TY - JOUR A1 - Nitze, Ingmar A1 - Grosse, Guido A1 - Jones, Benjamin M. A1 - Romanovsky, Vladimir E. A1 - Boike, Julia T1 - Remote sensing quantifies widespread abundance of permafrost region disturbances across the Arctic and Subarctic JF - Nature Communications N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1038/s41467-018-07663-3 SN - 2041-1723 VL - 9 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Roos, Saskia T1 - The Dirac operator under collapse to a smooth limit space JF - Annals of global analysis and geometry N2 - 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. KW - Collapse KW - Dirac operator KW - Spin geometry Y1 - 2019 U6 - https://doi.org/10.1007/s10455-019-09691-8 SN - 0232-704X SN - 1572-9060 VL - 57 IS - 1 SP - 121 EP - 151 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Güneysu, Batu A1 - Keller, Matthias T1 - Scattering the Geometry of Weighted Graphs JF - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics N2 - 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. KW - Graphs KW - Laplacian KW - Scattering theory Y1 - 2018 U6 - https://doi.org/10.1007/s11040-018-9285-1 SN - 1385-0172 SN - 1572-9656 VL - 21 IS - 3 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Rado theorem for the porous medium equation JF - Boletin de la Sociedad Matemática Mexicana N2 - 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. KW - Quasilinear equations KW - Removable sets KW - Porous medium equation Y1 - 2017 U6 - https://doi.org/10.1007/s40590-017-0169-3 SN - 1405-213X SN - 2296-4495 VL - 24 IS - 2 SP - 427 EP - 437 PB - Springer CY - Cham ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On the semigroup of all partial fence-preserving injections on a finite set JF - Journal of Algebra and Its Applications N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1017/etds.2017.9 SN - 0143-3857 SN - 1469-4417 VL - 38 SP - 3012 EP - 3041 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Leung, Tsz Yan A1 - Leutbecher, Martin A1 - Reich, Sebastian A1 - Shepherd, Theodore G. T1 - Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier JF - Journal of the atmospheric sciences N2 - 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. KW - Atmosphere KW - Turbulence KW - Error analysis KW - Spectral analysis KW - models KW - distribution KW - Numerical weather prediction KW - forecasting Y1 - 2019 U6 - https://doi.org/10.1175/JAS-D-19-0057.1 SN - 0022-4928 SN - 1520-0469 VL - 76 IS - 12 SP - 3883 EP - 3892 PB - American Meteorological Soc. CY - Boston ER - TY - GEN A1 - Beckus, Siegfried A1 - Bellissard, Jean A1 - De Nittis, Giuseppe T1 - Corrigendum to: Spectral continuity for aperiodic quantum systems I. General theory. - [Journal of functional analysis. - 275 (2018), 11, S. 2917 – 2977] T2 - Journal of functional analysis N2 - A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results. KW - Haar system Y1 - 2019 U6 - https://doi.org/10.1016/j.jfa.2019.06.001 SN - 0022-1236 SN - 1096-0783 VL - 277 IS - 9 SP - 3351 EP - 3353 PB - Elsevier CY - San Diego ER - 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 -