@article{NitzeGrosseJonesetal.2018, author = {Nitze, Ingmar and Grosse, Guido and Jones, Benjamin M. and Romanovsky, Vladimir E. and Boike, Julia}, title = {Remote sensing quantifies widespread abundance of permafrost region disturbances across the Arctic and Subarctic}, series = {Nature Communications}, volume = {9}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-018-07663-3}, pages = {11}, year = {2018}, abstract = {Local observations indicate that climate change and shifting disturbance regimes are causing permafrost degradation. However, the occurrence and distribution of permafrost region disturbances (PRDs) remain poorly resolved across the Arctic and Subarctic. Here we quantify the abundance and distribution of three primary PRDs using time-series analysis of 30-m resolution Landsat imagery from 1999 to 2014. Our dataset spans four continental-scale transects in North America and Eurasia, covering similar to 10\% of the permafrost region. Lake area loss (-1.45\%) dominated the study domain with enhanced losses occurring at the boundary between discontinuous and continuous permafrost regions. Fires were the most extensive PRD across boreal regions (6.59\%), but in tundra regions (0.63\%) limited to Alaska. Retrogressive thaw slumps were abundant but highly localized (< 10(-5)\%). Our analysis synergizes the global-scale importance of PRDs. The findings highlight the need to include PRDs in next-generation land surface models to project the permafrost carbon feedback.}, language = {en} } @article{Roos2019, author = {Roos, Saskia}, title = {The Dirac operator under collapse to a smooth limit space}, series = {Annals of global analysis and geometry}, volume = {57}, journal = {Annals of global analysis and geometry}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {0232-704X}, doi = {10.1007/s10455-019-09691-8}, pages = {121 -- 151}, year = {2019}, abstract = {Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B.}, language = {en} } @article{GueneysuKeller2018, author = {G{\"u}neysu, Batu and Keller, Matthias}, title = {Scattering the Geometry of Weighted Graphs}, series = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics}, volume = {21}, journal = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics}, number = {3}, publisher = {Springer}, address = {Dordrecht}, issn = {1385-0172}, doi = {10.1007/s11040-018-9285-1}, pages = {15}, year = {2018}, abstract = {Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal.}, language = {en} } @article{FedchenkoTarkhanov2017, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Rado theorem for the porous medium equation}, series = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, volume = {24}, journal = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, number = {2}, publisher = {Springer}, address = {Cham}, issn = {1405-213X}, doi = {10.1007/s40590-017-0169-3}, pages = {427 -- 437}, year = {2017}, abstract = {We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.}, language = {en} } @article{DimitrovaKoppitz2017, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On the semigroup of all partial fence-preserving injections on a finite set}, series = {Journal of Algebra and Its Applications}, volume = {16}, journal = {Journal of Algebra and Its Applications}, number = {12}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-4988}, doi = {10.1142/S0219498817502231}, pages = {14}, year = {2017}, abstract = {For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn; infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.}, language = {en} } @article{LeungLeutbecherReichetal.2019, author = {Leung, Tsz Yan and Leutbecher, Martin and Reich, Sebastian and Shepherd, Theodore G.}, title = {Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier}, series = {Journal of the atmospheric sciences}, volume = {76}, journal = {Journal of the atmospheric sciences}, number = {12}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0022-4928}, doi = {10.1175/JAS-D-19-0057.1}, pages = {3883 -- 3892}, year = {2019}, abstract = {The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz's 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier-Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz's theory. Aided by numerical simulations, the present work reexamines Lorenz's model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than -3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than -3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz's theory is reconciled.}, language = {en} } @misc{BeckusBellissardDeNittis2019, author = {Beckus, Siegfried and Bellissard, Jean and De Nittis, Giuseppe}, title = {Corrigendum to: Spectral continuity for aperiodic quantum systems I. General theory. - [Journal of functional analysis. - 275 (2018), 11, S. 2917 - 2977]}, series = {Journal of functional analysis}, volume = {277}, journal = {Journal of functional analysis}, number = {9}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-1236}, doi = {10.1016/j.jfa.2019.06.001}, pages = {3351 -- 3353}, year = {2019}, abstract = {A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results.}, language = {en} } @article{FernandesKoppitzMusunthia2019, author = {Fernandes, Vitor H. and Koppitz, J{\"o}rg and Musunthia, Tiwadee}, title = {The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence}, series = {Bulletin of the Malaysian Mathematical Sciences Society volume}, volume = {42}, journal = {Bulletin of the Malaysian Mathematical Sciences Society volume}, number = {5}, publisher = {Malaysian mathematical sciences sciences soc}, address = {Pulau Punang}, issn = {0126-6705}, doi = {10.1007/s40840-017-0598-1}, pages = {2191 -- 2211}, year = {2019}, abstract = {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.}, language = {en} } @article{BeniniCapoferriDappiaggi2017, author = {Benini, Marco and Capoferri, Matteo and Dappiaggi, Claudio}, title = {Hadamard States for Quantum Abelian Duality}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {18}, journal = {Annales de l'Institut Henri Poincar{\´e}}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-017-0593-y}, pages = {3325 -- 3370}, year = {2017}, abstract = {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.}, language = {en} } @article{ShcherbakovZhuangZoelleretal.2019, author = {Shcherbakov, Robert and Zhuang, Jiancang and Z{\"o}ller, Gert and Ogata, Yosihiko}, title = {Forecasting the magnitude of the largest expected earthquake}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-019-11958-4}, pages = {11}, year = {2019}, abstract = {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.}, language = {en} } @article{KhalilSchulze2019, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Calculus on a Manifold with Edge and Boundary}, series = {Complex analysis and operator theory}, volume = {13}, journal = {Complex analysis and operator theory}, number = {6}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-018-0800-y}, pages = {2627 -- 2670}, year = {2019}, abstract = {We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel's algebra (Acta Math 126:11-51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.}, language = {en} } @article{ConfortiKosenkovaRoelly2019, author = {Conforti, Giovanni and Kosenkova, Tetiana and Roelly, Sylvie}, title = {Conditioned Point Processes with Application to Levy Bridges}, series = {Journal of theoretical probability}, volume = {32}, journal = {Journal of theoretical probability}, number = {4}, publisher = {Springer}, address = {New York}, issn = {0894-9840}, doi = {10.1007/s10959-018-0863-8}, pages = {2111 -- 2134}, year = {2019}, abstract = {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 L{\´e}vy 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 L{\´e}vy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample L{\´e}vy 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 L{\´e}vy processes like periodic Ornstein-Uhlenbeck processes driven by L{\´e}vy noise.}, language = {en} } @article{SalamatZoellerAmini2019, author = {Salamat, Mona and Z{\"o}ller, Gert and Amini, Morteza}, title = {Prediction of the Maximum Expected Earthquake Magnitude in Iran:}, series = {Pure and applied geophysics}, volume = {176}, journal = {Pure and applied geophysics}, number = {8}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-019-02141-3}, pages = {3425 -- 3438}, year = {2019}, abstract = {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 Z{\"o}ller 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 }}, language = {en} } @article{StaniforthWoodReich2006, author = {Staniforth, Andrew and Wood, Nigel and Reich, Sebastian}, title = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {132}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {621C}, publisher = {Wiley}, address = {Weinheim}, issn = {0035-9009}, doi = {10.1256/qj.06.30}, pages = {3107 -- 3116}, year = {2006}, abstract = {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.}, language = {en} } @article{KirscheBoeckmann2006, author = {Kirsche, Andreas and B{\"o}ckmann, Christine}, title = {Pade iteration method for regularization}, series = {Applied mathematics and computation}, volume = {180}, journal = {Applied mathematics and computation}, number = {2}, publisher = {Elsevier}, address = {New York}, issn = {0096-3003}, doi = {10.1016/j.amc.2006.01.011}, pages = {648 -- 663}, year = {2006}, abstract = {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.}, language = {en} } @article{Junek2020, author = {Junek, Heinz}, title = {Zyklizit{\"a}t in Raum, zeit und geist : {\"u}ber Pflasterungen, Rollkurven, Dezimalbr{\"u}che, Schwingungen, Wellen, Iteration und Neuronale Netze}, series = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {trafo}, address = {Berlin}, isbn = {978-3-86464-169-5}, pages = {85 -- 103}, year = {2020}, language = {de} } @article{Reich2006, author = {Reich, Sebastian}, title = {Linearly implicit time stepping methods for numerical weather prediction}, series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, volume = {46}, journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, publisher = {Springer}, address = {Dordrecht}, issn = {0006-3835}, doi = {10.1007/s10543-006-0065-0}, pages = {607 -- 616}, year = {2006}, abstract = {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.}, language = {en} } @article{BaerStrohmaier2019, author = {B{\"a}r, Christian and Strohmaier, Alexander}, title = {An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary}, series = {American Journal of Mathematics}, volume = {141}, journal = {American Journal of Mathematics}, number = {5}, publisher = {Johns Hopkins Univ. Press}, address = {Baltimore}, issn = {0002-9327}, doi = {10.1353/ajm.2019.0037}, pages = {1421 -- 1455}, year = {2019}, abstract = {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.}, language = {en} } @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} } @book{Denecke1997, author = {Denecke, Klaus-Dieter}, title = {Hyperequational theory}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 29}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {33 Bl.}, year = {1997}, language = {en} } @article{DeneckeWelke1997, author = {Denecke, Klaus-Dieter and Welke, Dirk}, title = {Solid varieties of partial algebras}, isbn = {5-7782-0175-3 (vol}, year = {1997}, language = {en} } @article{DeneckeLauPoescheletal.1995, author = {Denecke, Klaus-Dieter and Lau, Dietlinde and P{\"o}schel, Reinhard and Schweigert, D.}, title = {Free clones and solid varieties}, year = {1995}, language = {en} } @article{Denecke1994, author = {Denecke, Klaus-Dieter}, title = {On the characterization of primal partial algebras by strong regular hyperidentities}, year = {1994}, language = {en} } @article{DeneckeHalkowska1994, author = {Denecke, Klaus-Dieter and Halkowska, Katarzcyna}, title = {P-compatible hybrid-identities and hyperidentities}, year = {1994}, language = {en} } @article{DeneckeMalcev1994, author = {Denecke, Klaus-Dieter and Malcev, I. A.}, title = {Separation of clones by means of hyperidentities}, year = {1994}, language = {en} } @article{DeneckeWismath1994, author = {Denecke, Klaus-Dieter and Wismath, Shelly}, title = {Solid varieties of semigroups}, year = {1994}, language = {en} } @article{DeneckeKoppitz1994, author = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg}, title = {Hyperassociative semigroups}, year = {1994}, language = {en} } @article{Denecke1994, author = {Denecke, Klaus-Dieter}, title = {Pre-solid varieties}, year = {1994}, language = {en} } @book{DeneckeTodorov1994, author = {Denecke, Klaus-Dieter and Todorov, Kalco}, title = {Algebraische Grundlagen der Arithmetik}, series = {Berliner Studienreihe zur Mathematik}, volume = {4}, journal = {Berliner Studienreihe zur Mathematik}, publisher = {Heldermann}, address = {Berlin}, pages = {VIII, 200 S.}, year = {1994}, language = {de} } @article{LekkoksungDenecke2019, author = {Lekkoksung, Nareupanat and Denecke, Klaus-Dieter}, title = {The partial clone of linear tree languages}, series = {Siberian mathematical journal}, volume = {60}, journal = {Siberian mathematical journal}, number = {3}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0037-4466}, doi = {10.1134/S0037446619030121}, pages = {497 -- 507}, year = {2019}, abstract = {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.}, language = {en} } @article{DeneckePibaljommee2005, author = {Denecke, Klaus-Dieter and Pibaljommee, Bundit}, title = {Clones of implicit operations}, issn = {0002-5240}, year = {2005}, abstract = {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}, language = {en} } @article{DeneckeRadeleckiRatanaprasert2005, author = {Denecke, Klaus-Dieter and Radelecki, S. and Ratanaprasert, C.}, title = {On constantive simple and order-primal algebras}, year = {2005}, abstract = {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}, language = {en} } @article{ChangphasDenecke2005, author = {Changphas, Thawhat and Denecke, Klaus-Dieter}, title = {Green's relation R on the monoid of clone endomorphisms}, issn = {1005-3867}, year = {2005}, abstract = {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}, language = {en} } @article{ChangphasDenecke2003, author = {Changphas, Thawhat and Denecke, Klaus-Dieter}, title = {Green's Relations on the Seminearring of Full Hypersubstitutions of Type (n)}, year = {2003}, language = {en} } @article{DeneckePibaljommee2003, author = {Denecke, Klaus-Dieter and Pibaljommee, Bundit}, title = {Locally finite M-solid Varieties of Semigroups}, year = {2003}, language = {en} } @article{ChangphasDenecke2003, author = {Changphas, Thawhat and Denecke, Klaus-Dieter}, title = {Complexity of Hypersubstitutions and Lattices of Varieties}, year = {2003}, language = {en} } @phdthesis{Supaporn2014, author = {Supaporn, Worakrit}, title = {Categorical equivalence of clones}, pages = {89}, year = {2014}, language = {en} } @book{Denecke2003, author = {Denecke, Klaus-Dieter}, title = {Algebra und Diskrete Mathematik f{\"u}r Informatiker}, publisher = {Teubner}, address = {Stuttgart u.a.}, pages = {297 S.}, year = {2003}, abstract = {Algebra und Diskrete Mathematik geh{\"o}ren 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 {\"U}bungsaufgaben und ihre L{\"o}sungen helfen dem Leser, den Stoff zu verstehen}, language = {de} } @article{DeneckeJampachon2003, author = {Denecke, Klaus-Dieter and Jampachon, Prakit}, title = {N-solid Varieties and free Menger Algebras of rRnk n}, year = {2003}, language = {en} } @article{DeneckeJampachonWismath2003, author = {Denecke, Klaus-Dieter and Jampachon, Prakit and Wismath, Shelly}, title = {Clones of n-ary algebras}, year = {2003}, language = {en} } @article{DeneckePibaljommee2003, author = {Denecke, Klaus-Dieter and Pibaljommee, Bundit}, title = {Lattices of M-solid Generalized Varieties and M-solid Pseudovarieties}, year = {2003}, language = {en} } @article{DeneckeChangphas2003, author = {Denecke, Klaus-Dieter and Changphas, Thawhat}, title = {Full hypersubstitutions and fully solid varieties of semigroups}, year = {2003}, language = {en} } @article{DeneckeWismath2003, author = {Denecke, Klaus-Dieter and Wismath, Shelly}, title = {Complexity of Terms, Composition and Hypersubstitution}, year = {2003}, language = {en} } @article{DeneckeLeeratanavalee2003, author = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak}, title = {Tree transformations defined by generalized hypersubstitutions}, year = {2003}, language = {en} } @article{DeneckeLeeratanavalee2003, author = {Denecke, Klaus-Dieter and Leeratanavalee, Sorasak}, title = {The Semantical Kernel of a Generalized Hypersubstitution}, year = {2003}, language = {en} }