 6-mo QOL outcomes were similar between arms. Cost analysis demonstrated an advantage to ORC compared with RARC. A limitation is the setting at a single high-volume, referral center; our findings may not be generalizable to all settings. Conclusions: This trial failed to identify a large advantage for robot-assisted techniques over standard open surgery for patients undergoing RC/PLND and urinary diversion. Similar 90-d complication rates, hospital stay, pathologic outcomes, and 3-and 6-mo QOL outcomes were observed regardless of surgical technique. Patient summary: Of 118 patients with bladder cancer who underwent radical cystectomy, pelvic lymph node dissection, and urinary diversion, half were randomized to open surgery and half to robot-assisted laparoscopic surgery. We compared the rate of complications within 90 d after surgery for the open group versus the robotic group and found no significant difference between the two groups. Trial Registration: ClinicalTrials. gov identifier NCT01076387, www.clinicaltrials.gov. (C) 2014 European Association of Urology. Published by Elsevier B.V. All rights reserved

Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure

International education: a force for peace and cross-cultural understanding?

This paper discusses the notion that the international sojourn has the potential to transform sojourners into cultural mediators who carry the power to improve global relations. A year-long ethnographic study of the adjustment experiences of international postgraduate students in England revealed a universal early enthusiasm for cross-cultural contact that was matched by a widespread adoption of segregated patterns of interacting. The most common friendship networks were described by bonds with conationals, and yet all students attested to an increase in their cultural learning and mindfulness by the end of the sojourn. Nevertheless, intercultural competence was maximised only in those few students who pursued a multicultural strategy of interaction, leading the researcher to call on Higher Education Institutions to instigate policies to encourage lasting cross-cultural contact