@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{Denecke2020,
  author    = {Denecke, Klaus-Dieter},
  title     = {Partial clones},
  series = {Asian-European journal of mathematics : AEJM},
  volume    = {13},
  journal   = {Asian-European journal of mathematics : AEJM},
  number    = {8},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557120501612},
  pages     = {19},
  year      = {2020},
  abstract  = {A set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.},
  language  = {en}
}
@article{SomogyvariReich2020,
  author    = {Somogyv{\´a}ri, M{\´a}rk and Reich, Sebastian},
  title     = {Convergence tests for transdimensional Markov chains in geoscience imaging},
  series = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences},
  volume    = {52},
  journal   = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences},
  number    = {5},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1874-8961},
  doi       = {10.1007/s11004-019-09811-x},
  pages     = {651 -- 668},
  year      = {2020},
  abstract  = {Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles that are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.},
  language  = {en}
}
@article{Ly2020,
  author    = {Ly, Ibrahim},
  title     = {A Cauchy problem for the Cauchy-Riemann operator},
  series = {Afrika Matematika},
  volume    = {32},
  journal   = {Afrika Matematika},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1012-9405},
  doi       = {10.1007/s13370-020-00810-4},
  pages     = {69 -- 76},
  year      = {2020},
  abstract  = {We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.},
  language  = {en}
}
@article{MalassTarkhanov2020,
  author    = {Malass, Ihsane and Tarkhanov, Nikolaj Nikolaevič},
  title     = {A perturbation of the de Rham complex},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {13},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {5},
  publisher = {Siberian Federal University},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-5-519-532},
  pages     = {519 -- 532},
  year      = {2020},
  abstract  = {We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.},
  language  = {en}
}
@article{AlSaedyTarchanov2020,
  author    = {Al-Saedy, Ammar Jaffar Muhesin and Tarchanov, Nikolaj Nikolaevič},
  title     = {A degree theory for Lagrangian boundary value problems},
  series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  volume    = {13},
  journal   = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  number    = {1},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-1-5-25},
  pages     = {5 -- 25},
  year      = {2020},
  abstract  = {We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.},
  language  = {en}
}
@incollection{ClavierGuoPaychaetal.2020,
  author    = {Clavier, Pierre J. and Guo, Li and Paycha, Sylvie and Zhang, Bin},
  title     = {Renormalisation and locality},
  series = {Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 2},
  booktitle = {Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 2},
  publisher = {European Mathematical Society Publishing House},
  address   = {Z{\"u}rich},
  isbn      = {978-3-03719-205-4 print},
  doi       = {10.4171/205},
  pages     = {85 -- 132},
  year      = {2020},
  language  = {en}
}
@article{ChelkhLyTarkhanov2020,
  author    = {Chelkh, W. and Ly, Ibrahim and Tarkhanov, Nikolai},
  title     = {A remark on the Laplace transform},
  series = {Siberian Mathematical Journal},
  volume    = {61},
  journal   = {Siberian Mathematical Journal},
  number    = {4},
  publisher = {Consultants Bureau, Springer},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446620040151},
  pages     = {755 -- 762},
  year      = {2020},
  abstract  = {The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.},
  language  = {en}
}
@article{KellerSchwarz2020,
  author    = {Keller, Matthias and Schwarz, Michael},
  title     = {Courant's nodal domain theorem for positivity preserving forms},
  series = {Journal of spectral theory},
  volume    = {10},
  journal   = {Journal of spectral theory},
  number    = {1},
  publisher = {EMS Publishing House},
  address   = {Z{\"u}rich},
  issn      = {1664-039X},
  doi       = {10.4171/JST/292},
  pages     = {271 -- 309},
  year      = {2020},
  abstract  = {We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.},
  language  = {en}
}
@article{LyTarkhanov2020,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolaj Nikolaevič},
  title     = {Asymptotic expansions at nonsymmetric cuspidal points},
  series = {Mathematical notes},
  volume    = {108},
  journal   = {Mathematical notes},
  number    = {1-2},
  publisher = {Springer Science},
  address   = {New York},
  issn      = {0001-4346},
  doi       = {10.1134/S0001434620070238},
  pages     = {219 -- 228},
  year      = {2020},
  abstract  = {We study the asymptotics of solutions to the Dirichlet problem in a domain X subset of R3 whose boundary contains a singular point O. In a small neighborhood of this point, the domain has the form {z > root x(2) + y(4)}, i.e., the origin is a nonsymmetric conical point at the boundary. So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently in the case of nonsymmetric singular points. This problem was posed by V.A. Kondrat'ev in 2000. We establish a complete asymptotic expansion of solutions near the singular point.},
  language  = {en}
}