@article{Lewandowski2022,
  author    = {Lewandowski, Max},
  title     = {Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes},
  series = {Journal of mathematical physics},
  volume    = {63},
  journal   = {Journal of mathematical physics},
  number    = {1},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/5.0055753},
  pages     = {34},
  year      = {2022},
  abstract  = {According to Radzikowski's celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF-G˜F+G˜A-G˜R) in the sense of Duistermaat and H{\"o}rmander [Acta Math. 128, 183-269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by B{\"a}r, Ginoux, and Pf{\"a}ffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Z{\"u}rich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF-G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.},
  language  = {en}
}
@article{StolleMichaelisRauberg2016,
  author    = {Stolle, Claudia and Michaelis, Ingo and Rauberg, Jan},
  title     = {The role of high-resolution geomagnetic field models for investigating ionospheric currents at low Earth orbit satellites},
  series = {Earth, planets and space},
  volume    = {68},
  journal   = {Earth, planets and space},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1880-5981},
  doi       = {10.1186/s40623-016-0494-1},
  pages     = {10},
  year      = {2016},
  abstract  = {Low Earth orbiting geomagnetic satellite missions, such as the Swarm satellite mission, are the only means to monitor and investigate ionospheric currents on a global scale and to make in situ measurements of F region currents. High-precision geomagnetic satellite missions are also able to detect ionospheric currents during quiet-time geomagnetic conditions that only have few nanotesla amplitudes in the magnetic field. An efficient method to isolate the ionospheric signals from satellite magnetic field measurements has been the use of residuals between the observations and predictions from empirical geomagnetic models for other geomagnetic sources, such as the core and lithospheric field or signals from the quiet-time magnetospheric currents. This study aims at highlighting the importance of high-resolution magnetic field models that are able to predict the lithospheric field and that consider the quiet-time magnetosphere for reliably isolating signatures from ionospheric currents during geomagnetically quiet times. The effects on the detection of ionospheric currents arising from neglecting the lithospheric and magnetospheric sources are discussed on the example of four Swarm orbits during very quiet times. The respective orbits show a broad range of typical scenarios, such as strong and weak ionospheric signal (during day- and nighttime, respectively) superimposed over strong and weak lithospheric signals. If predictions from the lithosphere or magnetosphere are not properly considered, the amplitude of the ionospheric currents, such as the midlatitude Sq currents or the equatorial electrojet (EEJ), is modulated by 10-15 \% in the examples shown. An analysis from several orbits above the African sector, where the lithospheric field is significant, showed that the peak value of the signatures of the EEJ is in error by 5 \% in average when lithospheric contributions are not considered, which is in the range of uncertainties of present empirical models of the EEJ.},
  language  = {en}
}
@article{ChajadaDeneckeHalas1999,
  author    = {Chajada, I. and Denecke, Klaus-Dieter and Halas, R.},
  title     = {Algebras induced by hypersubstitutions},
  year      = {1999},
  language  = {en}
}
@phdthesis{ArwornDenecke1999,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Sets of hypersubstitutions and set-solid varieties},
  year      = {1999},
  language  = {en}
}
@article{DeneckeKoppitz1999,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Normal forms of hypersubstitutions},
  year      = {1999},
  language  = {en}
}
@article{DeneckeLeeratanavalee1999,
  author    = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak},
  title     = {Weak hypersubstitutions and weakly derived algebras},
  year      = {1999},
  language  = {en}
}
@article{ArwornDenecke1999,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Left-edges solid varieties of differential groupoids},
  year      = {1999},
  language  = {en}
}
@article{DeneckeMruczek2000,
  author    = {Denecke, Klaus-Dieter and Mruczek, Krysztyna},
  title     = {P-compatible Hypersubstitutions},
  year      = {2000},
  language  = {en}
}
@book{ArwornDeneckePoeschel1998,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter and P{\"o}schel, Reinhard},
  title     = {Closure operators on complete lattices},
  series = {Preprint MATH-ALG / Technische Universit{\"a}t Dresden},
  volume    = {1998, 05},
  journal   = {Preprint MATH-ALG / Technische Universit{\"a}t Dresden},
  publisher = {Techn. Univ.},
  address   = {Dresden},
  year      = {1998},
  language  = {en}
}
@article{DeneckeKoppitz1998,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Finite monoids of hypersubstitutions of type € = (2)},
  year      = {1998},
  language  = {en}
}
@book{DeneckeTodorov1999,
  author    = {Denecke, Klaus-Dieter and Todorov, Kalco},
  title     = {Osnovi na Aritmetikata},
  publisher = {Univ. Press},
  address   = {Blagoevgrad [Bulgarian]},
  isbn      = {954-680-122-4},
  year      = {1999},
  language  = {de}
}
@article{Denecke1999,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones closed with respect to closed operators},
  year      = {1999},
  language  = {en}
}
@article{DeneckeFreiberg1998,
  author    = {Denecke, Klaus-Dieter and Freiberg, L.},
  title     = {The word problem for M-solid varieties of semigroups},
  isbn      = {981-3083-86-7},
  year      = {1998},
  language  = {en}
}
@article{DeneckePlonka1995,
  author    = {Denecke, Klaus-Dieter and Plonka, J.},
  title     = {Regularization and normalization of solid varieties},
  year      = {1995},
  language  = {en}
}
@article{DeneckeReichel1995,
  author    = {Denecke, Klaus-Dieter and Reichel, Mario},
  title     = {Monoids of hypersubstitutions and m-solid varieties},
  year      = {1995},
  language  = {en}
}
@article{DeneckePlonka1995,
  author    = {Denecke, Klaus-Dieter and Plonka, J.},
  title     = {Edge-solid varieties},
  year      = {1995},
  language  = {en}
}
@article{DeneckeMalcevReschke1995,
  author    = {Denecke, Klaus-Dieter and Malcev, I. A. and Reschke, M.},
  title     = {On separation of Boolean clones by means of hyperidentities},
  year      = {1995},
  language  = {en}
}
@article{DeneckeKoppitz1995,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Pre-solid varieties of commutative semigroups},
  year      = {1995},
  language  = {en}
}
@article{DeneckeKoppitz1995,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {M-solid varieties of semigroups},
  year      = {1995},
  language  = {en}
}
@article{DeneckeKoppitz1995,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Pre-solid varieties of semigroups},
  year      = {1995},
  language  = {en}
}
@article{Denecke1995,
  author    = {Denecke, Klaus-Dieter},
  title     = {Hybrid identities and hybrid equational logic},
  year      = {1995},
  language  = {en}
}
@article{Denecke1995,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones and hyperidentities},
  year      = {1995},
  language  = {en}
}
@article{DeneckeKoppitzŠtrakov2006,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Štrakov, Slavčo},
  title     = {Multi-hypersubstitutions and colored solid varieties},
  series = {International journal of algebra and computation},
  volume    = {16},
  journal   = {International journal of algebra and computation},
  number    = {4},
  publisher = {World Scient. Publ.},
  address   = {Singapore},
  issn      = {0218-1967},
  doi       = {10.1142/S0218196706003189},
  pages     = {797 -- 815},
  year      = {2006},
  abstract  = {Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by operation symbols and by colors, i.e. certain positive integers. We are interested in mappings which map differently-colored operation symbols to different terms. In this paper we extend the theory of hypersubstitutions and solid varieties to multi-hypersubstitutions and colored solid varieties. We develop the interconnections between such colored terms and multihypersubstitutions 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; multi-hypersubstitutions and colored solid varieties offer a new method to study complete sublattices of this lattice.},
  language  = {en}
}
@article{Denecke2019,
  author    = {Denecke, Klaus-Dieter},
  title     = {The partial clone of linear formulas},
  series = {Siberian mathematical journal},
  volume    = {60},
  journal   = {Siberian mathematical journal},
  number    = {4},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446619040037},
  pages     = {572 -- 584},
  year      = {2019},
  abstract  = {A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′).},
  language  = {en}
}
@article{ArwornDenecke1997,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Groupoids of hypersubstitutions and G-solid varieties},
  year      = {1997},
  language  = {en}
}
@article{DeneckePoomsaard1997,
  author    = {Denecke, Klaus-Dieter and Poomsa-ard, T.},
  title     = {Hyperidentities in graph algebras},
  year      = {1997},
  language  = {en}
}
@article{DeneckeWismath1997,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {The monoid of hypersubstitutions of type (2)},
  year      = {1997},
  language  = {en}
}
@article{ArwornDenecke1997,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {A new methods to study subvariety lattices of semigroup varieties},
  year      = {1997},
  language  = {en}
}
@article{DeneckeLueders1995,
  author    = {Denecke, Klaus-Dieter and L{\"u}ders, Otfried},
  title     = {Category equivalences of clones},
  year      = {1995},
  language  = {en}
}
@article{Denecke1996,
  author    = {Denecke, Klaus-Dieter},
  title     = {The entropy sequence of unary logical functions},
  year      = {1996},
  language  = {en}
}
@article{Denecke1997,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones and Hyperidentities},
  year      = {1997},
  language  = {en}
}
@book{DeneckeTodorov1996,
  author    = {Denecke, Klaus-Dieter and Todorov, Kalco},
  title     = {Allgemeine Algebra und Anwendungen},
  publisher = {Shaker},
  address   = {Aachen},
  pages     = {251 S.},
  year      = {1996},
  language  = {de}
}
@book{Denecke1996,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones and hyperidentities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1996, 14},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {33 Bl.},
  year      = {1996},
  language  = {en}
}
@article{Denecke2016,
  author    = {Denecke, Klaus-Dieter},
  title     = {The partial clone of linear terms},
  series = {Siberian Mathematical Journal},
  volume    = {57},
  journal   = {Siberian Mathematical Journal},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446616040030},
  pages     = {589 -- 598},
  year      = {2016},
  abstract  = {Generalizing a linear expression over a vector space, we call a term of an arbitrary type tau linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all terms in the case of linear terms, we define the partial many-sorted superposition operation and the partial many-sorted clone that satisfies the superassociative law as weak identity. The extensions of linear hypersubstitutions are weak endomorphisms of this partial clone. For a variety V of one-sorted total algebras of type tau, we define the partial many-sorted linear clone of V as the partial quotient algebra of the partial many-sorted clone of all linear terms by the set of all linear identities of V. We prove then that weak identities of this clone correspond to linear hyperidentities of V.},
  language  = {en}
}
@article{DeneckeWismath2009,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {The dimension of a variety and the kernel of a hypersubstitution},
  issn      = {0218-1967},
  doi       = {10.1142/S0218196709005342},
  year      = {2009},
  abstract  = {The dimension of a variety V of algebras of a given type was introduced by E. Graczynska and D. Schweigert in [7] as the cardinality of the set of all derived varieties of V which are properly contained in V. In this paper, we characterize all solid varieties of dimensions 0, 1, and 2; prove that the dimension of a variety of finite type is at most N-0; give an example of a variety which has infinite dimension; and show that for every n is an element of N there is a variety with dimension n. Finally, we show that the dimension of a variety is related to the concept of the semantical kernel of a hypersubstitution and apply this connection to calculate the dimension of the class of all algebras of type tau = (n).},
  language  = {en}
}
@article{DeneckeSaengsura2009,
  author    = {Denecke, Klaus-Dieter and Saengsura, Kittisak},
  title     = {Separation of clones of cooperations by cohyperidentities},
  issn      = {0012-365X},
  doi       = {10.1016/j.disc.2008.01.043},
  year      = {2009},
  abstract  = {An n-ary cooperation is a mapping from a nonempty set A to the nth copower of A. A clone of cooperations is a set of cooperations which is closed under superposition and contains all injections. Coalgebras are pairs consisting of a set and a set of cooperations defined on this set. We define terms for coalgebras, coidentities and cohyperidentities. These concepts will be applied to give a new solution of the completeness problem for clones of cooperations defined on a two-element set and to separate clones of cooperations by coidentities.},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Congruences on maximal partial clones and strong regular varieties generated by preprimal partial algebras II},
  year      = {1991},
  language  = {en}
}
@book{DeneckeWismath2009,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly L.},
  title     = {Universal Algebra and Coalgebra},
  publisher = {World Scientific Publ. Co},
  address   = {Singapore},
  isbn      = {978-981-283745-5},
  pages     = {278 S.},
  year      = {2009},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Strong regular varieties of partial algebras I},
  year      = {1991},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Minimal algebras and category equivalences},
  year      = {1991},
  language  = {en}
}
@book{OPUS4-28852,
  title     = {General algebra and applications},
  series = {Research and exposition in mathematics},
  volume    = {20},
  journal   = {Research and exposition in mathematics},
  editor    = {Denecke, Klaus-Dieter},
  publisher = {Heldermann},
  address   = {Berlin},
  isbn      = {3-88538-220-2},
  pages     = {237 S. : Ill.},
  year      = {1993},
  language  = {en}
}
@article{DeneckeKoppitz1999,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {A characterization of M-solid varieties of semigroups},
  year      = {1999},
  language  = {en}
}
@article{DeneckeJampachon1999,
  author    = {Denecke, Klaus-Dieter and Jampachon, Prakit},
  title     = {Regular-solid varieties of commutative and idempotent groupoids},
  year      = {1999},
  language  = {en}
}
@article{WismathKoppitzDenecke1997,
  author    = {Wismath, Shelly and Koppitz, J{\"o}rg and Denecke, Klaus-Dieter},
  title     = {Maps between M-solid varieties of emigroups},
  year      = {1997},
  language  = {en}
}
@article{DeneckeKoppitzMarszalek1998,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Marszalek, R.},
  title     = {Derived varieties and derived equational theories},
  year      = {1998},
  language  = {en}
}
@article{DeneckeKoppitz1998,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {M-solid monoids of hypersubstitutions of type 2},
  year      = {1998},
  language  = {en}
}
@article{DeneckeMarszalek1997,
  author    = {Denecke, Klaus-Dieter and Marszalek, R.},
  title     = {Binary relations on monoids of hypersubstitutions},
  year      = {1997},
  language  = {en}
}
@book{OPUS4-23744,
  title     = {General algebra and applications in discrete mathematics : proceedings of "Conference on General Algebra and Discrete Mathematics"},
  series = {Berichte aus der Mathematik},
  journal   = {Berichte aus der Mathematik},
  editor    = {Denecke, Klaus-Dieter},
  publisher = {Shaker},
  address   = {Aachen},
  isbn      = {3-8265-2431-4},
  pages     = {217 S. : graph. Darst.},
  year      = {1997},
  language  = {en}
}
@article{Denecke1998,
  author    = {Denecke, Klaus-Dieter},
  title     = {Tame congruence theory},
  year      = {1998},
  language  = {en}
}
@article{Denecke1998,
  author    = {Denecke, Klaus-Dieter},
  title     = {Hyperequational Theorie},
  year      = {1998},
  language  = {de}
}