TY - RPRT A1 - Sandor, V. A1 - Schalk, D. A1 - Sussmann, M. A1 - Wellisch, Ulrich T1 - Statistische Datenanalyse und Modellierung - Einsatzmöglichkeiten von Machine Learning Verfahren. Forschungsbericht 2016 Hochschule Rosenheim KW - Statistische Datenanalyse KW - Statistische Modellierung KW - Machine Learning Y1 - 2016 ER - TY - JOUR A1 - Frey, C. A1 - Schönfelder, F. A1 - Wellisch, Ulrich T1 - Anwendung von maschinellem Lernen in der Tarifierung JF - Der Aktuar KW - Maschinelles Lernen KW - Aktuarwissenschaften Y1 - 2016 ER - TY - CHAP A1 - Antretter, F. A1 - Mayer, C. A1 - Wellisch, Ulrich T1 - An approach for a statistical model for the user behaviour regarding window ventilation in residential buildings T2 - Proceedings of Building Simulation 2011: 12th Conference of International Building Performance Simulation Association, Sydney KW - Window Ventilation KW - Residential Buildings KW - Building Simulation Y1 - 2011 ER - TY - JOUR A1 - Steiger, S. A1 - Wellisch, Ulrich A1 - Hellwig, R. T. T1 - Untersuchung der Eignung verschiedener Fassaden für automatisierte Fensterlüftung in Schulen mit einem Entscheidungsbaumverfahren JF - Bauphysik N2 - Sollen Klassenräume über Fenster belüftet werden, kann dies über Stoßlüftung oder genau dosierte Dauerlüftung erfolgen. Messungen verschiedener Institutionen zeigen, dass die erforderliche regelmäßige Stoßlüftung in Schulen nicht praktiziert wird. Damit eine Dauerlüftung aber funktionieren kann, muss ermittelt werden, welcher Fenstertyp bei welcher Öffnungsweite bei behaglichen thermischen Verhältnissen im Raum den notwendigen Luftwechsel gewährleistet. Deshalb wurden an einem Freilandversuchsstand des Fraunhofer‐Instituts für Bauphysik Schwingflügel und Kippflügel auf ihre Eignung zur Dauerlüftung in Klassenräumen untersucht. Da sich bei den vielen Einflussfaktoren auf die freie Lüftung die deskriptive Analyse oft als sehr schwierig erweist, wird ein besonderes statistisches Verfahren, ein Entscheidungsbaumverfahren verwendet, das sowohl hinsichtlich der Auswahl der Einflussgrößen und der Modellüberanpassung sehr günstige statistischmethodische Eigenschaften besitzt. Mit diesem Verfahren können Einflussgrößen mit unterschiedlichen Skalenniveaus adäquat in die Auswertung einbezogen werden. Dabei erhält man ein intuitiv interpretierbares Regelwerk, welches dem Anwender einen erklärenden Einblick in die Zusammenhangsstruktur des untersuchten Prozesses liefert. KW - Fensterlüftung KW - Schulbelüftung KW - Raumthermik Y1 - 2010 ER - TY - THES A1 - Wellisch, Ulrich T1 - Asymptotic behaviour of solutions of estimating equations with functional parameter KW - Estimating equations KW - Gleichungen Y1 - 1999 ER - TY - RPRT A1 - Pruschka, H. A1 - Wellisch, Ulrich T1 - Asymptotic behaviour of estimation equations with functional nuisance or working parameter. N2 - We are concerned with the asymptotic theory of semiparametric estimation equations. We are dealing with estimation equations which have a parametric component of interest and a functional (nonparametric) nuisance component. We give sufficient conditions for the existence and the asymptotic normality of a consistent estimation equation estimator for the parameter of interest. These conditions concern the asymptotic distribution of the estimation function and of its derivative as well as the effect of the functional nuisance part in the estimation equation. In order to treat the nonparametric component we introduce a general differential calculus and a general mean value theorem. For the nonparametric part in the estimation equation we distinguish two cases: the situation of a (classical) nuisance parameter and the case of a so called working parameter. As a special case we get regularity conditions for estimation equations with finite dimensional nuisance or working parameter. As an example we present the semiparametric linear regression model. KW - Estimating equations KW - Asymptotic distribution KW - semiparametric linear regression model Y1 - 1997 ER - TY - RPRT A1 - Küchenhoff, H. A1 - Wellisch, Ulrich T1 - Asymptotics for generalized linear segmented regression models with an unknown breakpoint N2 - We consider asymptotic theory for the maximum likelihood estimator in the generalized linear model with an unknown breakpoint. A proof for the asymptotic normality is given. The methods are based on the work of Huber (1967). The main problem is the non--differentiability of the likelihood and the score function, which requires non--standard methods. An example from epidemiology is presented, where confidence intervals for the parameters are calculated with the asymptotic results. KW - Asymptotic theory KW - Linear segmentet regression models Y1 - 1997 ER - TY - JOUR A1 - Negele, Daniel A1 - Ott, Robert A1 - Wellisch, Ulrich T1 - Erfolg der Privatisierung von Krankenhäusern – Eine Einschätzung aus der Sicht ehemaliger öffentlicher Krankenhausträger T1 - Success of hospital privatisations – an assessment from the point of view of former public hospital owners JF - Gesundheitsökonomie & Qualitätsmanagement N2 - Zielsetzung In den letzten Jahren konnte eine Steigerung der Anzahl privater Krankenhäuser und Betten festgestellt werden. Die Probleme der Investitionsfinanzierung deutscher Krankenhäuser in Kombination mit verstärkenden Faktoren wie der Einführung der DRGs, aber auch die Erwartung einer höheren Effizienz nach der Privatisierung einer Klinik können als Hauptgründe bei Privatisierungsentscheidungen genannt werden. Es soll untersucht werden, wie ehemalige öffentliche Krankenhausträger den Erfolg der Privatisierung einschätzen. Methodik Alle 99 identifizierten ehemaligen öffentlichen Träger, die ihr Krankenhaus in den Jahren 2003–2013 an einen privaten Eigentümer verkauft hatten, wurden hinsichtlich ihrer Einschätzung von Zielen sowie Befürchtungen vor und nach der Privatisierung anonym und schriftlich befragt. Ergebnisse und Schlussfolgerung Zusammenfassend lässt sich feststellen, dass bei einer ausreichenden Finanzierung der Krankenhäuser aus Krankenkassenbeiträgen (Betriebsmittel) und Ländermittel (Investitionskosten) der Privatisierungsdruck rapide sinken würde. Wenn jedoch privatisiert wurde, hatte dies aus Sicht der ehemaligen Träger weder einen negativen Einfluss auf die medizinische Versorgung in der Region, noch auf die Qualität der medizinischen Behandlung und auf den Umgang mit den Mitarbeitern. Die Einschätzungen der ehemaligen Träger weisen eine statistisch überprüfte Übereinstimmung auf. Die mit einer Privatisierung verbundenen Erwartungen und Ziele werden prinzipiell als erfüllt wahrgenommen N2 - Aim In recent years, an increase in the number of private hospitals and beds could be determined. The problems of financing investments of German hospitals in combination with other reinforcing factors such as the introduction of DRGs, but also assumptions to higher efficiency after privatisation of a hospital can be identified as the main reasons for privatisation decisions. It should be examined how former public hospital operators assess the success of the privatisation. Method All 99 identified former public owners who had sold their hospitals during the years 2003 to 2013 to a private owner were interviewed anonymously and in written form with regard to their assessment of goals and fears before and after privatisation. Results and Conclusion In summary it can be said that with sufficient funding of hospitals from health insurance contributions (resources) and state funds (investment costs) privatisation pressure would fall sharply. But if privatized once, there was - from the view of the former public owners - neither a negative impact on medical care in the region, nor on the quality of medical treatment and the treatment of employees. The former public owners show a fair agreement on their assesments. The privatisations answer the expectations and the goals of the former public owners. KW - Privatisierung von Krankenhäusern KW - Gesundheitspolitik KW - Krankenhausfinanzierung KW - hospital privatisation KW - health policy KW - hospital financing Y1 - 2018 UR - https://doi.org/10.1055/s-0043-110761 IS - 1 SP - 43 EP - 50 ET - 23 ER - TY - RPRT A1 - Wellisch, Ulrich T1 - Erarbeitung von Prüfverfahren zur Vereinheitlichung der energetischen Bewertung von großformatigen, transparenten Bausystemen unter in situ Randbedingungen. Teilprojekt Hochschule Rosenheim: Analyseverfahren und Mitarbeit im IEA ECBCS Annex 58 „Reliable building performande characterisation and prediction based on full scale dynamic measurements“, Hochschule Rosenheim, 2016 KW - Bausysteme KW - Energetische Bewertung KW - in situ Randbedingungen Y1 - 2018 ER - TY - RPRT A1 - Bauer, L. A1 - Feldmeier, F. A1 - Paulus, F. A1 - Schreyer, M. A1 - Wellisch, Ulrich T1 - In situ Prüfverfahren für transparente Bauteile KW - transparente Bauteile KW - in situ Prüfverfahren Y1 - 2014 ER - TY - RPRT A1 - Sebald, D. A1 - Sussmann, M. A1 - Sandor, V. A1 - Wellisch, Ulrich T1 - Statistische Datenanalyse und Modellierung - Risikomodellierung in der Krafthaftpflichtversicherung. Forschungsbericht Hochschule Rosenheim 2015 KW - Statistische Datenanalyse KW - Risikomodellierung KW - Kfz- Haftpflichtversicherung Y1 - 2015 ER - TY - RPRT A1 - Sandor, V. A1 - Schalk, D. A1 - Sussmann, M. A1 - Wellisch, Ulrich T1 - Statistische Datenanalyse und Modellierung - Machine Learning in der Versicherung, Risikomodelle auf dem Prüfstand. Forschungsbericht 2016 Hochschule Rosenheim KW - Statistische Datenanalyse KW - Risikomodellierung KW - Machine Learning Y1 - 2016 ER - TY - JOUR A1 - Mayr, Andreas R. A1 - Nightingale, T.R.T. A1 - Fischer, Heinz Martin T1 - Metall macht leise. JF - Journal TrockenBau Akustik KW - Trockenbau KW - Metalldämmung KW - Schallschutz Y1 - 2006 IS - 3/2006 ER - TY - RPRT A1 - Bischof, Wolfgang T1 - On the Stability of Polling-Systems for General Arrival Processes T2 - Report No. 384 des Instituts für Mathematik, Universität Augsburg KW - Polling Systems KW - Arrival Processes KW - Server modelling Y1 - 1998 ER - TY - RPRT A1 - Bischof, Wolfgang T1 - M/G/1-queues with Setup Times and Vacations under Various Service Disciplines T2 - Report No. 417 des Instituts für Mathematik, Universität Augsburg KW - M/G/1-queues KW - Setup times Y1 - 1999 VL - 1999 ER - TY - BOOK A1 - Bischof, Wolfgang T1 - Analyse von M/G/1-Warteschlangen mit Bedienpausen und Bereitstellungszeiten unter sechs verschiedenen Bediendisziplinen T3 - Augsburger Mathematisch-Naturwissenschaftliche Schriften, Band 37 N2 - In dieser Arbeit werden M/G/1-Warteschlangen mit unendlich großem Warteraum und einem Server, der Bedienpausen und Bereitstellungszeiten benötigt, für die absperrende, begrenzende, binomiale, entleerende, vermindernde und bernoullische Bediendisziplin untersucht. Dabei bestimmt die Bediendisziplin, wie viele Kunden der Server in einem Zyklus, das ist die Zeit zwischen zwei Pausenenden, bedient. Wichtige Kenngrößen eines solchen Modells sind die Wartezeit eines Kunden, die Warteschlangenlänge zu einem beliebigen Zeitpunkt und die Zyklusdauer. Für jede der sechs Bediendisziplinen werden die Verteilung und die ersten beiden Momente dieser Kenngrößen berechnet. Die Ergebnisse werden benutzt, um die Abhängigkeit der ersten Momente der Kenngrößen von der Ankunftsrate, der Kundenbediendauer, der Pausenlänge und der Dauer der Bereitstellungszeit zu untersuchen. Ferner werden die sechs Bediendisziplinen bezüglich der Erwartungswerte der Kenngrößen miteinander verglichen. KW - Warteschlangentheorie KW - Statistik KW - Serverzyklus Y1 - 2000 SN - 978-3-89639-223-7 PB - Wißner-Verlag CY - Augsburg ET - 1 ER - TY - JOUR A1 - Bischof, Wolfgang T1 - Analysis of M/G/1-queues with Setup Times and Vacations under Six Different Service Disciplines JF - Queueing Systems: Theory and Applications (QUES) N2 - Single server M/G/1-queues with an infinite buffer are studied; these permit inclusion of server vacations and setup times. A service discipline determines the numbers of customers served in one cycle, that is, the time span between two vacation endings. Six service disciplines are investigated: the gated, limited, binomial, exhaustive, decrementing, and Bernoulli service disciplines. The performance of the system depends on three essential measures: the customer waiting time, the queue length, and the cycle duration. For each of the six service disciplines the distribution as well as the first and second moment of these three performance measures are computed. The results permit a detailed discussion of how the expected value of the performance measures depends on the arrival rate, the customer service time, the vacation time, and the setup time. Moreover, the six service disciplines are compared with respect to the first moments of the performance measures. KW - M/G/1-queues with setup times and vacations KW - Service disciplines KW - Waiting time KW - queue length Y1 - 2001 VL - 39 IS - 4/2001 SP - 265 EP - 302 PB - Springer US ER - TY - RPRT A1 - Bischof, Wolfgang T1 - Sag’ mir Deinen Beruf, ich errate Deine Automarke: Signifikante Zusammenhänge zwischen den Eingabewerten eines KFZ-Versicherungsvergleichs T2 - Forschungsbericht 2012 der Hochschule Rosenheim KW - Kfz-Versicherungsvergleich KW - Statistik Y1 - 2013 SP - 38 EP - 39 ER - TY - JOUR A1 - Bischof, Wolfgang A1 - Hindinger, Carina A1 - Pukelsheim, Friedrich T1 - Listenverbindungen - ein Relikt im bayerischen Gemeinde- und Landkreiswahlgesetz JF - Bayerische Verwaltungsblätter - Zeitschrift für öffentliches Recht und öffentliche Verwaltung (BayVBl.) N2 - Im Gemeinde- und Landkreiswahlgesetz haben Listenverbindungen eine lange Tradition. Sie sollen bei der Verrechnung von Stimmen in Sitze Verzerrungen dämpfen, die mit dem D’Hondt-Verfahren auftreten können. Da aber die Sitzzuteilung seit 2010 mit dem unverzerrten Hare/Niemeyer-Verfahren vorgenommen wird, haben Listenverbindungen ihre Berechtigung verloren. Wir demonstrieren die Problematik anhand der Kommunalwahlen 2014. In mehreren Kommunen passierte es, dass von zwei Listen diejenige mit mehr Stimmen weniger Sitze erhielt, was mit der Erfolgswertgleichheit der Wählerstimmen unvereinbar ist. Auch kam es vor, dass eine Liste den Einzug in den Gemeinderat nur deshalb verfehlte, weil sie einer Listenverbindung angehörte. KW - Listenverbindungen KW - Landkreiswahlgesetz Bayern Y1 - 2016 VL - 2016 IS - 2/2016 SP - 73 EP - 76 ER - TY - CHAP A1 - Hanfstaengl, Lucia A1 - Parzinger, Michael A1 - Spindler, Uli A1 - Wellisch, Ulrich A1 - Wirnsberger, Markus T1 - Identifying occupant presence in a room based on machine learning techniques by measuring indoor air conditions T2 - E3S Web of Conferences, 12th Nordic Symposium on Building Physics (NSB 2020) N2 - Knowing about the presence and number of people in a room can be of interest for precise control of heating, ventilation and air conditioning. To determine the number and presence of occupants cost-effectively, it is of interest to use already existing air condition sensors (temperature, humidity, CO2) of the building automation system. Different approaches and methods for determining presence have attracted attention in recent years. We propose an occupancy detection method based on a method of supervised machine learning. In an experiment, measurement data were recorded in a research apartment with controllable boundary conditions. The presence of people was simulated by artificial injection of water vapour, CO2 and heat dissipation. The variation of the number of artificial users, the duration of presence and the supply air volume flow of the ventilation resulted in a total of 720 combinations. By using artificial users, the boundary conditions were accurately defined, and different presence situations could be measured time-effectively. The data is evaluated with a method of supervised machine learning called random forest. The statistical model can determine precisely the number of people in over 93% of the cases in a disjoint test sample. The experiments took part in the Rosenheim Technical University of Applied Sciences laboratory. KW - occupancy KW - maschine learning KW - random forest Y1 - 2020 UR - https://doi.org/10.1051/e3sconf/202017222005 VL - 172 SP - 22005 ER - TY - JOUR A1 - Parzinger, Michael A1 - Hanfstaengl, Lucia A1 - Sigg, Ferdinand A1 - Spindler, Uli A1 - Wellisch, Ulrich A1 - Wirnsberger, Markus T1 - Residual Analysis of Predictive Modelling Data for Automated Fault Detection in Building’s Heating, Ventilation and Air Conditioning Systems JF - Sustainability N2 - Faults in Heating, Ventilation and Air Conditioning (HVAC) systems affect the energy efficiency of buildings. To date, there rarely exist methods to detect and diagnose faults during the operation of buildings that are both cost-effective and sufficient accurate. This study presents a method that uses artificial intelligence to automate the detection of faults in HVAC systems. The automated fault detection is based on a residual analysis of the predicted total heating power and the actual total heating power using an algorithm that aims to find an optimal decision rule for the determination of faults. The data for this study was provided by a detailed simulation of a residential case study house. A machine learning model and an ARX model predict the building operation. The model for fault detection is trained on a fault-free data set and then tested with a faulty operation. The algorithm for an optimal decision rule uses various statistical tests of residual properties such as the Sign Test, the Turning Point Test, the Box-Pierce Test and the Bartels-Rank Test. The results show that it is possible to predict faults for both known faults and unknown faults. The challenge is to find the optimal algorithm to determine the best decision rules. In the outlook of this study, further methods are presented that aim to solve this challenge. KW - fault detection KW - HVAC KW - residual analysis Y1 - 2020 UR - https://doi.org/10.3390/su12176758 VL - 12 IS - 17 SP - 6758 ER - TY - CHAP A1 - Parzinger, Michael A1 - Wellisch, Ulrich A1 - Hanfstaengl, Lucia A1 - Sigg, Ferdinand A1 - Wirnsberger, Markus A1 - Spindler, Uli T1 - Identifying faults in the building system based on model prediction and residuum analysis T2 - E3S Web of Conferences, 12th Nordic Symposium on Building Physics (NSB 2020) N2 - The energy efficiency of the building HVAC systems can be improved when faults in the running system are known. To this day, there are no cost-efficient, automatic methods that detect faults of the building HVAC systems to a satisfactory degree. This study induces a new method for fault detection that can replace a graphical, user-subjective evaluation of a building data measured on site with an automatic, data-based approach. This method can be a step towards cost-effective monitoring. For this research, the data from a detailed simulation of a residential case study house was used to compare a faultless operation of a building with a faulty operation. We argue that one can detect faults by analysing the properties of residuals of the prediction to the actual data. A machine learning model and an ARX model predict the building operation, and the method employs various statistical tests such as the Sign Test, the Turning Point Test, the Box-Pierce Test and the Bartels-Rank Test. The results show that the amount of data, the type and density of system faults significantly affect the accuracy of the prediction of faults. It became apparent that the challenge is to find a decision rule for the best combination of statistical tests on residuals to predict a fault. KW - fault detection KW - model prediction KW - HVAC KW - residuum analysis Y1 - 2020 UR - https://doi.org/10.1051/e3sconf/202017222001 VL - 172 SP - 22001 ER - TY - INPR A1 - Kimmerle, Sven-Joachim A1 - Dvorsky, Karl A1 - Liess, Hans-Dieter A1 - Avenhaus, Rudolf T1 - Time to Failure under Varying Thermal Stresses N2 - Varying thermal stresses influence significantly the time to failure of electric components as used, for instance, in automotive devices. For applications as autonomous driving a high reliability has to be guaranteed. In this article we discuss how to combine probability distributions for failure. Discrete and continuous changes of the probability distribution in time are both considered. It turns out that the temporal order of the distributions, corresponding to the succession of stresses in applications, is essential. The latter observation restricts the general applicability of the widely used temperature collectives where only the total time of a temperature stress is considered neglecting the order of the stresses. An application of our results are thermal overstress tests on electric components. We may explain yet not well understood measurements for automotive electric cables. KW - Reliability KW - Applied Probability KW - Data Science KW - Physics of Failure KW - Arrhenius Model Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:861-opus4-19126 ER - TY - GEN A1 - Kimmerle, Sven-Joachim A1 - Dvorsky, Karl A1 - Liess, Hans-Dieter T1 - Failure Rates from Data of Field Returns - How to Prove High Reliability for Electric Components? T2 - MATHMOD 2025 (11th Vienna International Conference on Mathematical Modelling) N2 - To determine failure rates is a challenge, if there are only a few failures and a low failure rate should be checked. As an application example, we are interested in failure rates of electrical automotive components for automated/autonomous driving. Basically, three methods are common: (i) exploitation of field data, (ii) standardized handbooks with failure rates, e.g. the FIDES guide, and (iii) laboratory long term exposure tests. We discuss shortly the (dis)advantages of each method and focus on the statistics behind method (i). Moreover, our poster sketches how this can be applied to data as available in industry. KW - Reliabilität KW - Statistik KW - Bordnetz KW - modelling uncertainties and stochastic systems KW - automotive vehicle electrical systems KW - reliability KW - autonomous driving/intelligent autonomous vehicles KW - field data Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:861-opus4-29421 ER - TY - JOUR A1 - Panahi, Benjamin A1 - Sandor, Viktor A1 - Tola, Imrane T1 - Das interne Moder der Feldafinger Brandkasse goes R JF - DAV Journal N2 - In diesem Artikel wird zum einen die Entwicklung eines Economic Scenario Generators zum anderen die Umsetzung des gesamten internen Modells der Feldafinger Brandkasse (FFBK) in R beschrieben. So erhält die FFBK ein vollständiges internes Modell in einer open source Programmierung. KW - FFBK_Feldafinger Brandkasse KW - Modellvalidierung KW - Schadenversicherung Y1 - 2025 IS - 04/24 SP - 280 EP - 286 PB - Deutsche Aktuarvereinigung (DAV) e.V. CY - Köln ER - TY - GEN A1 - Kimmerle, Sven-Joachim A1 - Dvorsky, Karl A1 - Liess, Hans-Dieter T1 - Failure Rates from Data of Field Returns T2 - MATHMOD Short Contribution Volume 2025 N2 - To determine failure rates is a challenge, if there are only a few failures and typical failure rates are low. As an application example we are interested in failure rates of electrical automotive components for automated/autonomous driving. As method we focus here on the exploitation of field data. Our contribution classifies different approaches from statistics and shows how this can be applied to real-world production figures as available in industry. KW - Mathematische Modellierung KW - Entscheidung bei Unsicherheit KW - Bordnetz KW - Reliabilität KW - Konfidenzbereich KW - modelling uncertainties and stochastic systems KW - automotive vehicle electrical systems KW - reliability KW - failure rates KW - autonomous driving Y1 - 2025 U6 - https://doi.org/10.34726/9011 SP - 23 EP - 24 PB - reposiTUm, TU Wien CY - Wien ER - TY - GEN A1 - Helbig, Michael A1 - Seliger, Norbert T1 - Combinatorics of Inductance States in Reconfigurable Air Coils T2 - Proceedings 2nd International Conference on Recent Advances in Mathematics and Informatics (ICRAMI'25) N2 - We propose a group theory based mathematical model for unambiguous inductance states of a reconfigurable air coil inductor utilizing elastic snapping of wire segments. Vertical (axial) and horizontal winding symmetries under group actions reveal distinguishable tuning regions and individual variation states therein. The model is applied to coils of prismatic (cylinder like) and truncated pyramidal (conical like) shape with edges forming a regular polygon as basis, and verified by numerical magnet field simulation. KW - Inductance KW - Magnetic devices KW - Matrices KW - Group theory KW - Combinatorial mathematics Y1 - 2025 SN - 978-9909-00-770-9 ER - TY - THES A1 - Helbig, Michael T1 - Lifting of Nichols Algebras N2 - Nichols algebras are a fundamental building block of pointed Hopf algebras. Part of the classi cation program of nite-dimensional pointed Hopf algebras with the lifting method of Andruskiewitsch and Schneider [6] is the determination of the liftings, i.e., all possible deformations of a given Nichols algebra. The classi cation was carried out in this way in [11] when the group of group-like elements is abelian and the prime divisors of the order of the group are > 7. In this case the appearing Nichols algebras are of Cartan type. Based on recent work of Heckenberger about diagonal Nichols algebras [29, 28, 27] we compute explicitly the liftings of some Nichols algebras not treated in [11]; namely we lift - all Nichols algebras with Cartan matrix of type A2 (Theorem 6.3.3), - some Nichols algebras with Cartan matrix of type B2 (Theorem 6.4.3), and - some Nichols algebras of two Weyl equivalence classes of non-standard type (Theorem 6.5.3), giving new classes of nite-dimensional pointed Hopf algebras. Crucial is the knowledge of a good presentation of the Nichols algebra and its liftings: We want to have an explicit description in terms of generators and (non-redundant) relations, and a basis; this requires new ideas and methods that generalize those in [11]. In this spirit, we describe Hopf algebras generated by skew-primitive elements and an abelian group with action given via characters (including Nichols algebras and their liftings) in Theorem 5.4.1. The relations form a Grobner basis and are given by a combinatorial property involving the theory of Lyndon words. Furthermore, in Theorem 7.3.1 we give a necessary and su cient criterion to check whether a given set of iterated q-commutators establishes a restricted PBW basis for a given realization of the relations. Also with the help of this criterion we determine the redundant relations in the examined Nichols algebras and their liftings. KW - Quantum Algebra KW - Hopf algebra KW - Nichols algebra Y1 - 2025 U6 - https://doi.org/10.5282/edoc.10378 ER - TY - BOOK A1 - Helbig, Michael T1 - Lifting of Nichols Algebras - A Contribution to the Classification of Pointed Hopf Algebras N2 - Nichols algebras are a fundamental building block of pointed Hopf algebras. Part of the classification program of finite-dimensional pointed Hopf algebras with the lifting method of Andruskiewitsch and Schneider is the determination of the liftings, i.e., all possible deformations of a given Nichols algebra. The classification was carried out in this way in several special cases when the appearing Nichols algebras are of Cartan type. We compute explicitly the liftings of some Nichols algebras not of Cartan type or of Cartan type without restrictions on the group order. These build up new classes of finite-dimensional pointed Hopf algebras. Furthermore, we give a necessary and sufficient PBW basis criterion for a class of pointed Hopf algebras and present them in terms of generators and relations. These Hopf algebras can be seen as generalized Quantum groups. KW - Quantum Algebra KW - Hopf algebra KW - Nichols algebra Y1 - 2025 SN - 978-3-8381-1084-4 PB - Südwestdeutscher Verlag für Hochschulschriften CY - Saarbrücken ER - TY - INPR A1 - Helbig, Michael T1 - A PBW basis criterion for pointed Hopf algebras N2 - We give a necessary and sufficient PBW basis criterion for Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of pointed Hopf algebras has shown great importance in the classification theory and can be seen as generalized quantum groups. We apply the criterion to classical examples and liftings of Nichols algebras which were determined in arxiv.org:1003.5882. KW - Quantum Algebra KW - Hopf algebra KW - Nichols algebra Y1 - 2025 U6 - https://doi.org/10.48550/arxiv.1011.0140 SP - 1 EP - 33 ER - TY - INPR A1 - Helbig, Michael T1 - On the presentation of pointed Hopf algebras N2 - We give a presentation in terms of generators and relations of Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of pointed Hopf algebras has shown great importance in the classification theory and can be seen as generalized quantum groups. As a consequence we get an analog presentation of Nichols algebras of diagonal type. KW - Quantum Algebra KW - Hopf algebra KW - Nichols algebra Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.1003.5879 SP - 1 EP - 13 ER - TY - GEN A1 - Schäfle, Claudia A1 - Stanzel, Silke A1 - Lux, Christine A1 - Neubert, Julia T1 - Aktives Lernen in MINT-Fächern mit dem ICAP-Modell charakterisieren, planen und reflektieren N2 - Um aktives Lernen in Lehrveranstaltungen zu klassifizieren, bietet das ICAP-Modell (Chi & Wylie, 2014) eine vierstufige Taxonomie, die in der Lehrpraxis anwendbar ist. Das von außen beobachtbare Verhalten wird in Kombination mit den von den Studierenden erzeugten „Produkten“ (z.B. ihren schriftlichen und mündlichen Äußerungen) verwendet, um das kognitive Engagement der Studierenden in Lehrveranstaltungen hinreichend gut einzuordnen (𝐼 Interactive, 𝐶 Constructive, 𝐴 Active und 𝑃 Passive). Die ICAP-Hypothese postuliert, dass es eine Hierarchie der ICAP-Stufen 𝐼 > 𝐶 > 𝐴 > 𝑃 hinsichtlich der Tiefe der zu erwartenden Lernergebnisse gibt. In diesem Beitrag berichten wir über Erkenntnisse aus systematischen Beobachtungen hinsichtlich des ICAP-Modells in Physik- und Mathematik-Lehrveranstaltungen an der TH Rosenheim. Die Lehrveranstaltungen finden nach dem SCALE-UP Raum- und Lehrkonzept statt (Beichner et al., 2007). Studierenden arbeiten dabei größtenteils an unterschiedlichen Lernaktivitäten in kleinen Gruppen an runden Tischen, während die Lehrperson die Rolle eines „guide on the side“ einnimmt. Das Verhalten der Studierenden und der Lehrperson wird in zweiminütigen Zeitintervallen zusammen mit dem „output“ der Studierenden registriert und auf die ICAP-Stufen abgebildet. Die Ergebnisse dienen der Reflexion und unterstützen die Planung und Verbesserung geeigneter Lernaktivitäten, insbesondere um zwischen den Stufen 𝐶 und 𝐴 zu unterscheiden. KW - Active Learning KW - ICAP KW - Classroom Observation KW - Innovative Lehrräume KW - SCALE-UP Y1 - 2026 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:861-opus4-32422 ER - TY - GEN A1 - Schäfle, Claudia A1 - Lux, Christine A1 - Neubert, Julia T1 - Classroom observation in SCALE-UP settings - first results N2 - SCALE-UP (Student-Centered Active Learning Environment for Upside-down Pedagogies) is a pedagogic approach to foster active learning, originally developed for undergraduate physics courses (Beichner et al., 2007). Instead of receiving lectures in SCALE1UP students work actively together in small groups, mostly at round tables and are guided by teaching staff. This concept is implemented at Rosenheim University of Applied Sciences, Germany, in several classes of physics and mathematics for engineering students. Classroom observations have been carried out in summer term 2023and winter term 2023/24 in order to investigate student learning in the SCALE-UP setting. The observations are based on ELCOT-3, the Engineering Learning Classroom Observation Tool (Sanders et al., 2018). An observation includes the overt student behavior in combination with the students’ output. The data have been analyzed with respect to the ICAP-framework (Chi&Wylie, 2014), where the different observed activities have been assigned to Interactive, Constructive, Active, and Passive mode. In this contribution we present examples on how students interact with the offered material, that means in which ICAP-modes students work with different learning activities in the SCALE-UP setting. Moreover, we show that in all observed courses students have been learning a substantial part of class time in interactive and constructive mode. KW - Active Learning KW - Classroom Observation KW - ICAP KW - SCALE-UP KW - Innovative Learning Spaces Y1 - 2026 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:861-opus4-32456 ER - TY - GEN A1 - Schäfle, Claudia A1 - Stanzel, Silke A1 - Lux, Christine A1 - Neubert, Julia A1 - Dölling, Hanna T1 - Using the ICAP model with classroom observations to improve active learning KW - ICAP KW - Classroom Observation KW - SCALE-UP KW - Active Learning KW - Whiteboard Activities Y1 - 2026 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:861-opus4-32833 ER -