@unpublished{ShlapunovTarkhanov2017,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Golusin-Krylov Formulas in Complex Analysis},
  series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  volume    = {6},
  journal   = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102774},
  pages     = {25},
  year      = {2017},
  abstract  = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.},
  language  = {en}
}
@article{ShlapunovTarkhanov2007,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Formal poincare lemma},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {36 S.},
  year      = {2007},
  language  = {en}
}
@article{ShlapunovTarkhanov2005,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Mixed problems with parameter},
  issn      = {1061-9208},
  year      = {2005},
  abstract  = {Let X be a smooth n-dimensional manifold and D be an open connected set in X with smooth boundary OD. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Gamma subset of partial derivativeD, we obtain a family of mixed problems depending on a small parameter epsilon > 0. Although the mixed problems are subjected to a noncoercive boundary condition on partial derivativeDF in general, each of them is uniquely solvable in an appropriate Hilbert space D-T and the corresponding family {u(epsilon)} of solutions approximates the solution of the Cauchy problem in D-T whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in D-T is equivalent to the boundedness of the family {u(epsilon)}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing the solution. Examples for Dirac operators in the Euclidean space R-n are treated. In this case, we obtain a family of mixed boundary problems for the Helmholtz equation},
  language  = {en}
}
@book{ShlapunovTarkhanov2004,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Mixed problems with a parameter},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {28 S.},
  year      = {2004},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2004,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Mixed problems with a parameter},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26677},
  year      = {2004},
  abstract  = {Let X be a smooth n -dimensional manifold and D be an open connected set in X with smooth boundary ∂D. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Γ ⊂ ∂D we obtain a family of mixed problems depending on a small parameter ε > 0. Although the mixed problems are subject to a non-coercive boundary condition on ∂D\Γ in general, each of them is uniquely solvable in an appropriate Hilbert space DT and the corresponding family {uε} of solutions approximates the solution of the Cauchy problem in DT whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in DT is equivalent to the boundedness of the family {uε}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing its solution. Examples for Dirac operators in the Euclidean space Rn are considered. In the latter case we obtain a family of mixed boundary problems for the Helmholtz equation.},
  language  = {en}
}
@misc{ShlapunovTarkhanov2017,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Golusin-Krylov formulas in complex analysis},
  series = {Complex variables and elliptic equations},
  volume    = {63},
  journal   = {Complex variables and elliptic equations},
  number    = {7-8},
  publisher = {Routledge},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2017.1395872},
  pages     = {1142 -- 1167},
  year      = {2017},
  abstract  = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2001,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Duality by reproducing kernels},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26095},
  year      = {2001},
  abstract  = {Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2007,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Formal Poincar{\´e} lemma},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30231},
  year      = {2007},
  abstract  = {We show how the multiple application of the formal Cauchy-Kovalevskaya theorem leads to the main result of the formal theory of overdetermined systems of partial differential equations. Namely, any sufficiently regular system Au = f with smooth coefficients on an open set U ⊂ Rn admits a solution in smooth sections of a bundle of formal power series, provided that f satisfies a compatibility condition in U.},
  language  = {en}
}
@article{ShlapunovTarkhanov2013,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators},
  series = {Journal of differential equations},
  volume    = {255},
  journal   = {Journal of differential equations},
  number    = {10},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-0396},
  doi       = {10.1016/j.jde.2013.07.029},
  pages     = {3305 -- 3337},
  year      = {2013},
  abstract  = {We consider a Sturm-Liouville boundary value problem in a bounded domain D of R-n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on partial derivative D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact selfadjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types. (C) 2013 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@book{ShlapunovTarkhanov2001,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Duality by reproducing kernels},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {78 S.},
  year      = {2001},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2013,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Sturm-Liouville problems in domains with non-smooth edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67336},
  year      = {2013},
  abstract  = {We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2012,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57759},
  year      = {2012},
  abstract  = {We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.},
  language  = {en}
}
@article{ShojaeiFard2013,
  author    = {Shojaei-Fard, Ali},
  title     = {A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER EQUATIONS},
  series = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A},
  volume    = {28},
  journal   = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A},
  number    = {32},
  publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD},
  address   = {SINGAPORE},
  issn      = {0217-751X},
  doi       = {10.1142/S0217751X13501704},
  pages     = {15},
  year      = {2013},
  abstract  = {We study Dyson-Schwinger equations (DSEs) in terms of some groups of diffeographisms to provide a new geometric formulation for their corresponding counterterms on the basis of systems of ordinary differential equations.},
  language  = {en}
}
@article{ShojaeiFard2013,
  author    = {Shojaei-Fard, Ali},
  title     = {The global beta-functions from solutions of dyson-schwinger equations},
  series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {28},
  journal   = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {34},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0217-7323},
  doi       = {10.1142/S0217732313501526},
  pages     = {12},
  year      = {2013},
  abstract  = {We apply the geometric interpretation of Dyson-Schwinger equations (DSEs) in terms of equi-singular flat connections to provide a process which relates beta-functions of a DSE under different regularization schemes.},
  language  = {en}
}
@article{ShojaeiFard2013,
  author    = {Shojaei-Fard, Ali},
  title     = {Motivic Dyson-Schwinger equations},
  series = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {28},
  journal   = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {20},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0217-751X},
  doi       = {10.1142/S0217751X13501029},
  pages     = {19},
  year      = {2013},
  abstract  = {We consider Dyson-Schwinger Equations (DSEs) in the context of Connes-Kreimer renormalization Hopf algebra of Feynman diagrams and Connes-Marcolli universal Tannakian formalism. This study leads us to formulate a family of Picard-Fuchs equations and a category of Feynman motivic sheaves with respect to each combinatorial DSE.},
  language  = {en}
}
@article{ShojaeiFard2014,
  author    = {Shojaei-Fard, Ali},
  title     = {Counterterms in the context of the universal Hopf algebra of renormalization},
  series = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {29},
  journal   = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {8},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0217-751X},
  doi       = {10.1142/S0217751X14500456},
  pages     = {15},
  year      = {2014},
  abstract  = {The manuscript discovers a new interpretation of counterterms of renormalizable Quantum Field Theories in terms of formal expansions of decorated rooted trees.},
  language  = {en}
}
@article{ShtrakovKoppitz2016,
  author    = {Shtrakov, Slavcho and Koppitz, J{\"o}rg},
  title     = {Stable varieties of semigroups and groupoids},
  series = {Algebra universalis},
  volume    = {75},
  journal   = {Algebra universalis},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0002-5240},
  doi       = {10.1007/s00012-015-0359-7},
  pages     = {85 -- 106},
  year      = {2016},
  abstract  = {The paper deals with Sigma-composition and Sigma-essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type tau - (2) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms.},
  language  = {en}
}
@article{SiddiquiMautePedatellaetal.2018,
  author    = {Siddiqui, Tarique Adnan and Maute, Astrid and Pedatella, Nick and Yamazaki, Yosuke and L{\"u}hr, Hermann and Stolle, Claudia},
  title     = {On the variability of the semidiurnal solar and lunar tides of the equatorial electrojet during sudden stratospheric warmings},
  series = {Annales geophysicae},
  volume    = {36},
  journal   = {Annales geophysicae},
  number    = {6},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {0992-7689},
  doi       = {10.5194/angeo-36-1545-2018},
  pages     = {1545 -- 1562},
  year      = {2018},
  abstract  = {The variabilities of the semidiurnal solar and lunar tides of the equatorial electrojet (EEJ) are investigated during the 2003, 2006, 2009 and 2013 major sudden stratospheric warming (SSW) events in this study. For this purpose, ground-magnetometer recordings at the equatorial observatories in Huancayo and Fuquene are utilized. Results show a major enhancement in the amplitude of the EEJ semidiurnal lunar tide in each of the four warming events. The EEJ semidiurnal solar tidal amplitude shows an amplification prior to the onset of warmings, a reduction during the deceleration of the zonal mean zonal wind at 60 degrees N and 10 hPa, and a second enhancement a few days after the peak reversal of the zonal mean zonal wind during all four SSWs. Results also reveal that the amplitude of the EEJ semidiurnal lunar tide becomes comparable or even greater than the amplitude of the EEJ semidiurnal solar tide during all these warming events. The present study also compares the EEJ semidiurnal solar and lunar tidal changes with the variability of the migrating semidiurnal solar (SW2) and lunar (M2) tides in neutral temperature and zonal wind obtained from numerical simulations at E-region heights. A better agreement between the enhancements of the EEJ semidiurnal lunar tide and the M2 tide is found in comparison with the enhancements of the EEJ semidiurnal solar tide and the SW2 tide in both the neutral temperature and zonal wind at the E-region altitudes.},
  language  = {en}
}
@article{SinclairBussideVilliersetal.2016,
  author    = {Sinclair, Nathalie and Bussi, Maria G. Bartolini and de Villiers, Michael and Jones, Keith and Kortenkamp, Ulrich and Leung, Allen and Owens, Kay},
  title     = {Recent research on geometry education: an ICME-13 survey team report},
  series = {ZDM : The International Journal on Mathematics Education},
  volume    = {48},
  journal   = {ZDM : The International Journal on Mathematics Education},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1863-9690},
  doi       = {10.1007/s11858-016-0796-6},
  pages     = {691 -- 719},
  year      = {2016},
  abstract  = {This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.},
  language  = {en}
}
@article{SiskaJonesJeonetal.2017,
  author    = {Siska, Veronika and Jones, Eppie Ruth and Jeon, Sungwon and Bhak, Youngjune and Kim, Hak-Min and Cho, Yun Sung and Kim, Hyunho and Lee, Kyusang and Veselovskaya, Elizaveta and Balueva, Tatiana and Gallego-Llorente, Marcos and Hofreiter, Michael and Bradley, Daniel G. and Eriksson, Anders and Pinhasi, Ron and Bhak, Jong and Manica, Andrea},
  title     = {Genome-wide data from two early Neolithic East Asian individuals dating to 7700 years ago},
  series = {Science Advances},
  volume    = {3},
  journal   = {Science Advances},
  number    = {2},
  publisher = {American Assoc. for the Advancement of Science},
  address   = {Washington},
  issn      = {2375-2548},
  doi       = {10.1126/sciadv.1601877},
  pages     = {10},
  year      = {2017},
  abstract  = {Ancient genomes have revolutionized our understanding of Holocene prehistory and, particularly, the Neolithic transition in western Eurasia. In contrast, East Asia has so far received little attention, despite representing a core region at which the Neolithic transition took place independently ~3 millennia after its onset in the Near East. We report genome-wide data from two hunter-gatherers from Devil's Gate, an early Neolithic cave site (dated to ~7.7 thousand years ago) located in East Asia, on the border between Russia and Korea. Both of these individuals are genetically most similar to geographically close modern populations from the Amur Basin, all speaking Tungusic languages, and, in particular, to the Ulchi. The similarity to nearby modern populations and the low levels of additional genetic material in the Ulchi imply a high level of genetic continuity in this region during the Holocene, a pattern that markedly contrasts with that reported for Europe.},
  language  = {en}
}