TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Golusin-Krylov Formulas in Complex Analysis T2 - Preprints des Instituts für Mathematik der Universität Potsdam N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 2 KW - analytic continuation KW - integral formulas KW - Cauchy problem Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102774 VL - 6 IS - 2 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Formal poincare lemma JF - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2007 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with parameter N2 - 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 Y1 - 2005 SN - 1061-9208 ER - TY - BOOK A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with a parameter T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with a parameter N2 - 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. T3 - Preprint - (2004) 02 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26677 ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Golusin-Krylov formulas in complex analysis JF - Complex variables and elliptic equations N2 - 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. KW - Analytic continuation KW - inegral formulas KW - Cauchy problem Y1 - 2017 U6 - https://doi.org/10.1080/17476933.2017.1395872 SN - 1747-6933 SN - 1747-6941 VL - 63 IS - 7-8 SP - 1142 EP - 1167 PB - Routledge CY - Abingdon ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Duality by reproducing kernels N2 - 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. T3 - Preprint - (2001) 26 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26095 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Formal Poincaré lemma N2 - 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. T3 - Preprint - (2007) 02 Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30231 ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators JF - Journal of differential equations N2 - 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. KW - Sturm-Liouville problem KW - Discontinuous Robin condition KW - Root function KW - Lipschitz domain KW - Non-coercive problem Y1 - 2013 U6 - https://doi.org/10.1016/j.jde.2013.07.029 SN - 0022-0396 SN - 1090-2732 VL - 255 IS - 10 SP - 3305 EP - 3337 PB - Elsevier CY - San Diego ER - TY - BOOK A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Duality by reproducing kernels T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Sturm-Liouville problems in domains with non-smooth edges N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)13 KW - Second order elliptic equations KW - non-coercive boundary conditions KW - root functions KW - weighted spaces Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67336 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)11 KW - Sturm-Liouville problems KW - discontinuous Robin condition KW - root functions KW - Lipschitz domains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57759 SN - 2193-6943 ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER EQUATIONS JF - INTERNATIONAL JOURNAL OF MODERN PHYSICS A N2 - 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. KW - Dyson-Schwinger equations KW - Hopf algebra of Feynman diagrams KW - counterterms KW - Picard-Fuchs equations KW - equi-singular connections Y1 - 2013 U6 - https://doi.org/10.1142/S0217751X13501704 SN - 0217-751X SN - 1793-656X VL - 28 IS - 32 PB - WORLD SCIENTIFIC PUBL CO PTE LTD CY - SINGAPORE ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - The global beta-functions from solutions of dyson-schwinger equations JF - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - 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. KW - Dyson-Schwinger equations KW - beta-functions KW - renormalization Hopf algebra KW - equi-singular connections Y1 - 2013 U6 - https://doi.org/10.1142/S0217732313501526 SN - 0217-7323 SN - 1793-6632 VL - 28 IS - 34 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - Motivic Dyson-Schwinger equations JF - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - 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. KW - Connes-Kreimer Hopf algebra KW - Dyson-Schwinger equations KW - equi-singular connections KW - motivic Feynman rules KW - Picard-Fuchs equations KW - universal Hopf algebra of renormalization Y1 - 2013 U6 - https://doi.org/10.1142/S0217751X13501029 SN - 0217-751X VL - 28 IS - 20 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - Counterterms in the context of the universal Hopf algebra of renormalization JF - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - The manuscript discovers a new interpretation of counterterms of renormalizable Quantum Field Theories in terms of formal expansions of decorated rooted trees. KW - Perturbative renormalization KW - renormalization Hopf algebra KW - counterterms KW - rooted trees Y1 - 2014 U6 - https://doi.org/10.1142/S0217751X14500456 SN - 0217-751X SN - 1793-656X VL - 29 IS - 8 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Shtrakov, Slavcho A1 - Koppitz, Jörg T1 - Stable varieties of semigroups and groupoids JF - Algebra universalis N2 - 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. KW - composition of terms KW - essential position in terms KW - stable variety Y1 - 2016 U6 - https://doi.org/10.1007/s00012-015-0359-7 SN - 0002-5240 SN - 1420-8911 VL - 75 SP - 85 EP - 106 PB - Springer CY - Basel ER - TY - JOUR A1 - Siddiqui, Tarique Adnan A1 - Maute, Astrid A1 - Pedatella, Nick A1 - Yamazaki, Yosuke A1 - Lühr, Hermann A1 - Stolle, Claudia T1 - On the variability of the semidiurnal solar and lunar tides of the equatorial electrojet during sudden stratospheric warmings JF - Annales geophysicae N2 - 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. Y1 - 2018 U6 - https://doi.org/10.5194/angeo-36-1545-2018 SN - 0992-7689 SN - 1432-0576 VL - 36 IS - 6 SP - 1545 EP - 1562 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Sinclair, Nathalie A1 - Bussi, Maria G. Bartolini A1 - de Villiers, Michael A1 - Jones, Keith A1 - Kortenkamp, Ulrich A1 - Leung, Allen A1 - Owens, Kay T1 - Recent research on geometry education: an ICME-13 survey team report JF - ZDM : The International Journal on Mathematics Education N2 - 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. KW - Geometry KW - Technology KW - Diagrams KW - Definitions KW - Gestures KW - Proving KW - Digital technology KW - Visuospatial reasoning Y1 - 2016 U6 - https://doi.org/10.1007/s11858-016-0796-6 SN - 1863-9690 SN - 1863-9704 VL - 48 SP - 691 EP - 719 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Siska, Veronika A1 - Jones, Eppie Ruth A1 - Jeon, Sungwon A1 - Bhak, Youngjune A1 - Kim, Hak-Min A1 - Cho, Yun Sung A1 - Kim, Hyunho A1 - Lee, Kyusang A1 - Veselovskaya, Elizaveta A1 - Balueva, Tatiana A1 - Gallego-Llorente, Marcos A1 - Hofreiter, Michael A1 - Bradley, Daniel G. A1 - Eriksson, Anders A1 - Pinhasi, Ron A1 - Bhak, Jong A1 - Manica, Andrea T1 - Genome-wide data from two early Neolithic East Asian individuals dating to 7700 years ago JF - Science Advances N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1126/sciadv.1601877 SN - 2375-2548 VL - 3 IS - 2 PB - American Assoc. for the Advancement of Science CY - Washington ER -