TY  - JOUR
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence
JF  - Bulletin of the Malaysian Mathematical Sciences Society volume
N2  - A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.
KW  - Transformation semigroups
KW  - Rank of semigroup
KW  - Idempotents
KW  - Order-preserving
KW  - Fence
KW  - Zig-zag order
Y1  - 2019
U6  - https://doi.org/10.1007/s40840-017-0598-1
SN  - 0126-6705
SN  - 2180-4206
VL  - 42
IS  - 5
SP  - 2191
EP  - 2211
PB  - Malaysian mathematical sciences sciences soc
CY  - Pulau Punang
ER  - 
TY  - JOUR
A1  - Benini, Marco
A1  - Capoferri, Matteo
A1  - Dappiaggi, Claudio
T1  - Hadamard States for Quantum Abelian Duality
JF  - Annales de l'Institut Henri Poincaré
N2  - Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a -algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states on this algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three -algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor and in the case of ultra-static globally hyperbolic spacetimes with compact Cauchy surfaces, we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors, we obtain a state for the full theory, ultimately implementing Abelian duality transformations as Hilbert space isomorphisms.
Y1  - 2017
U6  - https://doi.org/10.1007/s00023-017-0593-y
SN  - 1424-0637
SN  - 1424-0661
VL  - 18
SP  - 3325
EP  - 3370
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Shcherbakov, Robert
A1  - Zhuang, Jiancang
A1  - Zöller, Gert
A1  - Ogata, Yosihiko
T1  - Forecasting the magnitude of the largest expected earthquake
JF  - Nature Communications
N2  - The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.
Y1  - 2019
U6  - https://doi.org/10.1038/s41467-019-11958-4
SN  - 2041-1723
VL  - 10
PB  - Nature Publishing Group
CY  - London
ER  - 
TY  - JOUR
A1  - Conforti, Giovanni
A1  - Kosenkova, Tetiana
A1  - Roelly, Sylvie
T1  - Conditioned Point Processes with Application to Levy Bridges
JF  - Journal of theoretical probability
N2  - Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke’s formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump Lévy process in Rd with a height a can be interpreted as a Poisson point process on space–time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of Lévy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample Lévy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein–Uhlenbeck processes driven by Lévy noise.
KW  - Ornstein-Uhlenbeck
Y1  - 2019
U6  - https://doi.org/10.1007/s10959-018-0863-8
SN  - 0894-9840
SN  - 1572-9230
VL  - 32
IS  - 4
SP  - 2111
EP  - 2134
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Salamat, Mona
A1  - Zöller, Gert
A1  - Amini, Morteza
T1  - Prediction of the Maximum Expected Earthquake Magnitude in Iran:
BT  - from a Catalog with Varying Magnitude of Completeness and Uncertain Magnitudes
JF  - Pure and applied geophysics
N2  - This paper concerns the problem of predicting the maximum expected earthquake magnitude μ in a future time interval Tf given a catalog covering a time period T in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude m_{ max } for high levels of confidence (Salamat et al. 2017). Therefore, m_{ max } should be better replaced by μ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), μ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness ( {m0 = 5.5} ). In the current study, the Bayesian methodology developed by Zöller et al. (2014, 2015) is applied for the purpose of predicting μ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg-Richter law in the magnitude domain with a priori unknown a and b values which are first estimated by Bayes' theorem and subsequently used to estimate μ. Imposing different values of m_{ max } for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with Mw ≥ 7.5 in short Tf , whereas for long Tf, μ is almost equal to m_{ max }
KW  - Maximum expected earthquake magnitude
KW  - completeness levels
KW  - magnitude errors
KW  - Bayesian method
KW  - Iran
Y1  - 2019
U6  - https://doi.org/10.1007/s00024-019-02141-3
SN  - 0033-4553
SN  - 1420-9136
VL  - 176
IS  - 8
SP  - 3425
EP  - 3438
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Staniforth, Andrew
A1  - Wood, Nigel
A1  - Reich, Sebastian
T1  - A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations
JF  - Quarterly journal of the Royal Meteorological Society
N2  - A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations is proposed and analysed. Application of regularization to the geopotential field used in the momentum equations leads to an unconditionally stable scheme. The analysis, together with a fully nonlinear example application, suggests that this approach is a promising, efficient, and accurate alternative to traditional schemes.
KW  - regularization
KW  - temporal discretization
Y1  - 2006
U6  - https://doi.org/10.1256/qj.06.30
SN  - 0035-9009
VL  - 132
IS  - 621C
SP  - 3107
EP  - 3116
PB  - Wiley
CY  - Weinheim
ER  - 
TY  - JOUR
A1  - Kirsche, Andreas
A1  - Böckmann, Christine
T1  - Pade iteration method for regularization
JF  - Applied mathematics and computation
N2  - In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved.
KW  - Pade approximants
KW  - iterative regularization
KW  - ill-posed problem
Y1  - 2006
U6  - https://doi.org/10.1016/j.amc.2006.01.011
SN  - 0096-3003
VL  - 180
IS  - 2
SP  - 648
EP  - 663
PB  - Elsevier
CY  - New York
ER  - 
TY  - JOUR
A1  - Junek, Heinz
T1  - Zyklizität in Raum, zeit und geist : über Pflasterungen, Rollkurven, Dezimalbrüche, Schwingungen, Wellen, Iteration und Neuronale Netze
JF  - Zyklizität & Rhythmik: eine multidisziplinäre Vorlesungsreihe
Y1  - 2020
SN  - 978-3-86464-169-5
SP  - 85
EP  - 103
PB  - trafo
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Reich, Sebastian
T1  - Linearly implicit time stepping methods for numerical weather prediction
JF  - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2  - The efficient time integration of the dynamic core equations for numerical weather prediction (NWP) remains a key challenge. One of the most popular methods is currently provided by implementations of the semi-implicit semi-Lagrangian (SISL) method, originally proposed by Robert (J. Meteorol. Soc. Jpn., 1982). Practical implementations of the SISL method are, however, not without certain shortcomings with regard to accuracy, conservation properties and stability. Based on recent work by Gottwald, Frank and Reich (LNCSE, Springer, 2002), Frank, Reich, Staniforth, White and Wood (Atm. Sci. Lett., 2005) and Wood, Staniforth and Reich (Atm. Sci. Lett., 2006) we propose an alternative semi-Lagrangian implementation based on a set of regularized equations and the popular Stormer-Verlet time stepping method in the context of the shallow-water equations (SWEs). Ultimately, the goal is to develop practical implementations for the 3D Euler equations that overcome some or all shortcomings of current SISL implementations.
KW  - numerical weather prediction
KW  - linearly implicit time stepping methods
KW  - semi-Lagrangian method
KW  - Stormer-Verlet method
KW  - shallow-water equations
Y1  - 2006
U6  - https://doi.org/10.1007/s10543-006-0065-0
SN  - 0006-3835
VL  - 46
SP  - 607
EP  - 616
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Strohmaier, Alexander
T1  - An index theorem for Lorentzian manifolds with compact
spacelike Cauchy boundary
JF  - American Journal of Mathematics
N2  - We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.
Y1  - 2019
U6  - https://doi.org/10.1353/ajm.2019.0037
SN  - 0002-9327
SN  - 1080-6377
VL  - 141
IS  - 5
SP  - 1421
EP  - 1455
PB  - Johns Hopkins Univ. Press
CY  - Baltimore
ER  - 
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  - 
TY  - BOOK
A1  - Denecke, Klaus-Dieter
T1  - Hyperequational theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 29
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Welke, Dirk
T1  - Solid varieties of partial algebras
Y1  - 1997
SN  - 5-7782-0175-3 (vol
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Lau, Dietlinde
A1  - Pöschel, Reinhard
A1  - Schweigert, D.
T1  - Free clones and solid varieties
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - On the characterization of primal partial algebras by strong regular hyperidentities
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Halkowska, Katarzcyna
T1  - P-compatible hybrid-identities and hyperidentities
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Malcev, I. A.
T1  - Separation of clones by means of hyperidentities
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Wismath, Shelly
T1  - Solid varieties of semigroups
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Hyperassociative semigroups
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Pre-solid varieties
Y1  - 1994
ER  - 
TY  - BOOK
A1  - Denecke, Klaus-Dieter
A1  - Todorov, Kalco
T1  - Algebraische Grundlagen der Arithmetik
T3  - Berliner Studienreihe zur Mathematik
Y1  - 1994
VL  - 4
PB  - Heldermann
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Lekkoksung, Nareupanat
A1  - Denecke, Klaus-Dieter
T1  - The partial clone of linear tree languages
JF  - Siberian mathematical journal
N2  - A term, also called a tree, is said to be linear, if each variable occurs in the term only once. The linear terms and sets of linear terms, the so-called linear tree languages, play some role in automata theory and in the theory of formal languages in connection with recognizability. We define a partial superposition operation on sets of linear trees of a given type and study the properties of some many-sorted partial clones that have sets of linear trees as elements and partial superposition operations as fundamental operations. The endomorphisms of those algebras correspond to nondeterministic linear hypersubstitutions.
KW  - linear term
KW  - linear tree language
KW  - clone
KW  - partial clone
KW  - linear hypersubstitution
KW  - nondeterministic linear hypersubstitution
Y1  - 2019
U6  - https://doi.org/10.1134/S0037446619030121
SN  - 0037-4466
SN  - 1573-9260
VL  - 60
IS  - 3
SP  - 497
EP  - 507
PB  - Pleiades Publ.
CY  - New York
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Pibaljommee, Bundit
T1  - Clones of implicit operations
N2  - There is a close connection between a variety and its clone. The clone of a variety is a multibased algebra, where the different universes are the sets of n-ary terms over this variety for every natural number n and where the operations describe the superposition of terms of different arities. All projections are added as nullary operations. Subvarieties correspond to homomorphic images of clones. Subclones can be described by reducts of varieties, isomorphic clones by equivalent varieties. Clone identities correspond to hyperidentities and varieties of clones to hypervarieties. Pseudovarieties are classes of finite algebras which are closed under taking of subalgebras, homomorphic images and finite direct products. Pseudovarieties are important in the theories of finite state automata, rational languages, finite semigroups and their connections. In a very natural way, there arises the question for the clone of a pseudovariety. In the present paper, we will describe this algebraic structure
Y1  - 2005
SN  - 0002-5240
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Radelecki, S.
A1  - Ratanaprasert, C.
T1  - On constantive simple and order-primal algebras
N2  - A finite algebra A = (A; F-A) is said to be order-primal if its clone of all term operations is the set of all operations defined on A which preserve a given partial order <= on A. In this paper we study algebraic properties of order-primal algebras for connected ordered sets (A; <=). Such order-primal algebras are constantive, simple and have no non-identical automorphisms. We show that in this case F-A cannot have only unary fundamental operations or only one at least binary fundamental operation. We prove several properties of the varieties and the quasi-varieties generated by constantive and simple algebras and apply these properties to order-primal algebras. Further, we use the properties of order-primal algebras to formulate new primality criteria for finite algebras
Y1  - 2005
ER  - 
TY  - JOUR
A1  - Changphas, Thawhat
A1  - Denecke, Klaus-Dieter
T1  - Green's relation R on the monoid of clone endomorphisms
N2  - A hypersubstitution is a map which takes n-ary operation symbols to n-ary terms. Any such map can be uniquely extended to a map defined on the set W-tau(X) of all terms of type tau, and any two such extensions can be composed in a natural way. Thus, the set Hyp(tau) of all hypersubstitutions of type tau forms a monoid. In this paper, we characterize Green's relation R on the monoid Hyp(tau) for the type tau = (n, n). In this case, the monoid of all hypersubstitutions is isomorphic with the monoid of all Clone endomorphisms. The results can be applied to mutually derived varieties
Y1  - 2005
SN  - 1005-3867
ER  - 
TY  - JOUR
A1  - Changphas, Thawhat
A1  - Denecke, Klaus-Dieter
T1  - Green's Relations on the Seminearring of Full Hypersubstitutions of Type (n)
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Pibaljommee, Bundit
T1  - Locally finite M-solid Varieties of Semigroups
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Changphas, Thawhat
A1  - Denecke, Klaus-Dieter
T1  - Complexity of Hypersubstitutions and Lattices of Varieties
Y1  - 2003
ER  - 
TY  - THES
A1  - Supaporn, Worakrit
T1  - Categorical equivalence of clones
Y1  - 2014
ER  - 
TY  - BOOK
A1  - Denecke, Klaus-Dieter
T1  - Algebra und Diskrete Mathematik für Informatiker
N2  - Algebra und Diskrete Mathematik gehören zu den wesentlichen Grundlagen der Informatik. Sie sind unverzichtbare Werkzeuge eines jeden Informatikers und spielen daher auch im Studium eine zentrale Rolle. Das Lehrbuch vermittelt anschaulich und leicht nachvollziehbar die wichtigsten algebraischen Grundlagen der Informatik bis hin zur Gleichungstheorie der Universellen Algebra. Zahlreiche Übungsaufgaben und ihre Lösungen helfen dem Leser, den Stoff zu verstehen
Y1  - 2003
PB  - Teubner
CY  - Stuttgart u.a.
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Jampachon, Prakit
T1  - N-solid Varieties and free Menger Algebras of rRnk n
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Jampachon, Prakit
A1  - Wismath, Shelly
T1  - Clones of n-ary algebras
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Pibaljommee, Bundit
T1  - Lattices of M-solid Generalized Varieties and M-solid Pseudovarieties
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Changphas, Thawhat
T1  - Full hypersubstitutions and fully solid varieties of semigroups
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Wismath, Shelly
T1  - Complexity of Terms, Composition and Hypersubstitution
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Leeratanavalee, Sorasak
T1  - Tree transformations defined by generalized hypersubstitutions
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Leeratanavalee, Sorasak
T1  - The Semantical Kernel of a Generalized Hypersubstitution
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Wismath, Shelly
T1  - Valuations and Hypersubstitutions
Y1  - 2003
ER  - 
TY  - BOOK
A1  - Denecke, Klaus-Dieter
A1  - Wismath, Shelly
T1  - Hyperidentities and clones
T3  - Algebra, logic and aplications
N2  - The theory of hyperidentities generalises the equational theory of universal algebras and is applicable in several fields of science, especially in computer sciences. This book presents the theory of hyperidentities and its relation to clone identities. The basic concept of hypersubstitution is used to introduce the monoid of hypersubstitutions, hyperidentities, M-hyperidentities, solid and M-solid varieties. This work integrates into a coherent framework many results scattered throughout the literature over the last eighteen years. In addition, the book contains some applications of hyperidentities to the functional completenes problem in multiple-valued logic. The general theory is also extended to partial algberas. The last chapter contains a list of exercises and open problems with suggestions of future work in this area of research.
Y1  - 2000
SN  - 90-5699-235-X
VL  - 14
PB  - Gordon & Breach
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Solid polynomial varieties of semigroups which are definable by identities
Y1  - 2000
SN  - 3-85366-951-4
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Essential variables in weak hypersubstitutions
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Generalized hypersubstitutions and strongly solid varieties
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - BOOK
ED  - Denecke, Klaus-Dieter
ED  - Vogel, Hans-Jürgen
T1  - General algebra and applications : proceedings of the 59th Workshop on General Algebra ; 15th Conference for Young Algebraists, Potsdam 2000
T3  - Berichte aus der Mathematik
Y1  - 2000
SN  - 3-8265-7983-6
PB  - Shaker
CY  - Aachen
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - P-compatible hypersubstitutions and M_P -solid varieties
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Mahdavi, Kazem
T1  - The order of normal form hypersubstitutions of type 2
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Fluid, unsolid, and completely unsolid varieties
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Pabhapote, Nittiya
T1  - Tree-recognizers and tree-hyperrecognizers
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Arworn, Srichan
T1  - Intervals defined by M-solid varieties
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Hyperidentities in semigroups
Y1  - 2001
SN  - 90-5199-490-7
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - The galois correspondence between subvariety lattices and monoids of hypersubstitutions
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Arworn, Srichan
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Strongly luid and weakly unsolid varieties
Y1  - 2001
SN  - 1346-0862
ER  -