TY - JOUR A1 - Lewandowski, Max T1 - Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes JF - Journal of mathematical physics N2 - 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 Hörmander [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 Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 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. Y1 - 2022 U6 - https://doi.org/10.1063/5.0055753 SN - 0022-2488 SN - 1089-7658 VL - 63 IS - 1 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Stolle, Claudia A1 - Michaelis, Ingo A1 - Rauberg, Jan T1 - The role of high-resolution geomagnetic field models for investigating ionospheric currents at low Earth orbit satellites JF - Earth, planets and space N2 - 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. KW - Geomagnetic field KW - Ionospheric current KW - Geomagnetic models Y1 - 2016 U6 - https://doi.org/10.1186/s40623-016-0494-1 SN - 1880-5981 VL - 68 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Chajada, I. A1 - Denecke, Klaus-Dieter A1 - Halas, R. T1 - Algebras induced by hypersubstitutions Y1 - 1999 ER - TY - THES A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - Sets of hypersubstitutions and set-solid varieties Y1 - 1999 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Normal forms of hypersubstitutions Y1 - 1999 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Leeratanavalee, Sorasak T1 - Weak hypersubstitutions and weakly derived algebras Y1 - 1999 ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - Left-edges solid varieties of differential groupoids Y1 - 1999 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Mruczek, Krysztyna T1 - P-compatible Hypersubstitutions Y1 - 2000 ER - TY - BOOK A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter A1 - Pöschel, Reinhard T1 - Closure operators on complete lattices T3 - Preprint MATH-ALG / Technische Universität Dresden Y1 - 1998 VL - 1998, 05 PB - Techn. Univ. CY - Dresden ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Finite monoids of hypersubstitutions of type € = (2) Y1 - 1998 ER - TY - BOOK A1 - Denecke, Klaus-Dieter A1 - Todorov, Kalco T1 - Osnovi na Aritmetikata Y1 - 1999 SN - 954-680-122-4 PB - Univ. Press CY - Blagoevgrad [Bulgarian] ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Clones closed with respect to closed operators Y1 - 1999 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Freiberg, L. T1 - The word problem for M-solid varieties of semigroups Y1 - 1998 SN - 981-3083-86-7 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Plonka, J. T1 - Regularization and normalization of solid varieties Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Reichel, Mario T1 - Monoids of hypersubstitutions and m-solid varieties Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Plonka, J. T1 - Edge-solid varieties Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Malcev, I. A. A1 - Reschke, M. T1 - On separation of Boolean clones by means of hyperidentities Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Pre-solid varieties of commutative semigroups Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - M-solid varieties of semigroups Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Pre-solid varieties of semigroups Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Hybrid identities and hybrid equational logic Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Clones and hyperidentities Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg A1 - Štrakov, Slavčo T1 - Multi-hypersubstitutions and colored solid varieties JF - International journal of algebra and computation N2 - 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. KW - coloration of terms KW - multi-hypersubstitutions KW - colored solid varieties Y1 - 2006 U6 - https://doi.org/10.1142/S0218196706003189 SN - 0218-1967 VL - 16 IS - 4 SP - 797 EP - 815 PB - World Scient. Publ. CY - Singapore ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - The partial clone of linear formulas JF - Siberian mathematical journal N2 - 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′). KW - term KW - formula KW - superposition KW - linear term KW - linear formula KW - clone KW - partial clone KW - linear hypersubstitution Y1 - 2019 U6 - https://doi.org/10.1134/S0037446619040037 SN - 0037-4466 SN - 1573-9260 VL - 60 IS - 4 SP - 572 EP - 584 PB - Pleiades Publ. CY - New York ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - Groupoids of hypersubstitutions and G-solid varieties Y1 - 1997 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Poomsa-ard, T. T1 - Hyperidentities in graph algebras Y1 - 1997 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Wismath, Shelly T1 - The monoid of hypersubstitutions of type (2) Y1 - 1997 ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - A new methods to study subvariety lattices of semigroup varieties Y1 - 1997 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Lüders, Otfried T1 - Category equivalences of clones Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - The entropy sequence of unary logical functions Y1 - 1996 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Clones and Hyperidentities Y1 - 1997 ER - TY - BOOK A1 - Denecke, Klaus-Dieter A1 - Todorov, Kalco T1 - Allgemeine Algebra und Anwendungen Y1 - 1996 PB - Shaker CY - Aachen ER - TY - BOOK A1 - Denecke, Klaus-Dieter T1 - Clones and hyperidentities T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1996 VL - 1996, 14 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - The partial clone of linear terms JF - Siberian Mathematical Journal N2 - 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. KW - linear term KW - clone KW - partial clone KW - linear hypersubstitution KW - linear identity KW - linear hyperidentity Y1 - 2016 U6 - https://doi.org/10.1134/S0037446616040030 SN - 0037-4466 SN - 1573-9260 VL - 57 SP - 589 EP - 598 PB - Pleiades Publ. CY - New York ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Wismath, Shelly T1 - The dimension of a variety and the kernel of a hypersubstitution N2 - 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). Y1 - 2009 UR - http://www.worldscinet.com/ijac/ U6 - https://doi.org/10.1142/S0218196709005342 SN - 0218-1967 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Saengsura, Kittisak T1 - Separation of clones of cooperations by cohyperidentities N2 - 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. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/0012365X U6 - https://doi.org/10.1016/j.disc.2008.01.043 SN - 0012-365X ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Congruences on maximal partial clones and strong regular varieties generated by preprimal partial algebras II Y1 - 1991 ER - TY - BOOK A1 - Denecke, Klaus-Dieter A1 - Wismath, Shelly L. T1 - Universal Algebra and Coalgebra Y1 - 2009 SN - 978-981-283745-5 PB - World Scientific Publ. Co CY - Singapore ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Strong regular varieties of partial algebras I Y1 - 1991 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Minimal algebras and category equivalences Y1 - 1991 ER - TY - BOOK ED - Denecke, Klaus-Dieter T1 - General algebra and applications T3 - Research and exposition in mathematics Y1 - 1993 SN - 3-88538-220-2 VL - 20 PB - Heldermann CY - Berlin ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - A characterization of M-solid varieties of semigroups Y1 - 1999 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Jampachon, Prakit T1 - Regular-solid varieties of commutative and idempotent groupoids Y1 - 1999 ER - TY - JOUR A1 - Wismath, Shelly A1 - Koppitz, Jörg A1 - Denecke, Klaus-Dieter T1 - Maps between M-solid varieties of emigroups Y1 - 1997 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg A1 - Marszalek, R. T1 - Derived varieties and derived equational theories Y1 - 1998 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - M-solid monoids of hypersubstitutions of type 2 Y1 - 1998 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Marszalek, R. T1 - Binary relations on monoids of hypersubstitutions Y1 - 1997 ER - TY - BOOK ED - Denecke, Klaus-Dieter T1 - General algebra and applications in discrete mathematics : proceedings of "Conference on General Algebra and Discrete Mathematics" T3 - Berichte aus der Mathematik Y1 - 1997 SN - 3-8265-2431-4 PB - Shaker CY - Aachen ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Tame congruence theory Y1 - 1998 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Hyperequational Theorie Y1 - 1998 ER -