Strichartz estimates for partially periodic solutions to Schr\"odinger equations in 4d and applications

We consider the energy critical nonlinear Schr\"odinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds for solutions to the corresponding linear Schr\"odinger equation, we prove that the nonlinear problem is locally well-posed in the energy space. Then we verify that the L^4 estimate holds if m=2,3, leaving open the cases m=0,1.Comment: 15 page

A convolution estimate for two-dimensional hypersurfaces

Given three transversal and sufficiently regular hypersurfaces in R^3 it follows from work of Bennett-Carbery-Wright that the convolution of two L^2 functions supported of the first and second hypersurface, respectively, can be restricted to an L^2 function on the third hypersurface, which can be considered as a nonlinear version of the Loomis-Whitney inequality. We generalize this result to a class of C^{1,beta} hypersurfaces in R^3, under scaleable assumptions. The resulting uniform L^2 estimate has applications to nonlinear dispersive equations.Comment: 21 pages, 1 figur

Global well-posedness of the energy critical Nonlinear Schr\"odinger equation with small initial data in H^1(T^3)

A refined trilinear Strichartz estimate for solutions to the Schr\"odinger equation on the flat rational torus T^3 is derived. By a suitable modification of critical function space theory this is applied to prove a small data global well-posedness result for the quintic Nonlinear Schr\"odinger Equation in H^s(T^3) for all s \geq 1. This is the first energy-critical global well-posedness result in the setting of compact manifolds.Comment: v3: 19 page

Theories of financial crises: An overview

This paper analyses financial crises from a theoretical point of view. For this it reviews what different schools of economic thought have to say about financial crises. It examines first the approaches that regard financial crises as a disturbing factor of a generally stable real economy (Wicksell, Hayek, Schumpeter, Fisher, and the early Keynes). Thereafter, approaches, where the dichotomy between the monetary and the real sphere is lifted, are reviewed. Here in particular the later works of Keynes and the contributions of Minsky are of importance. Lastly, it is looked at the behavioural finance approaches. After having reviewed the different approaches, it is examined where those approaches have similarities and where they can be combined fruitfully. Based on this, we develop an own theoretical framework methodologically based on a Wicksellian cumulative process, however, overcoming the neoclassical dichotomy. The paper ends with some policy recommendations based on the developed theoretical framework

Validating the Demand Control Support Questionnaire among white-collar employees in Switzerland and the United States

Background: The Demand Control Support Questionnaire (DCSQ) is an established self-reported tool to measure a stressful work environment. Validated German and English versions are however currently missing. The aim of this study was therefore to evaluate the psychometric properties of German and English versions of the DCSQ among white-collar employees in Switzerland and the US. Methods: This cross-sectional study was carried out on 499 employees in Switzerland and 411 in the US, respectively. The 17-item DCSQ with three scales assessed psychosocial stress at work (psychological demands, decision latitude, and social support at work). Depressive symptoms were measured by the 2-item Patient Health Questionnaire. Cronbach’s α and item-total correlations tested the scale reliability (internal consistency). Construct validity of the questionnaire was examined using exploratory factor analysis (EFA). Logistic regressions estimated associations of each scale and job strain with depressive symptoms (criterion validity). Results: In both samples, all DCSQ scales presented satisfactory internal consistency (Cronbach’s α ≥ 0.72; item-total correlations ≥ 0.33), and EFA showed the 17 items loading on three factors, which is in line with the theoretically assumed structure of the DCSQ construct. Moreover, all three scales as well as high job strain were significantly associated with depressive symptoms. The associations were stronger in the US sample. Conclusions: The German and the English versions of the DCSQ seem to be reliable and valid instruments to measure psychosocial stress based on the job demand-control-support model in the workplace of white-collar employees in Switzerland and the US

Probing Within Partially Coherent Microcavity Frequency Combs via Optical Pulse Shaping

Recent investigations of microcavity frequency combs based on cascaded four-wave mixing have revealed a link between the evolution of the optical spectrum and the observed temporal coherence. Here we study a silicon nitride microresonator for which the initial four-wave mixing sidebands are spaced by multiple free spectral ranges (FSRs) from the pump, then fill in to yield a comb with single FSR spacing, resulting in partial coherence. By using a pulse shaper to select and manipulate the phase of various subsets of spectral lines, we are able to probe the structure of the coherence within the partially coherent comb. Our data demonstrate strong variation in the degree of mutual coherence between different groups of lines and provide support for a simple model of partially coherent comb formation

Core competencies for pain management: results of an interprofessional consensus summit.

ObjectiveThe objective of this project was to develop core competencies in pain assessment and management for prelicensure health professional education. Such core pain competencies common to all prelicensure health professionals have not been previously reported.MethodsAn interprofessional executive committee led a consensus-building process to develop the core competencies. An in-depth literature review was conducted followed by engagement of an interprofessional Competency Advisory Committee to critique competencies through an iterative process. A 2-day summit was held so that consensus could be reached.ResultsThe consensus-derived competencies were categorized within four domains: multidimensional nature of pain, pain assessment and measurement, management of pain, and context of pain management. These domains address the fundamental concepts and complexity of pain; how pain is observed and assessed; collaborative approaches to treatment options; and application of competencies across the life span in the context of various settings, populations, and care team models. A set of values and guiding principles are embedded within each domain.ConclusionsThese competencies can serve as a foundation for developing, defining, and revising curricula and as a resource for the creation of learning activities across health professions designed to advance care that effectively responds to pain

Coherent terabit communications with microresonator Kerr frequency combs

Optical frequency combs enable coherent data transmission on hundreds of wavelength channels and have the potential to revolutionize terabit communications. Generation of Kerr combs in nonlinear integrated microcavities represents a particularly promising option enabling line spacings of tens of GHz, compliant with wavelength-division multiplexing (WDM) grids. However, Kerr combs may exhibit strong phase noise and multiplet spectral lines, and this has made high-speed data transmission impossible up to now. Recent work has shown that systematic adjustment of pump conditions enables low phase-noise Kerr combs with singlet spectral lines. Here we demonstrate that Kerr combs are suited for coherent data transmission with advanced modulation formats that pose stringent requirements on the spectral purity of the optical source. In a first experiment, we encode a data stream of 392 Gbit/s on subsequent lines of a Kerr comb using quadrature phase shift keying (QPSK) and 16-state quadrature amplitude modulation (16QAM). A second experiment shows feedback-stabilization of a Kerr comb and transmission of a 1.44 Tbit/s data stream over a distance of up to 300 km. The results demonstrate that Kerr combs can meet the highly demanding requirements of multi-terabit/s coherent communications and thus offer a solution towards chip-scale terabit/s transceivers

I-BEAT: New ultrasonic method for single bunch measurement of ion energy distribution

The shape of a wave carries all information about the spatial and temporal structure of its source, given that the medium and its properties are known. Most modern imaging methods seek to utilize this nature of waves originating from Huygens' principle. We discuss the retrieval of the complete kinetic energy distribution from the acoustic trace that is recorded when a short ion bunch deposits its energy in water. This novel method, which we refer to as Ion-Bunch Energy Acoustic Tracing (I-BEAT), is a generalization of the ionoacoustic approach. Featuring compactness, simple operation, indestructibility and high dynamic ranges in energy and intensity, I-BEAT is a promising approach to meet the needs of petawatt-class laser-based ion accelerators. With its capability of completely monitoring a single, focused proton bunch with prompt readout it, is expected to have particular impact for experiments and applications using ultrashort ion bunches in high flux regimes. We demonstrate its functionality using it with two laser-driven ion sources for quantitative determination of the kinetic energy distribution of single, focused proton bunches.Comment: Paper: 17 Pages, 3 figures Supplementary Material 16 pages, 7 figure

Table of Contents and Prologue

Editorial board, Table of contents, and Prologue, an introduction to volume 1