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

Lieb-Thirring Bound for Schr\"odinger Operators with Bernstein Functions of the Laplacian

A Lieb-Thirring bound for Schr\"odinger operators with Bernstein functions of the Laplacian is shown by functional integration techniques. Several specific cases are discussed in detail.Comment: We revised the first versio

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

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

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

The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feyman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard "free" case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schr\"{o}dinger problem, the "free noise" can also be extended to any infinitely divisible probability law, as covered by the L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians $|\nabla |$ and $\sqrt {-\triangle +m^2}-m$ are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger evolution is analyzed in detail. The relativistic covariance of related waveComment: Latex fil

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

Phenotype MicroArray Profiling of Zymomonas mobilis ZM4

In this study, we developed a Phenotype MicroArray™ (PM) protocol to profile cellular phenotypes in Zymomonas mobilis, which included a standard set of nearly 2,000 assays for carbon, nitrogen, phosphorus and sulfur source utilization, nutrient stimulation, pH and osmotic stresses, and chemical sensitivities with 240 inhibitory chemicals. We observed two positive assays for C-source utilization (fructose and glucose) using the PM screen, which uses redox chemistry and cell respiration as a universal reporter to profile growth phenotypes in a high-throughput 96-well plate-based format. For nitrogen metabolism, the bacterium showed a positive test results for ammonia, aspartate, asparagine, glutamate, glutamine, and peptides. Z. mobilis appeared to use a diverse array of P-sources with two exceptions being pyrophosphate and tripolyphosphate. The assays suggested that Z. mobilis uses both inorganic and organic compounds as S-sources. No stimulation by nutrients was detected; however, there was evidence of partial inhibition by purines and pyrimidines, NAD, and deferoxamine. Z. mobilis was relatively resistant to acid pH, tolerating a pH down to about 4.0. It also tolerated phosphate, sulfate, and nitrate, but was rather sensitive to chloride and nitrite. Z. mobilis showed resistance to a large number of diverse chemicals that inhibit most bacteria. The information from PM analysis provides an overview of Z. mobilis physiology and a foundation for future comparisons of other wild-type and mutant Z. mobilis strains

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