@article{ArwornDenecke2001,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Tree Transformations defined by Hypersubstitutions},
  issn      = {1509 - 9415},
  year      = {2001},
  language  = {en}
}
@article{DeneckeKoppitzWismath2001,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Wismath, Shelly},
  title     = {The semantical hyperunification problem},
  year      = {2001},
  language  = {en}
}
@article{DeneckeLeeratanavalee2001,
  author    = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak},
  title     = {M-solid polynomial varieties of semigroups},
  year      = {2001},
  language  = {en}
}
@article{DeneckeLueders2001,
  author    = {Denecke, Klaus-Dieter and L{\"u}ders, Otfried},
  title     = {Categorical Equivalences and Invariant Relations},
  year      = {2001},
  language  = {en}
}
@article{DeneckeWismath2003,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Valuations of Terms},
  year      = {2003},
  abstract  = {Let tau be a type of algebras. There are several commonly used measurements of the complexity of terms of type tau, including the depth or height of a term and the number of variable symbols appearing in a term. In this paper we formalize these various measurements, by defining a complexity or valuation mapping on terms. A valuation of terms is thus a mapping from the absolutely free term algebra of type tau into another algebra of the same type on which an order relation is defined. We develop the interconnections between such term valuations and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; valuations of terms offer a new method to study complete sublattices of this lattice},
  language  = {en}
}
@article{ArwornDenecke2002,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Intervals and complete congruences defined by M-solid varieties},
  year      = {2002},
  language  = {en}
}
@article{DeneckeKoppitzNiwczyk2002,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Niwczyk, St.},
  title     = {Equational theories generated by generalized hypersubstitutions of type (n)},
  year      = {2002},
  language  = {en}
}
@book{DeneckeKoppitzShtraklov2001,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Shtraklov, Slavcho},
  title     = {The Depth of a Hypersubstitution},
  year      = {2001},
  language  = {en}
}
@book{DeneckeWismath2002,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Universal algebra and applications in theoretical computer science},
  publisher = {Chapman \& Hall/CRC},
  address   = {Boca Raton},
  isbn      = {1-584-88254-9},
  pages     = {383 S.},
  year      = {2002},
  language  = {en}
}
@article{DeneckeKoppitzWismath2002,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Wismath, Shelly},
  title     = {Solid Varietie of Arbitrary Type},
  year      = {2002},
  language  = {en}
}
@article{DeneckeKoppitz2001,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Fluid, unsolid and completely unsolid varieties},
  year      = {2001},
  language  = {en}
}
@article{DeneckeWismath2002,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {M-solidity testing systems},
  year      = {2002},
  language  = {en}
}
@article{DeneckeKoppitz2001,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Essential variables in hypersubstitution},
  year      = {2001},
  language  = {en}
}
@article{DeneckeLeeratanavalee2000,
  author    = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak},
  title     = {Generalized hypersubstitutions and strongly solid varieties},
  isbn      = {3-8265- 7983-6},
  year      = {2000},
  language  = {en}
}
@article{DeneckeLeeratanavalee2000,
  author    = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak},
  title     = {Solid polynomial varieties of semigroups which are definable by identities},
  year      = {2000},
  language  = {en}
}
@phdthesis{Trappmann2007,
  author    = {Trappmann, Henryk},
  title     = {Arborescent numbers : higher arithmetic operations and division trees},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15247},
  school      = {Universit{\"a}t Potsdam},
  year      = {2007},
  abstract  = {The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the hassle-free definition of arbitrary high arithmetic operations (hyper ... hyperpowers). To construct the division trees the algebraic structure "coppice" is introduced which is a group with an addition over which the multiplication is right-distributive. Q+ is the initial associative coppice. The present work accomplishes one step in the program "arborescent numbers". That is the construction of the arborescent equivalent(s) of the positive fractional numbers. These equivalents are the "division binary trees" and the "fractional trees". A representation with decidable word problem for each of them is given. The set of functions f:R1->R1 generated from identity by taking powers is isomorphic to P and can be embedded into a coppice by taking inverses.},
  language  = {en}
}
@article{HaferKiyLucke2014,
  author    = {Hafer, J{\"o}rg and Kiy, Alexander and Lucke, Ulrike},
  title     = {Moodle \& Co. auf dem Weg zur Personal Learning Environment},
  series = {eleed},
  volume    = {2014},
  journal   = {eleed},
  number    = {10},
  issn      = {1860-7470},
  year      = {2014},
  abstract  = {Ausgehend von der typischen IT-Infrastruktur f{\"u}r E-Learning an Hochschulen auf der einen Seite sowie vom bisherigen Stand der Forschung zu Personal Learning Environments (PLEs) auf der anderen Seite zeigt dieser Beitrag auf, wie bestehende Werkzeuge bzw. Dienste zusammengef{\"u}hrt und f{\"u}r die Anforderungen der modernen, rechnergest{\"u}tzten Pr{\"a}senzlehre aufbereitet werden k{\"o}nnen. F{\"u}r diesen interdisziplin{\"a}ren Entwicklungsprozess bieten sowohl klassische Softwareentwicklungsverfahren als auch bestehende PLE-Modelle wenig Hilfestellung an. Der Beitrag beschreibt die in einem campusweiten Projekt an der Universit{\"a}t Potsdam verfolgten Ans{\"a}tze und die damit erzielten Ergebnisse. Daf{\"u}r werden zun{\"a}chst typische Lehr-/Lern-bzw. Kommunikations-Szenarien identifiziert, aus denen Anforderungen an eine unterst{\"u}tzende Plattform abgeleitet werden. Dies f{\"u}hrt zu einer umfassenden Sammlung zu ber{\"u}cksichtigender Dienste und deren Funktionen, die gem{\"a}ß den Spezifika ihrer Nutzung in ein Gesamtsystem zu integrieren sind. Auf dieser Basis werden grunds{\"a}tzliche Integrationsans{\"a}tze und technische Details dieses Mash-Ups in einer Gesamtschau aller relevanten Dienste betrachtet und in eine integrierende Systemarchitektur {\"u}berf{\"u}hrt. Deren konkrete Realisierung mit Hilfe der Portal-Technologie Liferay wird dargestellt, wobei die eingangs definierten Szenarien aufgegriffen und exemplarisch vorgestellt werden. Erg{\"a}nzende Anpassungen im Sinne einer personalisierbaren bzw. adaptiven Lern-(und Arbeits-)Umgebung werden ebenfalls unterst{\"u}tzt und kurz aufgezeigt.},
  language  = {en}
}
@article{FischerKeller2021,
  author    = {Fischer, Florian and Keller, Matthias},
  title     = {Riesz decompositions for Schr{\"o}dinger operators on graphs},
  series = {Journal of mathematical analysis and applications},
  volume    = {495},
  journal   = {Journal of mathematical analysis and applications},
  number    = {1},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0022-247X},
  doi       = {10.1016/j.jmaa.2020.124674},
  pages     = {22},
  year      = {2021},
  abstract  = {We study superharmonic functions for Schrodinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.},
  language  = {en}
}
@article{Zoeller2022,
  author    = {Z{\"o}ller, Gert},
  title     = {A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field},
  series = {The bulletin of the Seismological Society of America : BSSA},
  volume    = {112},
  journal   = {The bulletin of the Seismological Society of America : BSSA},
  number    = {4},
  publisher = {Seismological Society of America},
  address   = {El Cerito, Calif.},
  issn      = {0037-1106},
  doi       = {10.1785/0120210307},
  pages     = {1825 -- 1831},
  year      = {2022},
  abstract  = {Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.},
  language  = {en}
}
@article{Denecke2020,
  author    = {Denecke, Klaus-Dieter},
  title     = {Partial clones},
  series = {Asian-European journal of mathematics : AEJM},
  volume    = {13},
  journal   = {Asian-European journal of mathematics : AEJM},
  number    = {8},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557120501612},
  pages     = {19},
  year      = {2020},
  abstract  = {A set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.},
  language  = {en}
}