Wie schwierig ist eine Modellierungsaufgabe? Denkstrukturen von Lösungsansätzen als Instrument zur Schwierigkeitsanalyse

In der mathematikdidaktischen Forschungsgemeinschaft ist man sich fast immer einig: Anwendungen, Modellieren und Realitätsbezüge sind wichtig und sollen in den Unterricht integriert werden. Allerdings zeigen viele Studien, dass der Anteil des Modellierens im Alltagsunterricht eher gering ist (z. B. Brunner, et al., 2006). Von Lehrern wird dabei häufig u.a. die Komplexität von Modellierungsaufgaben und die mangelnde Planbarkeit der Unterrichtsstunde beim Einsatz von Modellierungsaufgaben angeführt (Schmidt, 2010). Gerade Modellierungsaufgaben weisen scheinbar einige Unwägbarkeiten auf wie z.B. ihr vergleichbar großer Lösungsraum, d.h. dem zur Verfügung stehen mehrerer Lösungswege. Damit verbunden ist das Problem, die Schwierigkeit der Modellierungsaufgabe einzuschätzen. Im Folgenden wird ein Modell vorgestellt, das auf Denkstrukturen von Lösungsansätzen basiert, um den Schwierigkeitsgrad einer Modellierungsaufgabe einschätzen zu können. In einer Studie mit 600 Schülerinnen und Schülern der 9. gymnasialen Jahrgangsstufe soll der theoretisch ermittelte Schwierigkeitsgrad auf Validität überprüft werden

Entwurfskonzept einer Car2Car-Multiband-Dachantenne

Due to the vastly increasing use of wireless services in the car, such as WiFi, Car2Car and LTE, the requirements on bandwidth and radiation pattern of the roof antenna systems become more challenging. In this work, a design concept for multi-band roof antenna systems is presented. We aim to get a higher bandwidth and an almost circular radiation pattern on the horizontal plane. Moreover, the antenna length is considered in order to fulfill the requirements set by construction ECE-regulations (ECE, 2010). The applicability of the design concept is not limited to multi-band roof antennas, it can also be used for a general wideband antenna design. For illustration of this concept, a multi-band roof antenna with a bandwidth of 780 MHz to 5.9 GHz and a near circular radiation pattern with an average gain of <i>G</i> = 3 dBi (at 5.9 GHz) on the horizontal plane is designed. The simulation and measurement results are presented

Discretization analysis of bifurcation based nonlinear amplifiers

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation. A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations. © Author(s) 2017

Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation

Ansätze zur Ordnungsreduktion von nichtlinearen Oszillatormodellen zur Anwendung im Schaltungsentwurf

Im Rahmen dieser Arbeit wird ein Konzept zur Ordnungsreduktion von höherdimensionalen nichtlinearen Oszillatormodellen vorgestellt. Hierbei werden zwei wesentliche Ziele verfolgt. Zum einen wird eine höherdimensionale Modellierung der Oszillatorschaltung verwendet. Hierdurch lassen sich die Einflüsse parasitärer Effekte sowie struktureller Erweiterungen auf das dynamische Verhalten des Systems berücksichtigen. Zum anderen wird durch eine anschließende Ordnungsreduktion über die Methode der Zentrumsmannigfaltigkeit eine zweidimensionale Systembeschreibung erzeugt, deren wesentliche Dynamik derjenigen des höherdimensionalen Systems entspricht. Durch diese, in der Ordnung reduzierte, nichtlineare und parameterabhängige Systembeschreibung wird die Anwendbarkeit nichtlinearer Analysemethoden ermöglicht bzw. vereinfacht. Mit der Anwendung der Andronov-Hopf-Bifurkationsanalyse auf das reduzierte System lässt sich eine Stabilitätsuntersuchung durchführen sowie die Amplitude und Frequenz aller Zustandsgrößen approximieren. Das vorgestellte Konzept wird anhand des Beispielsystems eines LC-Tank-VCOs durchgeführt. <br><br> In this paper, an order reduction technique for higher-dimensional nonlinear oscillator models, based on a center manifold approach, is presented. By modeling the oscillator circuit in the higher-dimensional state space, influences of parasitic elements and of structural extensions of the oscillator architecture on the dynamical system behavior can be examined. Using the proposed order reduction technique, a generalized second order model will be derived, which includes selected design parameters of the higher order model. By using an Andronov-Hopf bifurcation analysis, the reduced system can be studied with respect to stability as well as the amplitude and frequency of the individual state variables. The concept is applied to the design of LC-tank VCOs

The effect of parathyroidectomy and thyroidectomy upon the subsequent levels of calcium and phosphorus in the blood of swine

Although considerable -work has been conducted on thyroid and parathyroid function in several species of animals, thus far, such studies in swine are obscure. The results of early studies on the effects of thyroidectomy in other species were badly clouded because of the simultaneous removal of the parathyroids. It is now accepted that the two organs are anatomically and physiologically separate structures. In most mammals the thyroid gland consists of two lobes—one on each side of the trachea close to its junction with the larynx. The Lobes are usually connected by an isthmus crossing the ventral surface of the trachea. The pig is an exception in that the thyroid gland is a mono lobed structure located on the ventral surface of the trachea just above the thoracic aperture. The parathyroids, present in amphibians, reptiles, birds and mammals, are believed to have essentially the same function. There are usually two pairs of parathyroids. Marked variations the position of the glands are seen in the different species, and, indeed, the position varies somewhat in animals of the same species. Location of these pyriform bodies is commonly on the posterior s\irface of the lateral lobes of the thyroid. Again, the pig proves to be an exception by having only two parathyroid glands—one in each anterior tip of the thymus gland (Schlotthauer and Higgins, 1934;Littledike, 1965). Optimal activity in animals is expected to occur when there is a proper balance of secretory activity of all the endocrine glands. Both The thyroid and parathyroid glands play an important part in this balance.Thyroid effects on metabolism, growth, and sexual maturity are well known; parathyroid regulation of calcium and phosphorus metabolism in many species is also well documented. Extirpation of these glands produces a well-established syndrome of clinical symptoms; however, most of this knowledge is based on data compiled from research on dogs, cats,and rats. Relatively little attention has been devoted to the effects of the hormones of these glands on calcium and phosphorus metabolism in the pig. The present investigation was conducted to determine the specific effects of parathyroidectomy and thyroidectomy on levels of calcium and phosphorus in the blood. The pig was chosen as the experimental animal because it is the only mammal that has an anatomically separated parathyroid and thyroid gland

The Relationship between the Military\u27s Masculine Culture and Service Members\u27 Help-Seeking Behaviors

Since the terrorist attacks on September 11, 2001, over 2.5 million active duty U.S. military service members have deployed to Iraq and Afghanistan (Knobloch & Wilson, 2015). Of those who return as veterans, twenty percent experience serious mental health problems, and only 30-40% of them seek help or treatment (Tanielian & Jaycox, 2008; Wilson, Gettings, Hall, & Pastor, 2015). Recently, the military has increased efforts to encourage help-seeking behaviors among service members and to normalize mental health treatment. However, the military’s masculine culture and emphasis on strength and toughness inhibits the success of these efforts. The present studies investigate the tension between military masculinity and mental health help-seeking behaviors. Study 1 uses ideological criticism to examine the recruitment websites of the four main branches of the military in order to assess the ways in which they communicate about masculine values and mental health. Study 2 presents an ideological analysis of two memoirs from individuals who have experienced life in the military and mental health problems upon returning home. The authors’ accounts are evaluated in comparison to the messages portrayed on the websites in order to determine whether real veterans have experiences that reflect the messages conveyed on recruitment websites. The two studies reveal what the military communicates about its culture and about mental health (Study 1) and what service members actually experience of military culture and mental health (Study 2). Suggestions for the normalization of mental health treatment among service members are discussed

Exploring access to end of life care for ethnic minorities with end stage kidney disease through recruitment in action research

BACKGROUND: Variation in provision of palliative care in kidney services and practitioner concerns to provide equitable access led to the development of this study which focussed on the perspectives of South Asian patients and their care providers. As people with a South Asian background experience a higher risk of Type 2 Diabetes (T2DM) and end stage kidney failure (ESKF) compared to the majority population but wait longer for a transplant, there is a need for end of life care to be accessible for this group of patients. Furthermore because non English speakers and people at end of life are often excluded from research there is a dearth of research evidence with which to inform service improvement. This paper aims to explore issues relating to the process of recruitment of patients for a research project which contribute to our understanding of access to end of life care for ethnic minority patients in the kidney setting. METHODS: The study employed an action research methodology with interviews and focus groups to capture and reflect on the process of engaging with South Asian patients about end of life care. Researchers and kidney care clinicians on four NHS sites in the UK recruited South Asian patients with ESKF who were requiring end of life care to take part in individual interviews; and other clinicians who provided care to South Asian kidney patients at end of life to take part in focus groups exploring end of life care issues. In action research planning, action and evaluation are interlinked and data were analysed with emergent themes fed back to care providers through the research cycle. Reflections on the process of patient recruitment generated focus group discussions about access which were analysed thematically and reported here. RESULTS: Sixteen patients were recruited to interview and 45 different care providers took part in 14 focus groups across the sites. The process of recruiting patients to interview and subsequent focus group data highlighted some of the key issues concerning access to end of life care. These were: the identification of patients approaching end of life; and their awareness of end of life care; language barriers and informal carers' roles in mediating communication; and contrasting cultures in end of life kidney care. CONCLUSIONS: Reflection on the process of recruitment in this action research study provided insight into the complex scenario of end of life in kidney care. Some of the emerging issues such as the difficulty identifying patients are likely to be common across all patient groups, whilst others concerning language barriers and third party communication are more specific to ethnic minorities. A focus on South Asian ethnicity contributes to better understanding of patient perspectives and generic concepts as well as access to end of life kidney care for this group of patients in the UK. Action research was a useful methodology for achieving this and for informing future research to include informal carers and other ethnic groups.Peer reviewedFinal Published versio