Sammlung von leicht ausführbaren Vorschriften zu den schönsten und elegantesten Strumpf-Rändern und andern feinen Strickereien : ein Hülfsbuch für das schöne Geschlecht

gesammelt und hrsg. von Nanette Andreä

Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters

Thesis (Ph.D.)--University of Washington, 2016-08

Proprioception in ankle sprain from exercises and bandages

Ankle sprains are the most common injuries in sports, usually causing damage to the lateral ligaments. Recurrence has as usual result permanent instability, and thus loss of proprioception. This fact, together with residual symptoms, is what is known as chronic ankle instability, CAI, or FAI, if it is functional. This problem tries to be solved by improving musculoskeletal stability and proprioception by the application of bandages and performing exercises. The aim of this study has been to review articles (meta-analisis, systematic reviews and revisions) published in 2009-2015 in PubMed, Medline, ENFISPO and BUCea, using keywords such as “sprain instability”, “sprain proprioception”, “chronic ankle instability”. Evidence affirms that there does exist decreased proprioception in patients who suffer from CAI. Rehabilitation exercise regimen is indicated as a treatment because it generates a subjective improvement reported by the patient, and the application of bandages works like a sprain prevention method limiting the range of motion, reducing joint instability and increasing confidence during exercise. As podiatrists we should recommend proprioception exercises to all athletes in a preventive way, and those with CAI or FAI, as a rehabilitation programme, together with the application of bandages. However, further studies should be generated focusing on ways of improving proprioception, and on the exercise patterns that provide the maximum benefit.

Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction

We consider a parametric semilinear Dirichlet problem driven by the Laplacian plus an indefinite unbounded potential and with a reaction of superdifissive type. Using variational and truncation techniques, we show that there exists a critical parameter value λ_{∗}>0 such that for all λ> λ_{∗} the problem has least two positive solutions, for λ= λ_{∗} the problem has at least one positive solutions, and no positive solutions exist when λ∈(0,λ_{∗}). Also, we show that for λ≥ λ_{∗} the problem has a smallest positive solution.

Migration und kulturelle Vielfalt. Zur Einleitung in das Themenheft

Der Artikel führt in das Themenheft ein. "Migration ist […] Thema einer inzwischen breiten aktuellen Forschung. Ein Teil der Beiträge des Themenschwerpunktes entstammt einem solchen Forschungszusammenhang, dem DFG-Schwerpunktprogramm 'Folgen der Arbeitsmigration für Bildung und Erziehung' (Faber); zusammen mit Beiträgen aus anderen Forschungsvorhaben zeigen sie exemplarisch die europäische Problematik, die Migration und Multikulturalität gewonnen haben (u. a. Allemann-Ghionda; Hopf/Hatzichristou; Jungbluth; Reich). Die historische Dimension des Themas und seine Konflikte repräsentieren die Beiträge von Depaepe/Simon/Verbeeck und Krüger-Potratz. Die Autoren richten ihr Augenmerk auf so unterschiedliche Nationen wie Polen, Türken, Griechen und Marokkaner, auf Aussiedler aus der ehemaligen Sowjetunion und auf Kinder von Einwohnern ehemals niederländischer Kolonien (Jungbluth); sie thematisieren ihre Situation als Erwachsene, Sekundarschüler, Grundschüler oder als Kinder vor dem Schulalter; sie behandeln die Lebensmöglichkeiten von Frauen (Gümen/Herwartz-Emden/Westphal) und sie gehen der Frage nach, mit welchen Schwierigkeiten Remigranten in ihren Herkunftsländern zu kämpfen haben (Hopf/Hatzichristou). Gestützt auf unterschiedliche methodische Zugänge - quantitativ-empirisch, qualitativ oder historisch-hermeneutisch - versuchen sie sowohl die Lebenssituation der Migranten wie Möglichkeiten pädagogischer Arbeit darzustellen. Die Beiträge von Reich und Auernheimer tragen schließlich der Tatsache Rechnung, daß man über die Praxis interkultureller Erziehung in Europa und über die Möglichkeiten der Erforschung von Migration inzwischen so viel weiß, daß auch bilanzierende und begriffskritische Analysen möglich sind." (DIPF/Orig.)

Dynamics of coupled modes in two-section semiconductor lasers with saturable absorption

Semiconductor lasers have the potential to address a number of critical applications in advanced telecommunications and signal processing. These include applications that require pulsed output that can be obtained from self-pulsing and mode-locked states of two-section devices with saturable absorption. Many modern applications place stringent performance requirements on the laser source, and a thorough understanding of the physical mechanisms underlying these pulsed modes of operation is therefore highly desirable. In this thesis, we present experimental measurements and numerical simulations of a variety of self-pulsation phenomena in two-section semiconductor lasers with saturable absorption. Our theoretical and numerical results will be based on rate equations for the field intensities and the carrier densities in the two sections of the device, and we establish typical parameter ranges and assess the level of agreement with experiment that can be expected from our models. For each of the physical examples that we consider, our model parameters are consistent with the physical net gain and absorption of the studied devices. Following our introductory chapter, the first system that we consider is a two-section Fabry-Pérot laser. This example serves to introduce our method for obtaining model parameters from the measured material dispersion, and it also allows us to present a detailed discussion of the bifurcation structure that governs the appearance of selfpulsations in two-section devices. In the following two chapters, we present two distinct examples of experimental measurements from dual-mode two-section devices. In each case we have found that single mode self-pulsations evolve into complex coupled dualmode states following a characteristic series of bifurcations. We present optical and mode resolved power spectra as well as a series of characteristic intensity time traces illustrating this progression for each example. Using the results from our study of a twosection Fabry-Pérot device as a guide, we find physically appropriate model parameters that provide qualitative agreement with our experimental results. We highlight the role played by material dispersion and the underlying single mode self-pulsing orbits in determining the observed dynamics, and we use numerical continuation methods to provide a global picture of the governing bifurcation structure. In our concluding chapter we summarise our work, and we discuss how the presented results can inform the development of optimised mode-locked lasers for performance applications in integrated optics.

Rückkehr in die Heimat. Zur schulischen und sozialpsychologischen Situation griechischer Schüler nach der Remigration

Dieser Aufsatz berichtet über die Ergebnisse einer umfassenden empirischen Untersuchung zur Schulsituation griechischer Kinder und Jugendlicher, die aus der BRD in ihre Heimat zurückgewandert sind. An Stichproben aus Grundschulen und Sekundarstufen wird überprüft, welche Probleme in den Schulleistungen und im psychosozialen Befinden bei Rückkehrern im Vergleich zu Einheimischen auftreten. Die Informationen über jeden Schüler enthalten mehrere Perspektiven: Lehrerurteil, Einschätzung durch die Mitschüler, Selbstkonzept sowie Schulleistungsindikatoren. Es zeigt sich, daß die Rückkehrerkinder schulisch im Rückstand liegen sowie eine Reihe psychosozialer Belastungen aufweisen, die je nach Remigrationszeitpunkt, Geschlecht etc, unterschiedlich ausgeprägt sind. Unproblematisch verläuft die Rückkehr in die Heimat und die schulische Integration nur, wenn sie vor dem 8. Lebensjahr erfolgt. (DIPF/Orig.)

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.

Hexagonal patterns in finite domains

In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patterns. In finite rectangular domains, it is shown that a regular hexagonal pattern cannot occur if the aspect ratio is rational. In practice, it is found experimentally that in a rectangular region, patterns of irregular hexagons are often observed. This work analyses the geometry and dynamics of irregular hexagonal patterns. These patterns occur in two different symmetry types, either with a reflection symmetry, involving two wavenumbers, or without symmetry, involving three different wavenumbers. The relevant amplitude equations are studied to investigate the detailed bifurcation structure in each case. It is shown that hexagonal patterns can bifurcate subcritically either from the trivial solution or from a pattern of rolls. Numerical simulations of a model partial differential equation are also presented to illustrate the behaviour.

Pattern formation with a conservation law

Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern formation near onset. Near a stationary bifurcation, the usual Ginzburg--Landau equation for the amplitude of the pattern is then coupled to an equation for the large-scale mode. These amplitude equations show that for certain parameters all roll-type solutions are unstable. This new instability differs from the Eckhaus instability in that it is amplitude-driven and is supercritical. Beyond the stability boundary, there exist stable stationary solutions in the form of strongly modulated patterns. The envelope of these modulations is calculated in terms of Jacobi elliptic functions and, away from the onset of modulation, is closely approximated by a sech profile. Numerical simulations indicate that as the modulation becomes more pronounced, the envelope broadens. A number of applications are considered, including convection with fixed-flux boundaries and convection in a magnetic field, resulting in new instabilities for these systems.

Evans functions for integral neural field equations with Heaviside firing rate function

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The theory is illustrated with the construction and stability analysis of front solutions to a scalar neural field model and a limiting case is shown to recover recent results of L. Zhang [On stability of traveling wave solutions in synaptically coupled neuronal networks, Differential and Integral Equations, 16, (2003), pp.513-536.]. Traveling fronts and pulses are considered in more general models possessing either a linear or piecewise constant recovery variable. We establish the stability of coexisting traveling fronts beyond a front bifurcation and consider parameter regimes that support two stable traveling fronts of different speed. Such fronts may be connected and depending on their relative speed the resulting region of activity can widen or contract. The conditions for the contracting case to lead to a pulse solution are established. The stability of pulses is obtained for a variety of examples, in each case confirming a previously conjectured stability result. Finally we show how this theory may be used to describe the dynamic instability of a standing pulse that arises in a model with slow recovery. Numerical simulations show that such an instability can lead to the shedding of a pair of traveling pulses.