@techreport{SandorSchalkSussmannetal.2016, author = {Sandor, V. and Schalk, D. and Sussmann, M. and Wellisch, Ulrich}, title = {Statistische Datenanalyse und Modellierung - Einsatzm{\"o}glichkeiten von Machine Learning Verfahren. Forschungsbericht 2016 Hochschule Rosenheim}, year = {2016}, language = {de} } @article{FreySchoenfelderWellisch2016, author = {Frey, C. and Sch{\"o}nfelder, F. and Wellisch, Ulrich}, title = {Anwendung von maschinellem Lernen in der Tarifierung}, series = {Der Aktuar}, journal = {Der Aktuar}, year = {2016}, language = {de} } @inproceedings{AntretterMayerWellisch2011, author = {Antretter, F. and Mayer, C. and Wellisch, Ulrich}, title = {An approach for a statistical model for the user behaviour regarding window ventilation in residential buildings}, series = {Proceedings of Building Simulation 2011: 12th Conference of International Building Performance Simulation Association, Sydney}, booktitle = {Proceedings of Building Simulation 2011: 12th Conference of International Building Performance Simulation Association, Sydney}, year = {2011}, language = {en} } @article{SteigerWellischHellwig2010, author = {Steiger, S. and Wellisch, Ulrich and Hellwig, R. T.}, title = {Untersuchung der Eignung verschiedener Fassaden f{\"u}r automatisierte Fensterl{\"u}ftung in Schulen mit einem Entscheidungsbaumverfahren}, series = {Bauphysik}, journal = {Bauphysik}, year = {2010}, abstract = {Sollen Klassenr{\"a}ume {\"u}ber Fenster bel{\"u}ftet werden, kann dies {\"u}ber Stoßl{\"u}ftung oder genau dosierte Dauerl{\"u}ftung erfolgen. Messungen verschiedener Institutionen zeigen, dass die erforderliche regelm{\"a}ßige Stoßl{\"u}ftung in Schulen nicht praktiziert wird. Damit eine Dauerl{\"u}ftung aber funktionieren kann, muss ermittelt werden, welcher Fenstertyp bei welcher {\"O}ffnungsweite bei behaglichen thermischen Verh{\"a}ltnissen im Raum den notwendigen Luftwechsel gew{\"a}hrleistet. Deshalb wurden an einem Freilandversuchsstand des Fraunhofer-Instituts f{\"u}r Bauphysik Schwingfl{\"u}gel und Kippfl{\"u}gel auf ihre Eignung zur Dauerl{\"u}ftung in Klassenr{\"a}umen untersucht. Da sich bei den vielen Einflussfaktoren auf die freie L{\"u}ftung die deskriptive Analyse oft als sehr schwierig erweist, wird ein besonderes statistisches Verfahren, ein Entscheidungsbaumverfahren verwendet, das sowohl hinsichtlich der Auswahl der Einflussgr{\"o}ßen und der Modell{\"u}beranpassung sehr g{\"u}nstige statistischmethodische Eigenschaften besitzt. Mit diesem Verfahren k{\"o}nnen Einflussgr{\"o}ßen mit unterschiedlichen Skalenniveaus ad{\"a}quat in die Auswertung einbezogen werden. Dabei erh{\"a}lt man ein intuitiv interpretierbares Regelwerk, welches dem Anwender einen erkl{\"a}renden Einblick in die Zusammenhangsstruktur des untersuchten Prozesses liefert.}, language = {de} } @phdthesis{Wellisch1999, author = {Wellisch, Ulrich}, title = {Asymptotic behaviour of solutions of estimating equations with functional parameter}, school = {Technische Hochschule Rosenheim}, year = {1999}, language = {en} } @techreport{PruschkaWellisch1997, author = {Pruschka, H. and Wellisch, Ulrich}, title = {Asymptotic behaviour of estimation equations with functional nuisance or working parameter.}, year = {1997}, abstract = {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.}, language = {en} } @techreport{KuechenhoffWellisch1997, author = {K{\"u}chenhoff, H. and Wellisch, Ulrich}, title = {Asymptotics for generalized linear segmented regression models with an unknown breakpoint}, year = {1997}, abstract = {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.}, language = {en} } @article{NegeleOttWellisch2018, author = {Negele, Daniel and Ott, Robert and Wellisch, Ulrich}, title = {Erfolg der Privatisierung von Krankenh{\"a}usern - Eine Einsch{\"a}tzung aus der Sicht ehemaliger {\"o}ffentlicher Krankenhaustr{\"a}ger}, series = {Gesundheits{\"o}konomie \& Qualit{\"a}tsmanagement}, journal = {Gesundheits{\"o}konomie \& Qualit{\"a}tsmanagement}, number = {1}, edition = {23}, pages = {43 -- 50}, year = {2018}, abstract = {Zielsetzung In den letzten Jahren konnte eine Steigerung der Anzahl privater Krankenh{\"a}user und Betten festgestellt werden. Die Probleme der Investitionsfinanzierung deutscher Krankenh{\"a}user in Kombination mit verst{\"a}rkenden Faktoren wie der Einf{\"u}hrung der DRGs, aber auch die Erwartung einer h{\"o}heren Effizienz nach der Privatisierung einer Klinik k{\"o}nnen als Hauptgr{\"u}nde bei Privatisierungsentscheidungen genannt werden. Es soll untersucht werden, wie ehemalige {\"o}ffentliche Krankenhaustr{\"a}ger den Erfolg der Privatisierung einsch{\"a}tzen. Methodik Alle 99 identifizierten ehemaligen {\"o}ffentlichen Tr{\"a}ger, die ihr Krankenhaus in den Jahren 2003-2013 an einen privaten Eigent{\"u}mer verkauft hatten, wurden hinsichtlich ihrer Einsch{\"a}tzung von Zielen sowie Bef{\"u}rchtungen vor und nach der Privatisierung anonym und schriftlich befragt. Ergebnisse und Schlussfolgerung Zusammenfassend l{\"a}sst sich feststellen, dass bei einer ausreichenden Finanzierung der Krankenh{\"a}user aus Krankenkassenbeitr{\"a}gen (Betriebsmittel) und L{\"a}ndermittel (Investitionskosten) der Privatisierungsdruck rapide sinken w{\"u}rde. Wenn jedoch privatisiert wurde, hatte dies aus Sicht der ehemaligen Tr{\"a}ger weder einen negativen Einfluss auf die medizinische Versorgung in der Region, noch auf die Qualit{\"a}t der medizinischen Behandlung und auf den Umgang mit den Mitarbeitern. Die Einsch{\"a}tzungen der ehemaligen Tr{\"a}ger weisen eine statistisch {\"u}berpr{\"u}fte {\"U}bereinstimmung auf. Die mit einer Privatisierung verbundenen Erwartungen und Ziele werden prinzipiell als erf{\"u}llt wahrgenommen}, language = {de} } @techreport{Wellisch2016, author = {Wellisch, Ulrich}, title = {Erarbeitung von Pr{\"u}fverfahren 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}, year = {2016}, language = {de} } @techreport{BauerFeldmeierPaulusetal.2014, author = {Bauer, L. and Feldmeier, F. and Paulus, F. and Schreyer, M. and Wellisch, Ulrich}, title = {In situ Pr{\"u}fverfahren f{\"u}r transparente Bauteile}, year = {2014}, language = {de} } @techreport{SebaldSussmannSandoretal.2015, author = {Sebald, D. and Sussmann, M. and Sandor, V. and Wellisch, Ulrich}, title = {Statistische Datenanalyse und Modellierung - Risikomodellierung in der Krafthaftpflichtversicherung. Forschungsbericht Hochschule Rosenheim 2015}, year = {2015}, language = {de} } @techreport{SandorSchalkSussmannetal.2016, author = {Sandor, V. and Schalk, D. and Sussmann, M. and Wellisch, Ulrich}, title = {Statistische Datenanalyse und Modellierung - Machine Learning in der Versicherung, Risikomodelle auf dem Pr{\"u}fstand. Forschungsbericht 2016 Hochschule Rosenheim}, year = {2016}, language = {de} } @article{MayrNightingaleFischer2006, author = {Mayr, Andreas R. and Nightingale, T.R.T. and Fischer, Heinz Martin}, title = {Metall macht leise.}, series = {Journal TrockenBau Akustik}, journal = {Journal TrockenBau Akustik}, number = {3/2006}, year = {2006}, language = {de} } @techreport{Bischof1998, author = {Bischof, Wolfgang}, title = {On the Stability of Polling-Systems for General Arrival Processes}, series = {Report No. 384 des Instituts f{\"u}r Mathematik, Universit{\"a}t Augsburg}, journal = {Report No. 384 des Instituts f{\"u}r Mathematik, Universit{\"a}t Augsburg}, pages = {3}, year = {1998}, language = {en} } @techreport{Bischof1999, author = {Bischof, Wolfgang}, title = {M/G/1-queues with Setup Times and Vacations under Various Service Disciplines}, series = {Report No. 417 des Instituts f{\"u}r Mathematik, Universit{\"a}t Augsburg}, volume = {1999}, journal = {Report No. 417 des Instituts f{\"u}r Mathematik, Universit{\"a}t Augsburg}, year = {1999}, language = {en} } @book{Bischof2000, author = {Bischof, Wolfgang}, title = {Analyse von M/G/1-Warteschlangen mit Bedienpausen und Bereitstellungszeiten unter sechs verschiedenen Bediendisziplinen}, series = {Augsburger Mathematisch-Naturwissenschaftliche Schriften, Band 37}, journal = {Augsburger Mathematisch-Naturwissenschaftliche Schriften, Band 37}, edition = {1}, publisher = {Wißner-Verlag}, address = {Augsburg}, isbn = {978-3-89639-223-7}, publisher = {Technische Hochschule Rosenheim}, year = {2000}, abstract = {In dieser Arbeit werden M/G/1-Warteschlangen mit unendlich großem Warteraum und einem Server, der Bedienpausen und Bereitstellungszeiten ben{\"o}tigt, f{\"u}r 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 Kenngr{\"o}ßen eines solchen Modells sind die Wartezeit eines Kunden, die Warteschlangenl{\"a}nge zu einem beliebigen Zeitpunkt und die Zyklusdauer. F{\"u}r jede der sechs Bediendisziplinen werden die Verteilung und die ersten beiden Momente dieser Kenngr{\"o}ßen berechnet. Die Ergebnisse werden benutzt, um die Abh{\"a}ngigkeit der ersten Momente der Kenngr{\"o}ßen von der Ankunftsrate, der Kundenbediendauer, der Pausenl{\"a}nge und der Dauer der Bereitstellungszeit zu untersuchen. Ferner werden die sechs Bediendisziplinen bez{\"u}glich der Erwartungswerte der Kenngr{\"o}ßen miteinander verglichen.}, language = {de} } @article{Bischof2001, author = {Bischof, Wolfgang}, title = {Analysis of M/G/1-queues with Setup Times and Vacations under Six Different Service Disciplines}, series = {Queueing Systems: Theory and Applications (QUES)}, volume = {39}, journal = {Queueing Systems: Theory and Applications (QUES)}, number = {4/2001}, publisher = {Springer US}, pages = {265 -- 302}, year = {2001}, abstract = {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.}, language = {en} } @techreport{Bischof2013, author = {Bischof, Wolfgang}, title = {Sag' mir Deinen Beruf, ich errate Deine Automarke: Signifikante Zusammenh{\"a}nge zwischen den Eingabewerten eines KFZ-Versicherungsvergleichs}, series = {Forschungsbericht 2012 der Hochschule Rosenheim}, journal = {Forschungsbericht 2012 der Hochschule Rosenheim}, pages = {38 -- 39}, year = {2013}, language = {de} } @article{BischofHindingerPukelsheim2016, author = {Bischof, Wolfgang and Hindinger, Carina and Pukelsheim, Friedrich}, title = {Listenverbindungen - ein Relikt im bayerischen Gemeinde- und Landkreiswahlgesetz}, series = {Bayerische Verwaltungsbl{\"a}tter - Zeitschrift f{\"u}r {\"o}ffentliches Recht und {\"o}ffentliche Verwaltung (BayVBl.)}, volume = {2016}, journal = {Bayerische Verwaltungsbl{\"a}tter - Zeitschrift f{\"u}r {\"o}ffentliches Recht und {\"o}ffentliche Verwaltung (BayVBl.)}, number = {2/2016}, pages = {73 -- 76}, year = {2016}, abstract = {Im Gemeinde- und Landkreiswahlgesetz haben Listenverbindungen eine lange Tradition. Sie sollen bei der Verrechnung von Stimmen in Sitze Verzerrungen d{\"a}mpfen, die mit dem D'Hondt-Verfahren auftreten k{\"o}nnen. 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 W{\"a}hlerstimmen unvereinbar ist. Auch kam es vor, dass eine Liste den Einzug in den Gemeinderat nur deshalb verfehlte, weil sie einer Listenverbindung angeh{\"o}rte.}, language = {de} } @inproceedings{HanfstaenglParzingerSpindleretal.2020, author = {Hanfstaengl, Lucia and Parzinger, Michael and Spindler, Uli and Wellisch, Ulrich and Wirnsberger, Markus}, title = {Identifying occupant presence in a room based on machine learning techniques by measuring indoor air conditions}, series = {E3S Web of Conferences, 12th Nordic Symposium on Building Physics (NSB 2020)}, volume = {172}, booktitle = {E3S Web of Conferences, 12th Nordic Symposium on Building Physics (NSB 2020)}, pages = {22005}, year = {2020}, abstract = {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.}, language = {en} } @article{ParzingerHanfstaenglSiggetal.2020, author = {Parzinger, Michael and Hanfstaengl, Lucia and Sigg, Ferdinand and Spindler, Uli and Wellisch, Ulrich and Wirnsberger, Markus}, title = {Residual Analysis of Predictive Modelling Data for Automated Fault Detection in Building's Heating, Ventilation and Air Conditioning Systems}, series = {Sustainability}, volume = {12}, journal = {Sustainability}, number = {17}, pages = {6758}, year = {2020}, abstract = {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.}, language = {en} } @inproceedings{ParzingerWellischHanfstaengletal.2020, author = {Parzinger, Michael and Wellisch, Ulrich and Hanfstaengl, Lucia and Sigg, Ferdinand and Wirnsberger, Markus and Spindler, Uli}, title = {Identifying faults in the building system based on model prediction and residuum analysis}, series = {E3S Web of Conferences, 12th Nordic Symposium on Building Physics (NSB 2020)}, volume = {172}, booktitle = {E3S Web of Conferences, 12th Nordic Symposium on Building Physics (NSB 2020)}, pages = {22001}, year = {2020}, abstract = {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.}, language = {en} } @unpublished{KimmerleDvorskyLiessetal.2022, author = {Kimmerle, Sven-Joachim and Dvorsky, Karl and Liess, Hans-Dieter and Avenhaus, Rudolf}, title = {Time to Failure under Varying Thermal Stresses}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:861-opus4-19126}, pages = {30}, year = {2022}, abstract = {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.}, language = {en} } @misc{KimmerleDvorskyLiess2025, author = {Kimmerle, Sven-Joachim and Dvorsky, Karl and Liess, Hans-Dieter}, title = {Failure Rates from Data of Field Returns - How to Prove High Reliability for Electric Components?}, series = {MATHMOD 2025 (11th Vienna International Conference on Mathematical Modelling)}, journal = {MATHMOD 2025 (11th Vienna International Conference on Mathematical Modelling)}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:861-opus4-29421}, pages = {1}, year = {2025}, abstract = {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.}, subject = {Reliabilit{\"a}t}, language = {en} } @article{PanahiSandorTola2024, author = {Panahi, Benjamin and Sandor, Viktor and Tola, Imrane}, title = {Das interne Moder der Feldafinger Brandkasse goes R}, series = {DAV Journal}, journal = {DAV Journal}, number = {04/24}, publisher = {Deutsche Aktuarvereinigung (DAV) e.V.}, address = {K{\"o}ln}, pages = {280 -- 286}, year = {2024}, abstract = {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 erh{\"a}lt die FFBK ein vollst{\"a}ndiges internes Modell in einer open source Programmierung.}, language = {de} } @misc{KimmerleDvorskyLiess2025, author = {Kimmerle, Sven-Joachim and Dvorsky, Karl and Liess, Hans-Dieter}, title = {Failure Rates from Data of Field Returns}, series = {MATHMOD Short Contribution Volume 2025}, journal = {MATHMOD Short Contribution Volume 2025}, publisher = {reposiTUm, TU Wien}, address = {Wien}, doi = {10.34726/9011}, pages = {23 -- 24}, year = {2025}, abstract = {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.}, subject = {Mathematische Modellierung}, language = {en} } @misc{HelbigSeliger2025, author = {Helbig, Michael and Seliger, Norbert}, title = {Combinatorics of Inductance States in Reconfigurable Air Coils}, series = {Proceedings 2nd International Conference on Recent Advances in Mathematics and Informatics (ICRAMI'25)}, journal = {Proceedings 2nd International Conference on Recent Advances in Mathematics and Informatics (ICRAMI'25)}, isbn = {978-9909-00-770-9}, pages = {8}, year = {2025}, abstract = {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.}, language = {en} } @phdthesis{Helbig2009, author = {Helbig, Michael}, title = {Lifting of Nichols Algebras}, doi = {10.5282/edoc.10378}, school = {Technische Hochschule Rosenheim}, pages = {107}, year = {2009}, abstract = {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.}, language = {en} } @book{Helbig2009, author = {Helbig, Michael}, title = {Lifting of Nichols Algebras - A Contribution to the Classification of Pointed Hopf Algebras}, publisher = {S{\"u}dwestdeutscher Verlag f{\"u}r Hochschulschriften}, address = {Saarbr{\"u}cken}, isbn = {978-3-8381-1084-4}, publisher = {Technische Hochschule Rosenheim}, pages = {112}, year = {2009}, abstract = {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.}, language = {en} } @unpublished{Helbig2010, author = {Helbig, Michael}, title = {A PBW basis criterion for pointed Hopf algebras}, doi = {10.48550/arxiv.1011.0140}, pages = {1 -- 33}, year = {2010}, abstract = {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.}, language = {en} } @unpublished{Helbig2010, author = {Helbig, Michael}, title = {On the presentation of pointed Hopf algebras}, doi = {10.48550/arXiv.1003.5879}, pages = {1 -- 13}, year = {2010}, abstract = {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.}, language = {en} } @misc{SchaefleStanzelLuxetal.2025, author = {Sch{\"a}fle, Claudia and Stanzel, Silke and Lux, Christine and Neubert, Julia}, title = {Aktives Lernen in MINT-F{\"a}chern mit dem ICAP-Modell charakterisieren, planen und reflektieren}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:861-opus4-32422}, year = {2025}, abstract = {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 m{\"u}ndlichen {\"A}ußerungen) 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 {\"u}ber 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 gr{\"o}ßtenteils an unterschiedlichen Lernaktivit{\"a}ten in kleinen Gruppen an runden Tischen, w{\"a}hrend die Lehrperson die Rolle eines „guide on the side" einnimmt. Das Verhalten der Studierenden und der Lehrperson wird in zweimin{\"u}tigen Zeitintervallen zusammen mit dem „output" der Studierenden registriert und auf die ICAP-Stufen abgebildet. Die Ergebnisse dienen der Reflexion und unterst{\"u}tzen die Planung und Verbesserung geeigneter Lernaktivit{\"a}ten, insbesondere um zwischen den Stufen 𝐶 und 𝐴 zu unterscheiden.}, language = {de} } @misc{SchaefleLuxNeubert2024, author = {Sch{\"a}fle, Claudia and Lux, Christine and Neubert, Julia}, title = {Classroom observation in SCALE-UP settings - first results}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:861-opus4-32456}, year = {2024}, abstract = {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.}, language = {en} } @misc{SchaefleStanzelLuxetal.2025, author = {Sch{\"a}fle, Claudia and Stanzel, Silke and Lux, Christine and Neubert, Julia and D{\"o}lling, Hanna}, title = {Using the ICAP model with classroom observations to improve active learning}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:861-opus4-32833}, year = {2025}, language = {en} }