TY  - INPR
A1  - Abed, Jamil
A1  - Schulze, Bert-Wolfgang
T1  - Operators with corner-degenerate symbols
N2  - We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The “full” calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near the conical exit to infinity.
T3  - Preprint - (2008) 01 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30299
ER  - 
TY  - INPR
A1  - Abed, Jamil
A1  - Schulze, Bert-Wolfgang
T1  - Edge-degenerate families of ΨDO’s on an infinite cylinder
N2  - We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.
T3  - Preprint - (2009) 01 
KW  - Edge-degenerate operators
KW  - parameter-dependent pseudodifferential operators
KW  - norm estimates with respect to a parameter
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30365
ER  - 
TY  - INPR
A1  - Abutalebi, Jubin
A1  - Clahsen, Harald
T1  - Bilingualism, cognition, and aging
T2  - Bilingualism : language and cognition.
N2  - Extract: Topics in psycholinguistics and the neurocognition of language rarely attract the attention of journalists or the general public. One topic that has done so, however, is the potential benefits of bilingualism for general cognitive functioning and development, and as a precaution against cognitive decline in old age. Sensational claims have been made in the public domain, mostly by journalists and politicians. Recently (September 4, 2014) The Guardian reported that “learning a foreign language can increase the size of your brain”, and Michael Gove, the UK's previous Education Secretary, noted in an interview with The Guardian (September 30, 2011) that “learning languages makes you smarter”. The present issue of BLC addresses these topics by providing a state-of-the-art overview of theoretical and experimental research on the role of bilingualism for cognition in children and adults.
Y1  - 2015
U6  - https://doi.org/10.1017/S1366728914000741
SN  - 1366-7289
SN  - 1469-1841
VL  - 18
IS  - 1
SP  - 1
EP  - 2
PB  - Cambridge Univ. Press
CY  - New York
ER  - 
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A1  - Nolan, S.
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A1  - Nowak, N.
A1  - Nozato, A.
A1  - O'Brien, P.
A1  - Ohira, Y.
A1  - Ohishi, M.
A1  - Ohm, S.
A1  - Ohoka, H.
A1  - Okuda, T.
A1  - Okumura, A.
A1  - Olive, J. -F.
A1  - Ong, R. A.
A1  - Orito, R.
A1  - Orr, M.
A1  - Osborne, J.
A1  - Ostrowski, M.
A1  - Otero, L. A.
A1  - Otte, N.
A1  - Ovcharov, E.
A1  - Oya, I.
A1  - Ozieblo, A.
A1  - Padilla, L.
A1  - Paiano, S.
A1  - Paillot, D.
A1  - Paizis, A.
A1  - Palanque, S.
A1  - Palatka, M.
A1  - Pallota, J.
A1  - Panagiotidis, K.
A1  - Panazol, J. -L.
A1  - Paneque, D.
A1  - Panter, M.
A1  - Paoletti, R.
A1  - Papayannis, Alexandros
A1  - Papyan, G.
A1  - Paredes, J. M.
A1  - Pareschi, G.
A1  - Parks, G.
A1  - Parraud, J. -M.
A1  - Parsons, D.
A1  - Arribas, M. Paz
A1  - Pech, M.
A1  - Pedaletti, G.
A1  - Pelassa, V.
A1  - Pelat, D.
A1  - Perez, M. D. C.
A1  - Persic, M.
A1  - Petrucci, P-O
A1  - Peyaud, B.
A1  - Pichel, A.
A1  - Pita, S.
A1  - Pizzolato, F.
A1  - Platos, L.
A1  - Platzer, R.
A1  - Pogosyan, L.
A1  - Pohl, M.
A1  - Pojmanski, G.
A1  - Ponz, J. D.
A1  - Potter, W.
A1  - Poutanen, J.
A1  - Prandini, E.
A1  - Prast, J.
A1  - Preece, R.
A1  - Profeti, F.
A1  - Prokoph, H.
A1  - Prouza, M.
A1  - Proyetti, M.
A1  - Puerto-Gimenez, I.
A1  - Puehlhofer, G.
A1  - Puljak, I.
A1  - Punch, M.
A1  - Pyziol, R.
A1  - Quel, E. J.
A1  - Quinn, J.
A1  - Quirrenbach, A.
A1  - Racero, E.
A1  - Rajda, P. J.
A1  - Ramon, P.
A1  - Rando, R.
A1  - Rannot, R. C.
A1  - Rataj, M.
A1  - Raue, M.
A1  - Reardon, P.
A1  - Reimann, O.
A1  - Reimer, A.
A1  - Reimer, O.
A1  - Reitberger, K.
A1  - Renaud, M.
A1  - Renner, S.
A1  - Reville, B.
A1  - Rhode, W.
A1  - Ribo, M.
A1  - Ribordy, M.
A1  - Richer, M. G.
A1  - Rico, J.
A1  - Ridky, J.
A1  - Rieger, F.
A1  - Ringegni, P.
A1  - Ripken, J.
A1  - Ristori, P. R.
A1  - Riviere, A.
A1  - Rivoire, S.
A1  - Rob, L.
A1  - Roeser, U.
A1  - Rohlfs, R.
A1  - Rojas, G.
A1  - Romano, Patrizia
A1  - Romaszkan, W.
A1  - Romero, G. E.
A1  - Rosen, S.
A1  - Lees, S. Rosier
A1  - Ross, D.
A1  - Rouaix, G.
A1  - Rousselle, J.
A1  - Rousselle, S.
A1  - Rovero, A. C.
A1  - Roy, F.
A1  - Royer, S.
A1  - Rudak, B.
A1  - Rulten, C.
A1  - Rupinski, M.
A1  - Russo, F.
A1  - Ryde, F.
A1  - Sacco, B.
A1  - Saemann, E. O.
A1  - Saggion, A.
A1  - Safiakian, V.
A1  - Saito, K.
A1  - Saito, T.
A1  - Saito, Y.
A1  - Sakaki, N.
A1  - Sakonaka, R.
A1  - Salini, A.
A1  - Sanchez, F.
A1  - Sanchez-Conde, M.
A1  - Sandoval, A.
A1  - Sandaker, H.
A1  - Sant'Ambrogio, E.
A1  - Santangelo, A.
A1  - Santos, E. M.
A1  - Sanuy, A.
A1  - Sapozhnikov, L.
A1  - Sarkar, S.
A1  - Sartore, N.
A1  - Sasaki, H.
A1  - Satalecka, K.
A1  - Sawada, M.
A1  - Scalzotto, V.
A1  - Scapin, V.
A1  - Scarcioffolo, M.
A1  - Schafer, J.
A1  - Schanz, T.
A1  - Schlenstedt, S.
A1  - Schlickeiser, R.
A1  - Schmidt, T.
A1  - Schmoll, J.
A1  - Schovanek, P.
A1  - Schroedter, M.
A1  - Schultz, C.
A1  - Schultze, J.
A1  - Schulz, A.
A1  - Schure, K.
A1  - Schwab, T.
A1  - Schwanke, U.
A1  - Schwarz, J.
A1  - Schwarzburg, S.
A1  - Schweizer, T.
A1  - Schwemmer, S.
A1  - Segreto, A.
A1  - Seiradakis, J. -H.
A1  - Sembroski, G. H.
A1  - Seweryn, K.
A1  - Sharma, M.
A1  - Shayduk, M.
A1  - Shellard, R. C.
A1  - Shi, J.
A1  - Shibata, T.
A1  - Shibuya, A.
A1  - Shum, E.
A1  - Sidoli, L.
A1  - Sidz, M.
A1  - Sieiro, J.
A1  - Sikora, M.
A1  - Silk, J.
A1  - Sillanpaa, A.
A1  - Singh, B. B.
A1  - Sitarek, J.
A1  - Skole, C.
A1  - Smareglia, R.
A1  - Smith, A.
A1  - Smith, D.
A1  - Smith, J.
A1  - Smith, N.
A1  - Sobczynska, D.
A1  - Sol, H.
A1  - Sottile, G.
A1  - Sowinski, M.
A1  - Spanier, F.
A1  - Spiga, D.
A1  - Spyrou, S.
A1  - Stamatescu, V.
A1  - Stamerra, A.
A1  - Starling, R.
A1  - Stawarz, L.
A1  - Steenkamp, R.
A1  - Stegmann, Christian
A1  - Steiner, S.
A1  - Stergioulas, N.
A1  - Sternberger, R.
A1  - Sterzel, M.
A1  - Stinzing, F.
A1  - Stodulski, M.
A1  - Straumann, U.
A1  - Strazzeri, E.
A1  - Stringhetti, L.
A1  - Suarez, A.
A1  - Suchenek, M.
A1  - Sugawara, R.
A1  - Sulanke, K. -H.
A1  - Sun, S.
A1  - Supanitsky, A. D.
A1  - Suric, T.
A1  - Sutcliffe, P.
A1  - Sykes, J.
A1  - Szanecki, M.
A1  - Szepieniec, T.
A1  - Szostek, A.
A1  - Tagliaferri, G.
A1  - Tajima, H.
A1  - Takahashi, H.
A1  - Takahashi, K.
A1  - Takalo, L.
A1  - Takami, H.
A1  - Talbot, C.
A1  - Tammi, J.
A1  - Tanaka, M.
A1  - Tanaka, S.
A1  - Tasan, J.
A1  - Tavani, M.
A1  - Tavernet, J. -P.
A1  - Tejedor, L. A.
A1  - Telezhinsky, Igor O.
A1  - Temnikov, P.
A1  - Tenzer, C.
A1  - Terada, Y.
A1  - Terrier, R.
A1  - Teshima, M.
A1  - Testa, V.
A1  - Tezier, D.
A1  - Thuermann, D.
A1  - Tibaldo, L.
A1  - Tibolla, O.
A1  - Tiengo, A.
A1  - Tluczykont, M.
A1  - Todero Peixoto, C. J.
A1  - Tokanai, F.
A1  - Tokarz, M.
A1  - Toma, K.
A1  - Torii, K.
A1  - Tornikoski, M.
A1  - Torres, D. F.
A1  - Torres, M.
A1  - Tosti, G.
A1  - Totani, T.
A1  - Toussenel, C.
A1  - Tovmassian, G.
A1  - Travnicek, P.
A1  - Trifoglio, M.
A1  - Troyano, I.
A1  - Tsinganos, K.
A1  - Ueno, H.
A1  - Umehara, K.
A1  - Upadhya, S. S.
A1  - Usher, T.
A1  - Uslenghi, M.
A1  - Valdes-Galicia, J. F.
A1  - Vallania, P.
A1  - Vallejo, G.
A1  - van Driel, W.
A1  - van Eldik, C.
A1  - Vandenbrouke, J.
A1  - Vanderwalt, J.
A1  - Vankov, H.
A1  - Vasileiadis, G.
A1  - Vassiliev, V.
A1  - Veberic, D.
A1  - Vegas, I.
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A1  - Vergani, S.
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A1  - Vincent, P.
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A1  - Vink, J.
A1  - Vlahakis, N.
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A1  - Vollhardt, A.
A1  - von Gunten, H. P.
A1  - Vorobiov, S.
A1  - Vuerli, C.
A1  - Waegebaert, V.
A1  - Wagner, R.
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A1  - Webb, N.
A1  - Wegner, P.
A1  - Weinstein, A.
A1  - Weitzel, Q.
A1  - Welsing, R.
A1  - Werner, M.
A1  - Wetteskind, H.
A1  - White, R.
A1  - Wierzcholska, A.
A1  - Wiesand, S.
A1  - Wilkinson, M.
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A1  - Willingale, R.
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A1  - Wood, M.
A1  - Woernlein, A.
A1  - Xiong, Q.
A1  - Yadav, K. K.
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A1  - Yamamoto, T.
A1  - Yamazaki, R.
A1  - Yanagita, S.
A1  - Yebras, J. M.
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A1  - Yoshida, A.
A1  - Yoshida, T.
A1  - Yoshikoshi, T.
A1  - Zabalza, V.
A1  - Zacharias, M.
A1  - Zajczyk, A.
A1  - Zanin, R.
A1  - Zdziarski, A.
A1  - Zech, Alraune
A1  - Zhao, A.
A1  - Zhou, X.
A1  - Zietara, K.
A1  - Ziolkowski, J.
A1  - Ziolkowski, P.
A1  - Zitelli, V.
A1  - Zurbach, C.
A1  - Zychowski, P.
T1  - Introducing the CTA concept
T2  - Astroparticle physics
N2  - The Cherenkov Telescope Array (CTA) is a new observatory for very high-energy (VHE) gamma rays. CTA has ambitions science goals, for which it is necessary to achieve full-sky coverage, to improve the sensitivity by about an order of magnitude, to span about four decades of energy, from a few tens of GeV to above 100 TeV with enhanced angular and energy resolutions over existing VHE gamma-ray observatories. An international collaboration has formed with more than 1000 members from 27 countries in Europe, Asia, Africa and North and South America. In 2010 the CTA Consortium completed a Design Study and started a three-year Preparatory Phase which leads to production readiness of CTA in 2014. In this paper we introduce the science goals and the concept of CTA, and provide an overview of the project.
KW  - TeV gamma-ray astronomy
KW  - Air showers
KW  - Cherenkov Telescopes
Y1  - 2013
U6  - https://doi.org/10.1016/j.astropartphys.2013.01.007
SN  - 0927-6505
SN  - 1873-2852
VL  - 43
IS  - 2
SP  - 3
EP  - 18
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - INPR
A1  - Airapetyan, Ruben
A1  - Witt, Ingo
T1  - Isometric properties of the Hankel Transformation in weighted sobolev spaces
N2  - It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.
T3  - Preprint - (1997) 14 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25001
ER  - 
TY  - INPR
A1  - Aizenberg, Lev A.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Bohr phenomenon for elliptic equations
N2  - In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.
T3  - Preprint - (1999) 18 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25547
ER  - 
TY  - INPR
A1  - Aizenberg, Lev A.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Stable expansions in homogeneous polynomials
N2  - An expansion for a class of functions is called stable if the partial sums are bounded uniformly in the class. Stable expansions are of key importance in numerical analysis where functions are given up to certain error. We show that expansions in homogeneous functions are always stable on a small ball around the origin, and evaluate the radius of the largest ball with this property.
T3  - Preprint - (2005) 16 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29925
ER  - 
TY  - INPR
A1  - Aizenberg, Lev A.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An integral formula for the number of lattice points in a domain
N2  - Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 3 
KW  - logarithmic residue
KW  - lattice point
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70453
SN  - 2193-6943
VL  - 3
IS  - 3
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
T1  - Variational primitive of a differential form
N2  - In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 4 
KW  - Dirichlet-to-Neumann operator
KW  - Cauchy problem
KW  - p-Laplace operator
KW  - calculus of variations
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-89223
SN  - 2193-6943
VL  - 5
IS  - 4
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The method of Fischer-Riesz equations for elliptic boundary value problems
N2  - We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)24 
KW  - Boundary value problems for first order systems
KW  - Green formula
KW  - Fischer-Riesz equations
KW  - regularisation
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-61792
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Weak boundary values of solutions of Lagrangian problems
N2  - We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result 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 the study of Lagrangian problems.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 2 
KW  - nonlinear equations
KW  - Lagrangian system
KW  - weak boundary values
KW  - quasilinear Fredholm operator
KW  - mapping degree
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72617
SN  - 2193-6943
VL  - 4
IS  - 2
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Spectral projection for the dbar-Neumann problem
N2  - We show that the spectral kernel function of the dbar-Neumann problem on a non-compact strongly pseudoconvex manifold is smooth up to the boundary.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)12 
KW  - dbar-Neumann problem
KW  - strongly pseudoconvex domains
KW  - spectral kernel function
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-58616
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Hilbert boundary value problem for generalised Cauchy-Riemann equations
N2  - We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed
problems, and construct an explicit formula for approximate solutions.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 1 
KW  - Dirac operator
KW  - Clifford algebra
KW  - Riemann-Hilbert problem
KW  - Fredholm operator
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86109
SN  - 2193-6943
VL  - 5
IS  - 1
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Normally solvable nonlinear boundary value problems
N2  - We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)11 
KW  - Nonlinear Laplace operator
KW  - boundary value problem
KW  - Dirichlet to Neumann operator
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-65077
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Anders, Martin
T1  - Martingale, Amarts und das starke Gesetz der Grossen Zahlen
N2  - Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ für identisch verteilte Zufallsvariablen 3. SGGZ für Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einführung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzsätze 5. Doob-Zerlegung 6. Eine äquivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichmäßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5.”reversed“ (Sub-,Super-)Martingale 1. Konvergenzsätze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. Äquivalente Formulierung eines (Sub-)Martingals 2. Konvergenzsätze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzsätze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9.”reversed“ Amarts und Semiamarts 1. Konvergenzsätze 2.”Aufwärts“- gegen ”Abwärts“-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilitätsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzsätze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabhängiger Zufallsvariablen B. Konvergenz
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 01 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49494
ER  - 
TY  - INPR
A1  - Angelow, Jürgen
T1  - Latest representations and perspectives on the outbreak of the first world war
T2  - Historisches Jahrbuch
Y1  - 2015
SN  - 0018-2621
VL  - 135
SP  - 569
EP  - 583
PB  - Alber
CY  - Freiburg Breisgau
ER  - 
TY  - INPR
A1  - Antoniouk, Alexandra Viktorivna
A1  - Kiselev, Oleg
A1  - Stepanenko, Vitaly
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point
N2  - The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)25 
KW  - Heat equation
KW  - the first boundary value problem
KW  - characteristic boundary point
KW  - cusp
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-61987
ER  - 
TY  - INPR
A1  - Arnold, Holger
T1  - A linearized DPLL calculus with clause learning (2nd, revised version)
N2  - Many formal descriptions of DPLL-based SAT algorithms either do not include all essential proof techniques applied by modern SAT solvers or are bound to particular heuristics or data structures. This makes it difficult to analyze proof-theoretic properties or the search complexity of these algorithms. In this paper we try to improve this situation by developing a nondeterministic proof calculus that models the functioning of SAT algorithms based on the DPLL calculus with clause learning. This calculus is independent of implementation details yet precise enough to enable a formal analysis of realistic DPLL-based SAT algorithms.
N2  - Viele formale Beschreibungen DPLL-basierter SAT-Algorithmen enthalten entweder nicht alle wesentlichen Beweistechniken, die in modernen SAT-Solvern implementiert sind, oder sind an bestimmte Heuristiken oder Datenstrukturen gebunden. Dies erschwert die Analyse beweistheoretischer Eigenschaften oder der Suchkomplexität derartiger Algorithmen. Mit diesem Artikel versuchen wir, diese Situation durch die Entwicklung eines nichtdeterministischen Beweiskalküls zu verbessern, der die Arbeitsweise von auf dem DPLL-Kalkül basierenden SAT-Algorithmen mit Klausellernen modelliert. Dieser Kalkül ist unabhängig von Implementierungsdetails, aber dennoch präzise genug, um eine formale Analyse realistischer DPLL-basierter SAT-Algorithmen zu ermöglichen.
KW  - Automatisches Beweisen
KW  - Logikkalkül
KW  - SAT
KW  - DPLL
KW  - Klausellernen
KW  - automated theorem proving
KW  - logical calculus
KW  - SAT
KW  - DPLL
KW  - clause learning
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29080
ER  - 
TY  - INPR
A1  - Asendorpf, Jens B.
A1  - Conner, Mark
A1  - De Fruyt, Filip
A1  - De Houwer, Jan
A1  - Denissen, Jaap J. A.
A1  - Fiedler, Klaus
A1  - Fiedler, Susann
A1  - Funder, David C.
A1  - Kliegl, Reinhold
A1  - Nosek, Brian A.
A1  - Perugini, Marco
A1  - Roberts, Brent W.
A1  - Schmitt, Manfred
A1  - Van Aken, Marcel A. G.
A1  - Weber, Hannelore
A1  - Wicherts, Jelte M.
T1  - Replication is more than hitting the lottery twice
T2  - European journal of personality
N2  - The main goal of our target article was to provide concrete recommendations for improving the replicability of research findings. Most of the comments focus on this point. In addition, a few comments were concerned with the distinction between replicability and generalizability and the role of theory in replication. We address all comments within the conceptual structure of the target article and hope to convince readers that replication in psychological science amounts to much more than hitting the lottery twice.
Y1  - 2013
SN  - 0890-2070
VL  - 27
IS  - 2
SP  - 138
EP  - 144
PB  - Wiley-Blackwell
CY  - Hoboken
ER  - 
TY  - INPR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Differential invariants of a class of Lagrangian systems with two degrees of freedom
N2  - We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 2 
KW  - equivalence
KW  - invariant
KW  - Euler-Lagrange equations
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63129
ER  - 
TY  - INPR
A1  - Bagdonavičius, Vilijandas B.
A1  - Levuliene, Ruta
A1  - Nikulin, Mikhail S.
A1  - Zdorova-Cheminade, Olga
T1  - Tests for homogeneity of survival distributions against non-location alternatives and analysis of the gastric cancer data
N2  - The two and k-sample tests of equality of the survival distributions against the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 03 
KW  - Censoring
KW  - Cross-effects
KW  - Kolmogorov-Smirnov type tests
KW  - Logrank test
KW  - Non-proportional hazards
KW  - Proportional hazards
KW  - Two-sample tests
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51527
ER  - 
TY  - INPR
A1  - Balazadeh, Salma
T1  - Stay-green not always stays green
T2  - Molecular plant
Y1  - 2014
U6  - https://doi.org/10.1093/mp/ssu076
SN  - 1674-2052
SN  - 1752-9867
VL  - 7
IS  - 8
SP  - 1264
EP  - 1266
PB  - Cell Press
CY  - Cambridge
ER  - 
TY  - INPR
A1  - Baret, Jean-Christophe
A1  - Belder, Detlev
A1  - Bier, Frank Fabian
A1  - Cao, Jialan
A1  - Gruschke, Oliver
A1  - Hardt, Steffen
A1  - Kirschbaum, Michael
A1  - Koehler, J. Michael
A1  - Schumacher, Soeren
A1  - Urban, G. A.
A1  - Viefhues, Martina
T1  - Contributors to the 10th Anniversary Germany issue
T2  - LAB on a chip : miniaturisation for chemistry and biology
Y1  - 2012
U6  - https://doi.org/10.1039/c1lc90139g
SN  - 1473-0197
VL  - 12
IS  - 3
SP  - 419
EP  - 421
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  - 
TY  - INPR
A1  - Baudis, Stefan
A1  - Behl, Marc
A1  - Lendlein, Andreas
T1  - Smart polymers for biomedical applications
T2  - Macromolecular chemistry and physics
Y1  - 2014
U6  - https://doi.org/10.1002/macp.201400561
SN  - 1022-1352
SN  - 1521-3935
VL  - 215
IS  - 24
SP  - 2399
EP  - 2402
PB  - Wiley-VCH
CY  - Weinheim
ER  - 
TY  - INPR
A1  - Baumann, Stefan
A1  - Kügler, Frank
T1  - Prosody and information status in typological perspective - Introduction to the Special Issue
T2  - Lingua : international review of general linguistics
Y1  - 2015
U6  - https://doi.org/10.1016/j.lingua.2015.08.001
SN  - 0024-3841
SN  - 1872-6135
VL  - 165
SP  - 179
EP  - 182
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - INPR
A1  - Baur, Heiner
A1  - Hoffmann, Jan
A1  - Reichmuth, Anne
A1  - Müller, Steffen
A1  - Mayer, Frank
T1  - Influence of carbon fiber foot orthoses on plantar pressure distribution in cycling
T2  - Sportverletzung, Sportschaden : Grundlagen, Prävention, Rehabilitation
N2  - Background: Several equipment interventions like optimizing seat position or optimizing shoe/insole/pedal interface are suggested to reduce overuse injury in cycling. Data analyzing clinical or biomechanical effects of those interventions is sparse. Foot orthoses out of carbon fiber are one possibility to alter the interface between foot and pedal. The aim of this study was therefore to analyze plantar pressure distribution in carbon fiber foot orthoses in comparison to standard insoles of commercially available cycling shoes. Materials and Methods: 11 pain-free triathletes (Age: 29 +/- 9, 1.77 +/- 0.04 m, 68 5 kg) were tested on a cycle ergometer at 60 and 90 rotations per minute (rpm) at workloads of 200 and 300 Watts. Subjects wore in randomized order a cycling shoe with its standard insole (control condition CO) or the shoe with carbon fiber foot orthoses (Condition CA). Mean peak pressure out of 30 movement cycles were extracted for the total foot and specific foot regions (rear, mid, fore foot (medial, central, lateral) and toe region). Three-factor ANOVAs (factor foot orthoses, rpm, workload) for repeated measures (alpha = 0.05) were used to analyze the main question of a foot orthoses effect on peak in-shoe plantar pressure. Results: Peak pressures in the total foot were in a range of 70-75 kPa for 200 Watts (W) (300 W: 85-110 kPa). The carbon fiber foot orthoses reduced peak pressures by -4,1% compared to the standard insole (p = 0,10). In the foot regions rear(-16,6%, p<0.001), mid (-20,0%, p<0.001) and fore foot (-5.9%, p < 0.03)CA reduced peak pressure compared to CO. In the toe region, peak pressure was higher in CA (+16,2%) compared to CO (p<0,001). The lateral fore foot showed higher peak pressures in CA (+34%) and CO (+59%) compared to medial and central fore foot. Conclusion: Carbon fiber can serve as a suitable material for foot orthoses manufacturing in cycling. Plantar pressures do not increase due to the stiffness of the carbon. Individual customization may have the potential to reduce peak pressure in certain foot areas.
KW  - Carbon
KW  - Cycling
KW  - Foot orthoses
KW  - In-shoe measurement
KW  - Plantar Pressure Distribution
Y1  - 2012
SN  - 0932-0555
VL  - 26
IS  - 1
SP  - 12
EP  - 17
PB  - Thieme
CY  - Stuttgart
ER  - 
TY  - INPR
A1  - Berman, Gennady
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Quantum dynamics in the Fermi-Pasta-Ulam problem
N2  - We study the dynamics of four wave interactions in a nonlinear quantum chain of oscillators under the "narrow packet" approximation. We determine the set of times for which the evolution of decay processes is essentially specified by quantum effects. Moreover, we highlight the quantum increment of instability.
T3  - Preprint - (2004) 05 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26695
ER  - 
TY  - INPR
A1  - Blanchard, Gilles
A1  - Delattre, Sylvain
A1  - Roquain, Étienne
T1  - Testing over a continuum of null hypotheses
N2  - We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochastic process over a continuum. As a measure of type I error, we extend the concept of false discovery rate (FDR) to this setting. The FDR is defined as the average ratio of the measure of two random sets, so that its study presents some challenge and is of some intrinsic mathematical interest. Our main result shows how to use the p-value process to control the FDR at a nominal level, either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting, the latter one leading to a less conservative procedure. The interest of this approach is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables. Conceptually, an interesting feature of the setting advocated here is that it focuses directly on the intrinsic hypothesis space associated with a testing model on a random process, without referring to an arbitrary discretization.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 1 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56877
ER  - 
TY  - INPR
A1  - Blanchard, Gilles
A1  - Krämer, Nicole
T1  - Convergence rates of kernel conjugate gradient for random design regression
N2  - We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true
regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 8 
KW  - nonparametric regression
KW  - reproducing kernel Hilbert space
KW  - conjugate gradient
KW  - partial least squares
KW  - minimax convergence rates
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-94195
SN  - 2193-6943
VL  - 5
IS  - 8
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Blanchard, Gilles
A1  - Mathé, Peter
T1  - Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration
N2  - The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 7 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57117
ER  - 
TY  - INPR
A1  - Blanchard, Gilles
A1  - Mücke, Nicole
T1  - Optimal rates for regularization of statistical inverse learning problems
N2  - We consider a statistical inverse learning problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points X_i, superposed with an additional noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependence of the constant factor in the variance of the noise and the radius of the source condition set.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 5 
KW  - statistical inverse problem
KW  - minimax rate
KW  - kernel method
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-89782
SN  - 2193-6943
VL  - 5
IS  - 5
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Brauer, Uwe
A1  - Karp, Lavi
T1  - Well-posedness of Einstein-Euler systems in asymptotically flat spacetimes
N2  - We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein{Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. In order to achieve our goals we are enforced, by the complexity of the problem, to deal with these equations in a new type of weighted Sobolev spaces of fractional order. Beside their construction, we develop tools for PDEs and techniques for hyperbolic and elliptic equations in these spaces. The well posedness is obtained in these spaces.
T3  - Preprint - (2008) 07 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30347
ER  - 
TY  - INPR
A1  - Brauer, Uwe
A1  - Karp, Lavi
T1  - Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order
N2  - We prove the existence of a class of local in time solutions, including static solutions, of the Einstein-Euler system. This result is the relativistic generalisation of a similar result for the Euler-Poisson system obtained by Gamblin [8]. As in his case the initial data of the density do not have compact support but fall off at infinity in an appropriate manner. An essential tool in our approach is the construction and use of weighted Sobolev spaces of fractional order. Moreover, these new spaces allow us to improve the regularity conditions for the solutions of evolution equations. The details of this construction, the properties of these spaces and results on elliptic and hyperbolic equations will be presented in a forthcoming article.
T3  - Preprint - (2006) 17 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30175
ER  - 
TY  - INPR
A1  - Braun, Karl-Heinz
A1  - Brechenmacher, Thomas
A1  - Damberg, Wilhelm
A1  - Felten, Franz J.
A1  - Kampmann, Christoph
A1  - Koerner, Hans-Michael
A1  - Schindling, Anton
T1  - Editiorial
T2  - Historisches Jahrbuch
Y1  - 2014
SN  - 0018-2621
VL  - 134
SP  - IX
EP  - IX
PB  - Alber
CY  - Freiburg Breisgau
ER  - 
TY  - INPR
A1  - Braun, Robert
A1  - Feudel, Fred
T1  - Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation
N2  - We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.
T3  - NLD Preprints - 29 
Y1  - 1996
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14099
ER  - 
TY  - INPR
A1  - Braun, Robert
A1  - Feudel, Fred
A1  - Guzdar, Parvez
T1  - The route to chaos for a two-dimensional externally driven flow
N2  - We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.
T3  - NLD Preprints - 46 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14717
ER  - 
TY  - INPR
A1  - Braun, Robert
A1  - Feudel, Fred
A1  - Seehafer, Norbert
T1  - Bifurcations and chaos in an array of forced vortices
N2  - We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.
T3  - NLD Preprints - 37 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14564
ER  - 
TY  - INPR
A1  - Buchholz, Thilo
A1  - Schulze, Bert-Wolfgang
T1  - Volterra operators and parabolicity : anisotropic pseudo-differential operators
N2  - Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.
T3  - Preprint - (1998) 11 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25231
ER  - 
TY  - INPR
A1  - Burgold, Julia
A1  - Frenzel, Fabian
A1  - Rolfes, Manfred
T1  - Observations on slums and their touristification
T2  - Die Erde : journal of the Geographical Society of Berlin ; Zeitschrift der Gesellschaft für Erdkunde zu Berlin
Y1  - 2013
SN  - 0013-9998
VL  - 144
IS  - 2
SP  - CP2
EP  - 104
PB  - Gesellschaft für Erdkunde
CY  - Berlin
ER  - 
TY  - INPR
A1  - Bär, Christian
T1  - Renormalized integrals and a path integral formula for the heat kernel on a manifold
N2  - We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an L^p function. We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)21 
KW  - Renormalized integral
KW  - path integral
KW  - Feynman-Kac formula
KW  - generalized Laplace operator
KW  - Riemannian manifold
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60052
ER  - 
TY  - INPR
A1  - Bär, Christian
T1  - Some properties of solutions to weakly hypoelliptic equations
N2  - A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all elliptic, overdetermined elliptic, subelliptic and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p solution must vanish.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)22 
KW  - Hypoelliptic operators
KW  - hypoelliptic estimate
KW  - Montel theorem
KW  - Vitali theorem
KW  - Liouville theorem
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60064
ER  - 
TY  - INPR
A1  - Bär, Christian
A1  - Ballmann, Werner
T1  - Boundary value problems for elliptic differential operators of first order
N2  - We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)18 
KW  - Elliptic operators
KW  - elliptic boundary conditions
KW  - completeness
KW  - coercivity
KW  - boundary regularity
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60023
ER  - 
TY  - INPR
A1  - Bär, Christian
A1  - Ginoux, Nicolas
T1  - Classical and quantum fields on Lorentzian manifolds
N2  - We construct bosonic and fermionic locally covariant quantum fields theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)15 
KW  - Wave operator
KW  - Dirac-type operator
KW  - globally hyperbolic spacetime
KW  - Green's operator
KW  - CCR-algebra
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59973
ER  - 
TY  - INPR
A1  - Bär, Christian
A1  - Pfäffle, Frank
T1  - Wiener measures on Riemannian manifolds and the Feynman-Kac formula
N2  - This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)17 
KW  - Wiener measure
KW  - conditional Wiener measure
KW  - Brownian motion
KW  - Brownian bridge
KW  - Riemannian manifold
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59998
ER  - 
TY  - INPR
A1  - Böckmann, Christine
A1  - Biele, Jens
A1  - Neuber, Roland
A1  - Niebsch, Jenny
T1  - Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data
N2  - The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.
T3  - NLD Preprints - 38 
KW  - Multiwavelength LIDAR
KW  - aerosol size distribution
KW  - ill-posed problem
KW  - inversion
KW  - mollifier method
KW  - coated and absorbing aerosols
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14360
ER  - 
TY  - INPR
A1  - Böckmann, Christine
A1  - Niebsch, Jenny
T1  - Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator
N2  - The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.
T3  - NLD Preprints - 47 
KW  - multiwavelength lidar
KW  - aerosol size distribution
KW  - inverse ill-posed problem
KW  - multilayered coated and absorbing aerosol
KW  - new recursive algorithm
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14725
ER  - 
TY  - INPR
A1  - Böckmann, Christine
A1  - Sarközi, Janos
T1  - The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection
N2  - The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.
T3  - NLD Preprints - 53 
KW  - Ill-posed problem
KW  - inversion
KW  - variable projection method
KW  - multiwavelength Lidar
KW  - aerosol distribution
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14847
ER  - 
TY  - INPR
A1  - Bühler, Markus J.
A1  - Rabu, Pierre
A1  - Taubert, Andreas
T1  - Advanced hybrid materials - design and applications
T2  - European journal of inorganic chemistry : a journal of ChemPubSoc Europe
Y1  - 2012
U6  - https://doi.org/10.1002/ejic.201201263
SN  - 1434-1948
IS  - 32
SP  - 5092
EP  - 5093
PB  - Wiley-VCH
CY  - Weinheim
ER  - 
TY  - INPR
A1  - Bürger, Gerd
T1  - Comment on "Bias correction, quantile mapping, and downscaling: revisiting the inflation issue"
T2  - Journal of climate
N2  - In a recent paper, Maraun describes the adverse effects of quantile mapping on downscaling. He argues that when large-scale GCM variables are rescaled directly to small-scale fields or even station data, genuine small-scale covariability is lost and replaced by uniform variability inherited from the larger scales. This leads to a misrepresentation mainly of areal means and long-term trends. This comment acknowledges the former point, although the argument is relatively old, but disagrees with the latter, showing that grid-size long-term trends can be different from local trends. Finally, because it is partly incorrectly addressed, some clarification is added regarding the inflation issue, stressing that neither randomization nor inflation is free of unverified assumptions.
KW  - Climate change
KW  - Statistics
KW  - Climate variability
Y1  - 2014
U6  - https://doi.org/10.1175/JCLI-D-13-00184.1
SN  - 0894-8755
SN  - 1520-0442
VL  - 27
IS  - 4
SP  - 1819
EP  - 1820
PB  - American Meteorological Soc.
CY  - Boston
ER  - 
TY  - INPR
A1  - Caliendo, Marco
A1  - Kritikos, Alexander
T1  - Searching for the entrepreneurial personality New evidence and avenues for further research
T2  - Journal of economic psychology : research in economic psychology and behavioral economics
Y1  - 2012
U6  - https://doi.org/10.1016/j.joep.2011.06.001
SN  - 0167-4870
VL  - 33
IS  - 2
SP  - 319
EP  - 324
PB  - Elsevier
CY  - Amsterdam
ER  -