@phdthesis{Busaman2006, author = {Busaman, Saofee}, title = {Hyperequational theory for partial algebras}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-12048}, school = {Universit{\"a}t Potsdam}, year = {2006}, abstract = {Our work goes in two directions. At first we want to transfer definitions, concepts and results of the theory of hyperidentities and solid varieties from the total to the partial case. (1) We prove that the operators chi^A_RNF and chi^E_RNF are only monotone and additive and we show that the sets of all fixed points of these operators are characterized only by three instead of four equivalent conditions for the case of closure operators. (2) We prove that V is n - SF-solid iff clone^SF V is free with respect to itself, freely generated by the independent set {[fi(x_1, . . . , x_n)]Id^SF_n V | i \in I}. (3) We prove that if V is n-fluid and ~V |P(V ) =~V -iso |P(V ) then V is kunsolid for k >= n (where P(V ) is the set of all V -proper hypersubstitutions of type \tau ). (4) We prove that a strong M-hyperquasi-equational theory is characterized by four equivalent conditions. The second direction of our work is to follow ideas which are typical for the partial case. (1) We characterize all minimal partial clones which are strongly solidifyable. (2)We define the operator Chi^A_Ph where Ph is a monoid of regular partial hypersubstitutions.Using this concept, we define the concept of a Phyp_R(\tau )-solid strong regular variety of partial algebras and we prove that a PHyp_R(\tau )-solid strong regular variety satisfies four equivalent conditions.}, language = {en} } @article{BusseSimonPetroffetal.2022, author = {Busse, David and Simon, Philipp and Petroff, David and El-Najjar, Nahed and Schmitt, Lisa and Bindellini, Davide and Dietrich, Arne and Zeitlinger, Markus and Huisinga, Wilhelm and Michelet, Robin and Wrigge, Hermann and Kloft, Charlotte}, title = {High-dosage fosfomycin results in adequate plasma and target-site exposure in morbidly obese and nonobese nonhyperfiltration patients}, series = {Antimicrobial agents and chemotherapy}, volume = {66}, journal = {Antimicrobial agents and chemotherapy}, number = {6}, publisher = {American Society for Microbiology}, address = {Washington}, issn = {0066-4804}, doi = {10.1128/aac.02302-21}, pages = {12}, year = {2022}, abstract = {The objectives of this study were the identification in (morbidly) obese and nonobese patients of (i) the most appropriate body size descriptor for fosfomycin dose adjustments and (ii) adequacy of the currently employed dosing regimens. Plasma and target site (interstitial fluid of subcutaneous adipose tissue) concentrations after fosfomycin administration (8 g) to 30 surgery patients (15 obese/15 nonobese) were obtained from a prospective clinical trial. After characterization of plasma and microdialysis-derived target site pharmacokinetics via population analysis, short-term infusions of fosfomycin 3 to 4 times daily were simulated. The adequacy of therapy was assessed by probability of pharmacokinetic/pharmacodynamic target attainment (PTA) analysis based on the unbound drug-related targets of an \%fT(>= MIC) (the fraction of time that unbound fosfomycin concentrations exceed the MIC during 24 h) of 70 and an fAUC(0-24h)/MIC (the area under the concentration-time curve from 0 to 24 h for the unbound fraction of fosfomycin relative to the MIC) of 40.8 to 83.3. Lean body weight, fat mass, and creatinine clearance calculated via adjusted body weight (ABW) (CLCRCG_ABW) of all patients (body mass index [BMI] = 20.1 to 52.0 kg/m(2)) explained a considerable proportion of between-patient pharmacokinetic variability (up to 31.0\% relative reduction). The steady-state unbound target site/plasma concentration ratio was 26.3\% lower in (morbidly) obese than nonobese patients. For infections with fosfomycin-susceptible pathogens (MIC <= 16 mg/L), intermittent "high-dosage" intravenous (i.v.) fosfomycin (8 g, three times daily) was sufficient to treat patients with a CLCRCG_ABW of,130 mL/min, irrespective of the pharmacokinetic/pharmacodynamic indices considered. For infections by Pseudomonas aeruginosa with a MIC of 32 mg/L, when the index fAUC0-24h/MIC is applied, fosfomycin might represent a promising treatment option in obese and nonobese patients, especially in combination therapy to complement beta-lactams, in which carbapenem-resistant P. aeruginosa is critical. In conclusion, fosfomycin showed excellent target site penetration in obese and nonobese patients. Dosing should be guided by renal function rather than obesity status.}, language = {en} } @phdthesis{Butkote2009, author = {Butkote, Runglawan}, title = {Universal-algebraic and Semigroup-theoretical Properties of Boolean Operations}, address = {Potsdam}, pages = {123 S.}, year = {2009}, language = {en} } @misc{ButuzovNefedovReckeetal.2019, author = {Butuzov, Valentin F. and Nefedov, N. N. and Recke, Lutz and Omel'chenko, Oleh}, title = {Partly dissipative system with multizonal initial and boundary layers}, series = {Journal of Physics: Conference Series}, volume = {1205}, journal = {Journal of Physics: Conference Series}, publisher = {IOP Publ.}, address = {Bristol}, issn = {1742-6588}, doi = {10.1088/1742-6596/1205/1/012009}, pages = {7}, year = {2019}, abstract = {For a singularly perturbed parabolic - ODE system we construct the asymptotic expansion in the small parameter in the case, when the degenerate equation has a double root. Such systems, which are called partly dissipative reaction-diffusion systems, are used to model various natural processes, including the signal transmission along axons, solid combustion and the kinetics of some chemical reactions. It turns out that the algorithm of the construction of the boundary layer functions and the behavior of the solution in the boundary layers essentially differ from that ones in case of a simple root. The multizonal initial and boundary layers behaviour was stated.}, language = {en} } @article{Baer2021, author = {B{\"a}r, Christian}, title = {The Faddeev-LeVerrier algorithm and the Pfaffian}, series = {Linear algebra and its applications}, volume = {630}, journal = {Linear algebra and its applications}, publisher = {Elsevier}, address = {New York}, issn = {0024-3795}, doi = {10.1016/j.laa.2021.07.023}, pages = {39 -- 55}, year = {2021}, abstract = {We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost O(n(beta+1)) where nis the size of the matrix and O(n(beta)) is the cost of multiplying n x n-matrices, beta is an element of [2, 2.37286). We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold using computer algebra.}, language = {en} } @article{Baer2019, author = {B{\"a}r, Christian}, title = {The curl operator on odd-dimensional manifolds}, series = {Journal of mathematical physics}, volume = {60}, journal = {Journal of mathematical physics}, number = {3}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.5082528}, pages = {16}, year = {2019}, abstract = {We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In three dimensions, its eigenvalues are the electromagnetic oscillation frequencies in vacuum without external sources. In general, the spectrum consists of the eigenvalue 0 with infinite multiplicity and further real discrete eigenvalues of finite multiplicity. We compute the Weyl asymptotics and study the zeta-function. We give a sharp lower eigenvalue bound for positively curved manifolds and analyze the equality case. Finally, we compute the spectrum for flat tori, round spheres, and 3-dimensional spherical space forms. Published under license by AIP Publishing.}, language = {en} } @article{Baer2009, author = {B{\"a}r, Christian}, title = {Spectral bounds for Dirac operators on open manifolds}, issn = {0232-704X}, doi = {10.1007/s10455-008-9149-1}, year = {2009}, abstract = {We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces.}, language = {en} } @article{Baer2015, author = {B{\"a}r, Christian}, title = {Geometrically formal 4-manifolds with nonnegative sectional curvature}, series = {Communications in analysis and geometry}, volume = {23}, journal = {Communications in analysis and geometry}, number = {3}, publisher = {International Press of Boston}, address = {Somerville}, issn = {1019-8385}, pages = {479 -- 497}, year = {2015}, abstract = {A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with nonnegative sectional curvature. If the sectional curvature is strictly positive, the manifold must be homeomorphic to S-4 or diffeomorphic to CP2. This conclusion stills holds true if the sectional curvature is strictly positive and we relax the condition of geometric formality to the requirement that the length of harmonic 2-forms is not too nonconstant. In particular, the Hopf conjecture on S-2 x S-2 holds in this class of manifolds.}, language = {en} } @article{Baer2015, author = {B{\"a}r, Christian}, title = {Green-Hyperbolic Operators on Globally Hyperbolic Spacetimes}, series = {Communications in mathematical physics}, volume = {333}, journal = {Communications in mathematical physics}, number = {3}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-014-2097-7}, pages = {1585 -- 1615}, year = {2015}, abstract = {Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green's operators. The most prominent examples are wave operators and Dirac-type operators. This paper is devoted to a systematic study of this class of differential operators. For instance, we show that this class is closed under taking restrictions to suitable subregions of the manifold, under composition, under taking "square roots", and under the direct sum construction. Symmetric hyperbolic systems are studied in detail.}, language = {en} } @unpublished{Baer2012, author = {B{\"a}r, Christian}, title = {Renormalized integrals and a path integral formula for the heat kernel on a manifold}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60052}, year = {2012}, abstract = {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.}, language = {en} } @unpublished{Baer2012, author = {B{\"a}r, Christian}, title = {Some properties of solutions to weakly hypoelliptic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60064}, year = {2012}, abstract = {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.}, language = {en} } @unpublished{BaerBallmann2012, author = {B{\"a}r, Christian and Ballmann, Werner}, title = {Boundary value problems for elliptic differential operators of first order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60023}, year = {2012}, abstract = {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.}, language = {en} } @article{BaerBandara2022, author = {B{\"a}r, Christian and Bandara, Lashi}, title = {Boundary value problems for general first-order elliptic differential operators}, series = {Journal of functional analysis}, volume = {282}, journal = {Journal of functional analysis}, number = {12}, publisher = {Elsevier}, address = {Amsterdam [u.a.]}, issn = {0022-1236}, doi = {10.1016/j.jfa.2022.109445}, pages = {69}, year = {2022}, abstract = {We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.}, language = {en} } @article{BaerBecker2014, author = {B{\"a}r, Christian and Becker, Christian}, title = {Differential characters and geometric chains}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2112}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-07034-6; 978-3-319-07033-9}, issn = {0075-8434}, doi = {10.1007/978-3-319-07034-6_1}, pages = {1 -- 90}, year = {2014}, abstract = {We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohomology theory and the model given by differential characters. Fiber integration for fibers with boundary is treated in the context of relative differential characters. As applications we treat higher-dimensional holonomy, parallel transport, and transgression.}, language = {en} } @article{BaerBessa2010, author = {B{\"a}r, Christian and Bessa, C. Pacelli}, title = {Stochastic completeness and volume growth}, issn = {0002-9939}, doi = {10.1090/S0002-9939-10-10281-0}, year = {2010}, abstract = {It was suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counterexamples to a converse implication.}, language = {en} } @article{BaerDahl2004, author = {B{\"a}r, Christian and Dahl, Matthias}, title = {The first dirac eigenvalue on manifolds with positive scalar curvature}, year = {2004}, abstract = {We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.}, language = {en} } @article{BaerDahl2003, author = {B{\"a}r, Christian and Dahl, Matthias}, title = {Small eigenvalues of the conformal laplacian}, year = {2003}, abstract = {We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give lower and upper bounds in terms of the alpha-genus.}, language = {en} } @unpublished{BaerGinoux2012, author = {B{\"a}r, Christian and Ginoux, Nicolas}, title = {Classical and quantum fields on Lorentzian manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59973}, year = {2012}, abstract = {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.}, language = {en} } @book{BaerGinouxPfaeffle2007, author = {B{\"a}r, Christian and Ginoux, Nicolas and Pf{\"a}ffle, Frank}, title = {Wave equations on lorentzian manifolds and quantization}, publisher = {European Math. Society}, address = {Z{\"u}rich}, isbn = {978-3-03719-037-1}, pages = {194 S.}, year = {2007}, language = {en} } @article{BaerGouduchonMoroianu2005, author = {B{\"a}r, Christian and Gouduchon, Paul and Moroianu, Andrei}, title = {Generalized Cylinders in Semi-Riemannian and Spin Geometry}, year = {2005}, abstract = {We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we show that generalized Killing spinors for Codazzi tensors are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1-parameter family of such metrics.}, language = {en} } @article{BaerHanke2022, author = {B{\"a}r, Christian and Hanke, Bernhard}, title = {Local flexibility for open partial differential relations}, series = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.}, volume = {75}, journal = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.}, number = {6}, publisher = {Wiley}, address = {Hoboken}, issn = {0010-3640}, doi = {10.1002/cpa.21982}, pages = {1377 -- 1415}, year = {2022}, abstract = {We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry. The main application is a general approximation result by sections that have very restrictive local properties on open dense subsets. This shows, for instance, that given any K is an element of Double-struck capital R every manifold of dimension at least 2 carries a complete C-1,C- 1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course, this is impossible for C-2-metrics in general.}, language = {en} } @article{BaerMazzeo2021, author = {B{\"a}r, Christian and Mazzeo, Rafe}, title = {Manifolds with many Rarita-Schwinger fields}, series = {Communications in mathematical physics}, volume = {384}, journal = {Communications in mathematical physics}, number = {1}, publisher = {Springer}, address = {Berlin}, issn = {0010-3616}, doi = {10.1007/s00220-021-04030-0}, pages = {533 -- 548}, year = {2021}, abstract = {The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.}, language = {en} } @article{BaerMoroianu2003, author = {B{\"a}r, Christian and Moroianu, Sergiu}, title = {Heat kernel asymptotics for roots of generalized laplacians}, year = {2003}, abstract = {We describe the heat kernel asymptotics for roots of a Laplace type operator on a closed manifold. A previously known relation between the Wodzicki residue and heat trace asymptotics is shown to hold pointwise for the corresponding densities.}, language = {en} } @article{BaerPfaeffle2010, author = {B{\"a}r, Christian and Pfaeffle, Frank}, title = {Asymptotic heat kernel expansion in the semi-classical limit}, issn = {0010-3616}, doi = {10.1007/s00220-009-0973-3}, year = {2010}, abstract = {Let H-h = h(2)L + V, where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of H-h as h SE arrow 0. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive h by the classical partition function.}, language = {en} } @unpublished{BaerPfaeffle2012, author = {B{\"a}r, Christian and Pf{\"a}ffle, Frank}, title = {Wiener measures on Riemannian manifolds and the Feynman-Kac formula}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59998}, year = {2012}, abstract = {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 Schr{\"o}dinger 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.}, language = {en} } @article{BaerSchopka2003, author = {B{\"a}r, Christian and Schopka, Sven}, title = {The dirac determinant of spherical space forms}, year = {2003}, abstract = {The zeta-regularized determinants of the Dirac operator and of its square are computed on spherical space forms. On S^2 the determinant of Dirac operators twisted by a complex line bundle is also calculated.}, language = {en} } @article{BaerStrohmaier2019, author = {B{\"a}r, Christian and Strohmaier, Alexander}, title = {An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary}, series = {American Journal of Mathematics}, volume = {141}, journal = {American Journal of Mathematics}, number = {5}, publisher = {Johns Hopkins Univ. Press}, address = {Baltimore}, issn = {0002-9327}, doi = {10.1353/ajm.2019.0037}, pages = {1421 -- 1455}, year = {2019}, abstract = {We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.}, language = {en} } @article{BaerStrohmaier2016, author = {B{\"a}r, Christian and Strohmaier, Alexander}, title = {A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds}, series = {Communications in mathematical physics}, volume = {347}, journal = {Communications in mathematical physics}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-016-2664-1}, pages = {703 -- 721}, year = {2016}, abstract = {We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.}, language = {en} } @article{BaerWafo2015, author = {B{\"a}r, Christian and Wafo, Roger Tagne}, title = {Initial value problems for wave equations on manifolds}, series = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics}, volume = {18}, journal = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {1385-0172}, doi = {10.1007/s11040-015-9176-7}, pages = {29}, year = {2015}, abstract = {We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hormander.}, language = {en} } @article{BaerenzungHolschneiderLesur2016, author = {B{\"a}renzung, Julien and Holschneider, Matthias and Lesur, Vincent}, title = {constraints}, series = {Journal of geophysical research : Solid earth}, volume = {121}, journal = {Journal of geophysical research : Solid earth}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1002/2015JB012464}, pages = {1343 -- 1364}, year = {2016}, abstract = {Prior information in ill-posed inverse problem is of critical importance because it is conditioning the posterior solution and its associated variability. The problem of determining the flow evolving at the Earth's core-mantle boundary through magnetic field models derived from satellite or observatory data is no exception to the rule. This study aims to estimate what information can be extracted on the velocity field at the core-mantle boundary, when the frozen flux equation is inverted under very weakly informative, but realistic, prior constraints. Instead of imposing a converging spectrum to the flow, we simply assume that its poloidal and toroidal energy spectra are characterized by power laws. The parameters of the spectra, namely, their magnitudes, and slopes are unknown. The connection between the velocity field, its spectra parameters, and the magnetic field model is established through the Bayesian formulation of the problem. Working in two steps, we determined the time-averaged spectra of the flow within the 2001-2009.5 period, as well as the flow itself and its associated uncertainties in 2005.0. According to the spectra we obtained, we can conclude that the large-scale approximation of the velocity field is not an appropriate assumption within the time window we considered. For the flow itself, we show that although it is dominated by its equatorial symmetric component, it is very unlikely to be perfectly symmetric. We also demonstrate that its geostrophic state is questioned in different locations of the outer core.}, language = {en} } @article{Boeckmann1996, author = {B{\"o}ckmann, Christine}, title = {Curve fitting and identification of physical spectra}, year = {1996}, language = {en} } @article{Boeckmann1996, author = {B{\"o}ckmann, Christine}, title = {Curve fitting and identification of physical spectra}, year = {1996}, language = {en} } @article{Boeckmann1995, author = {B{\"o}ckmann, Christine}, title = {A modification of the trust-region Gauss-Newton method to solve separable nonlinear least squares problems}, year = {1995}, language = {en} } @article{Boeckmann1997, author = {B{\"o}ckmann, Christine}, title = {Projection method for lidar measurements}, isbn = {981-02-2918-6}, year = {1997}, language = {en} } @book{Boeckmann1992, author = {B{\"o}ckmann, Christine}, title = {A modification of the Trust-Region Gauss-Newton method to solve separable nonlinear least squares problems}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 17}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {14 Bl.}, year = {1992}, language = {en} } @book{Boeckmann1992, author = {B{\"o}ckmann, Christine}, title = {Curve fitting and identification of physical spectra}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 18}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {17 Bl.}, year = {1992}, language = {en} } @article{Boeckmann2000, author = {B{\"o}ckmann, Christine}, title = {Evaluation of Multi-spectral Lidar Measurements of the Tropo- and Stratosphere via Modern Mathematical Methods for Inverse III- posed Problems to Determine the Aerosol Size Distribution}, year = {2000}, language = {en} } @article{BoeckmannBernutatFischer1998, author = {B{\"o}ckmann, Christine and Bernutat, Claudia and Fischer, Silva}, title = {The nonlinear LIDAR-equation : an inverse ill-posed problem}, year = {1998}, language = {en} } @article{BoeckmannBieleNeuber1998, author = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland}, title = {Analysis of multi-wavelength lidar data by inversion with mollifier method}, year = {1998}, language = {en} } @unpublished{BoeckmannBieleNeuberetal.1997, author = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny}, title = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360}, year = {1997}, abstract = {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.}, language = {en} } @article{BoeckmannBieleNeuberetal.1997, author = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny}, title = {Retrieval of Multimodal aerosol size distribution by Inversion of Multiwavelength data}, isbn = {0-8194-2525-7}, year = {1997}, language = {en} } @article{BoeckmannBrueckner2001, author = {B{\"o}ckmann, Christine and Br{\"u}ckner, Axel}, title = {100 years of the Runge-Kutta method : a brief editing for schools}, issn = {0268-3679}, year = {2001}, abstract = {This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.}, language = {en} } @article{BoeckmannKammanee2011, author = {B{\"o}ckmann, Christine and Kammanee, Athassawat}, title = {Broyden method for inverse non-symmetric Sturm-Liouville problems}, series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, volume = {51}, journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, number = {3}, publisher = {Springer}, address = {Dordrecht}, issn = {0006-3835}, doi = {10.1007/s10543-011-0317-5}, pages = {513 -- 528}, year = {2011}, abstract = {In this paper, we propose a derivative-free method for recovering symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. A class of boundary value methods obtained as an extension of Numerov's method is the major tool for approximating the eigenvalues in each Broyden iteration step. Numerical examples demonstrate that the method is able to reduce the number of iteration steps, in particular for non-symmetric potentials, without accuracy loss.}, language = {en} } @article{BoeckmannKammaneeBraunss2011, author = {B{\"o}ckmann, Christine and Kammanee, Athassawat and Braunss, Andreas}, title = {Logarithmic convergence rate of Levenberg-Marquardt method with application to an inverse potential problem}, series = {Journal of inverse and ill-posed problems}, volume = {19}, journal = {Journal of inverse and ill-posed problems}, number = {3}, publisher = {De Gruyter}, address = {Berlin}, issn = {0928-0219}, doi = {10.1515/JIIP.2011.034}, pages = {345 -- 367}, year = {2011}, abstract = {We prove logarithmic convergence rate of the Levenberg-Marquardt method in a Hilbert space if a logarithmic source condition is satisfied. This method is applied to an inverse potential problem. Numerical implementations demonstrate the convergence rate.}, language = {en} } @article{BoeckmannKirsche2006, author = {B{\"o}ckmann, Christine and Kirsche, Andreas}, title = {Iterative regularization method for lidar remote sensing}, issn = {0010-4655}, doi = {10.1016/j.cpc.2005.12.019}, year = {2006}, abstract = {In this paper we present an inversion algorithm for ill-posed problems arising in atmospheric remote sensing. The proposed method is an iterative Runge-Kutta type regularization method. Those methods are better well known for solving differential equations. We adapted them for solving inverse ill-posed problems. The numerical performances of the algorithm are studied by means of simulations concerning the retrieval of aerosol particle size distributions from lidar observations.}, language = {en} } @article{BoeckmannMironovaMuller2005, author = {B{\"o}ckmann, Christine and Mironova, I. and Muller, D.}, title = {Microphysical aerosol parameters from multiwavelength lidar}, issn = {1084-7529}, year = {2005}, abstract = {The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements. We present the continuation of investigations of the IMP method. Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented. Our analysis shows that the backscatter operator has a smaller degree of ill- posedness than the operator for extinction. This fact underlines the importance of backscatter data. Moreover, the degree of ill-posedness increases with increasing particle absorption, i.e., depends on the imaginary part of the refractive index and does not depend significantly on the real part. Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices. The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400. 710, 800 nm. additionally) and the same two extinction coefficients. For known complex refractive index and up to 20\% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15\% in both cases. Simulations were also made with unknown complex refractive index. In that case the integrated parameters stay below approximately 30\%, and the imaginary part of the refractive index stays below 35\% for input noise up to 10\% in both cases. In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness. It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion. The IMP algorithm was finally tested for a measurement case. (C) 2005 Optical Society of America}, language = {en} } @unpublished{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14725}, year = {1998}, abstract = {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.}, language = {en} } @article{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Inverse Scattering Problems of the Nonlinear LIDAR-Equation}, year = {1998}, language = {en} } @article{BoeckmannNiebsch1997, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Mollifier Methods for Aerosol Size Distribution}, year = {1997}, language = {en} } @book{BoeckmannNiebsch1996, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {A mollifier method for aerosol size}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1996, 07}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {[5] Bl.}, year = {1996}, language = {en} } @article{BoeckmannOsterloh2014, author = {B{\"o}ckmann, Christine and Osterloh, Lukas}, title = {Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data}, series = {Inverse problems in science and engineering}, volume = {22}, journal = {Inverse problems in science and engineering}, number = {1}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1741-5977}, doi = {10.1080/17415977.2013.830615}, pages = {150 -- 165}, year = {2014}, abstract = {The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information.}, language = {en} } @misc{BoeckmannRitterCappelletti2018, author = {B{\"o}ckmann, Christine and Ritter, Christoph and Cappelletti, David}, title = {Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data}, series = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium}, journal = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium}, publisher = {IEEE}, address = {New York}, isbn = {978-1-5386-7150-4}, issn = {2153-6996}, doi = {10.1109/IGARSS.2018.8518674}, pages = {5575 -- 5578}, year = {2018}, abstract = {We present a project combining lidar, photometer and particle counter data with a regularization software tool for a closure study of aerosol microphysical property retrieval. In a first step only lidar data are used to retrieve the particle size distribution (PSD). Secondly, photometer data are added, which results in a good consistency of the retrieved PSDs. Finally, those retrieved PSDs may be compared with the measured PSD from a particle counter. The data here were taken in Ny Alesund, Svalbard, as an example.}, language = {en} } @unpublished{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14847}, year = {1999}, abstract = {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.}, language = {en} } @article{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The Ill-posed Problem of Multiwavelength Lidar Data by a Hybrid Method of Variable Projection}, year = {1999}, language = {en} } @article{BoeckmannSarkoeziAlthausen1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos and Althausen, Dietrich}, title = {Collocation Methods for Ill-posed Inverse Problems of Multiwavelength Lidar Measurements and Applications on LACE 98-Data}, year = {1999}, language = {en} } @article{BoeckmannWandingerAnsmannetal.2004, author = {B{\"o}ckmann, Christine and Wandinger, Ulla and Ansmann, Albert and B{\"o}senberg, Jens and Amiridis, Vassilis and Boselli, Antonella and Delaval, Arnaud and De Tomasi, Ferdinando de and Frioud, Max and Grigorov, Ivan Videnov and Hagard, Arne and Horvat, Matej and Iarlori, Marco and Komguem, Leonce and Kreipl, Stephan and Larchevque, Gilles and Matthias, Volker and Papayannis, Alexandros and Pappalardo, GGelsomina and Rocadenbosch, Francesc and Rodrigues, Jose Ant{\´o}nio and Schneider, Johannes and Shcherbakov, Valery and Wiegner, Matthias}, title = {Aerosol lidar intercomparison in the framework of the EARLINET project : 2. Aerosol backscatter algorithms}, issn = {0003-6935}, year = {2004}, abstract = {An intercomparison of aerosol backscatter lidar algorithms was performed in 2001 within the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET). The objective of this research was to test the correctness of the algorithms and the influence of the lidar ratio used by the various lidar teams involved in the EARLINET for calculation of backscatter-coefficient profiles from the lidar signals. The exercise consisted of processing synthetic lidar signals of various degrees of difficulty. One of these profiles contained height- dependent lidar ratios to test the vertical influence of those profiles on the various retrieval algorithms. Furthermore, a realistic incomplete overlap of laser beam and receiver field of view was introduced to remind the teams to take great care in the nearest range to the lidar. The intercomparison was performed in three stages with increasing knowledge on the input parameters. First, only the lidar signals were distributed; this is the most realistic stage. Afterward the lidar ratio profiles and the reference values at calibration height were provided. The unknown height- dependent lidar ratio had the largest influence on the retrieval, whereas the unknown reference value was of minor importance. These results show the necessity of making additional independent measurements, which can provide us with a suitable approximation of the lidar ratio. The final stage proves in general, that the data evaluation schemes of the different groups of lidar systems work well. (C) 2004 Optical Society of America}, language = {en} } @misc{Boelling1997, author = {B{\"o}lling, Reinhard}, title = {Mathematics of the 19th century, geometry, analytic function theory / ed. by A. N. Kolmogorov ... ;Basel [u.a.], Birkh{\"a}user, 1996}, issn = {0036-6978}, year = {1997}, language = {en} } @article{Boelling1998, author = {B{\"o}lling, Reinhard}, title = {An unknown photograph of Kovalevskaja}, issn = {0343-6993}, year = {1998}, language = {en} } @article{Boelling1998, author = {B{\"o}lling, Reinhard}, title = {Weierstraß and some members of his circle : Kovalevskaja, Fuchs, Schwarz, Schottky}, isbn = {3-7643-5943- 9}, year = {1998}, language = {en} } @article{BoesenbergAlpersBoeckmannetal.1998, author = {B{\"o}senberg, Jens and Alpers, Matthias and B{\"o}ckmann, Christine and J{\"a}ger, Horst and Matthias, Volker and Trickl, Thomas and Wandinger, Ulla and Wiegner, Matthias}, title = {A Lidar Network for the Establishment of an Aerosol Climatology}, year = {1998}, language = {en} } @book{CalinChang2004, author = {Calin, Ovidium and Chang, Der-Chen}, title = {The Geometry on a Step 3 Grushin Model}, 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 = {22 S.}, year = {2004}, language = {en} } @unpublished{CalinDerChen2004, author = {Calin, Ovidium and Der-Chen, Chang}, title = {The geometry on a step 3 Grushin model}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26724}, year = {2004}, abstract = {In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis.}, language = {en} } @book{CalvoMartinSchulze2004, author = {Calvo, D. and Martin, Calin-Iulian and Schulze, Bert-Wolfgang}, title = {Symbolic Structures on Corner Manifolds}, 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 = {18 S.}, year = {2004}, language = {en} } @book{CalvoSchulze2005, author = {Calvo, D. and Schulze, Bert-Wolfgang}, title = {Operators on Corner Manifolds with Exit to Infinity}, 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 = {48 S.}, year = {2005}, language = {en} } @unpublished{CalvoSchulze2005, author = {Calvo, D. and Schulze, Bert-Wolfgang}, title = {Operators on corner manifolds with exit to infinity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29753}, year = {2005}, abstract = {We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo 'lower order terms') by a principal symbolic hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and σ ^(A)(y, η), (y, η) 2 T*Y \ 0, the (operator-valued) edge symbol of 'first generation', cf. [15]. The novelty here is the edge symbol σ^ of 'second generation', parametrised by (z, Ϛ) 2 T*Z \ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.}, language = {en} } @unpublished{CalvoSchulze2005, author = {Calvo, D. and Schulze, Bert-Wolfgang}, title = {Edge symbolic structures of second generation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29940}, year = {2005}, abstract = {Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.}, language = {en} } @book{Camales2003, author = {Camal{\`e}s, Renaud}, title = {A Note on the Ramified Cauchy Problem}, 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 = {11 S.}, year = {2003}, language = {en} } @book{Camales2003, author = {Camal{\`e}s, Renaud}, title = {Explicit formulation of the solution of hamada-leray-wagschal{\"i}s theorem}, 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 = {14 S.}, year = {2003}, language = {en} } @unpublished{Camales2003, author = {Camal{\`e}s, Renaud}, title = {A note on the ramified Cauchy problem}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26646}, year = {2003}, abstract = {In this paper, the ramified Cauchy problem in C² for operator with multiple characteristics of constant multiplicity and second member ramified around some analytic set is studied.}, language = {en} } @article{CanforaSchmidt2003, author = {Canfora, Fabrizio and Schmidt, Hans-J{\"u}rgen}, title = {Vacuum solutions which cannot be written in diagonal form}, year = {2003}, abstract = {A vacuum solution of the Einstein gravitational field equation is shown to follow from a general ansatz but fails to follow from it if the symmetric matrix in it is assumed to be in diagonal form.}, language = {en} } @article{CapozzielloLambiaseSchmidt2000, author = {Capozziello, Salvatore and Lambiase, G. and Schmidt, Hans-J{\"u}rgen}, title = {Nonminimal derivative couplings and inflation in generalized theories of gravity}, year = {2000}, language = {en} } @article{CarpentierKim2018, author = {Carpentier, Alexandra and Kim, Arlene K. H.}, title = {An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution}, series = {Statistica Sinica}, volume = {28}, journal = {Statistica Sinica}, number = {3}, publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica}, address = {Taipei}, issn = {1017-0405}, doi = {10.5705/ss.202016.0103}, pages = {1371 -- 1393}, year = {2018}, abstract = {We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.}, language = {en} } @article{CarpentierKloppLoeffleretal.2018, author = {Carpentier, Alexandra and Klopp, Olga and L{\"o}ffler, Matthias and Nickl, Richard}, title = {Adaptive confidence sets for matrix completion}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {24}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, number = {4A}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/17-BEJ933}, pages = {2429 -- 2460}, year = {2018}, abstract = {In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.}, language = {en} } @article{CarpentierNickl2015, author = {Carpentier, Alexandra and Nickl, Richard}, title = {On signal detection and confidence sets for low rank inference problems}, series = {Electronic journal of statistics}, volume = {9}, journal = {Electronic journal of statistics}, number = {2}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/15-EJS1087}, pages = {2675 -- 2688}, year = {2015}, abstract = {We consider the signal detection problem in the Gaussian design trace regression model with low rank alternative hypotheses. We derive the precise (Ingster-type) detection boundary for the Frobenius and the nuclear norm. We then apply these results to show that honest confidence sets for the unknown matrix parameter that adapt to all low rank sub-models in nuclear norm do not exist. This shows that recently obtained positive results in [5] for confidence sets in low rank recovery problems are essentially optimal.}, language = {en} } @unpublished{CattiauxDaiPraPoelly2007, author = {Cattiaux, Patrick and Dai Pra, Paolo and Poelly, Sylvie}, title = {A constructive approach to a class of ergodic HJB equations with nonsmooth cost}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49430}, year = {2007}, abstract = {We consider a class of ergodic Hamilton-Jacobi-Bellman (HJB) equations, related to large time asymptotics of non-smooth multiplicative functional of difusion processes. Under suitable ergodicity assumptions on the underlying difusion, we show existence of these asymptotics, and that they solve the related HJB equation in the viscosity sense.}, language = {en} } @article{CattiauxFradonKuliketal.2016, author = {Cattiaux, Patrick and Fradon, Myriam and Kulik, Alexei M. and Roelly, Sylvie}, title = {Long time behavior of stochastic hard ball systems}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {22}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/14-BEJ672}, pages = {681 -- 710}, year = {2016}, abstract = {We study the long time behavior of a system of n = 2, 3 Brownian hard balls, living in R-d for d >= 2, submitted to a mutual attraction and to elastic collisions.}, language = {en} } @unpublished{CattiauxFradonKuliketal.2013, author = {Cattiaux, Patrick and Fradon, Myriam and Kulik, Alexei Michajlovič and Roelly, Sylvie}, title = {Long time behavior of stochastic hard ball systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68388}, year = {2013}, abstract = {We study the long time behavior of a system of two or three Brownian hard balls living in the Euclidean space of dimension at least two, submitted to a mutual attraction and to elastic collisions.}, language = {en} } @article{ChajadaDeneckeHalas1999, author = {Chajada, I. and Denecke, Klaus-Dieter and Halas, R.}, title = {Algebras induced by hypersubstitutions}, year = {1999}, language = {en} } @book{ChampagnatRoelly2007, author = {Champagnat, Nicolas and Roelly, Sylvie}, title = {Multitype Dawson-Watanabe superprocesses conditioned by remote survival}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, publisher = {Univ.}, address = {Potsdam}, issn = {1613-3307}, pages = {39 S.}, year = {2007}, language = {en} } @misc{ChampagnatRoelly2008, author = {Champagnat, Nicolas and Roelly, Sylvie}, title = {Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-18610}, year = {2008}, abstract = {A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process - the conditioned multitype Feller branching diffusion - are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too .}, language = {en} } @unpublished{ChampagnatRoelly2007, author = {Champagnat, Nicolas and Roelly, Sylvie}, title = {Limit theorems for conditioned multitype Dawson-Watanabe processes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49426}, year = {2007}, abstract = {A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every nite time interval, its distribution law is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. The explicit form of the Laplace functional of the conditioned process is used to obtain several results on the long time behaviour of the mass of the conditioned and unconditioned processes. The general case is considered first, where the mutation matrix which modelizes the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are also analysed.}, language = {en} } @article{ChangSchulze2017, author = {Chang, D. -C. and Schulze, Bert-Wolfgang}, title = {Calculus on spaces with higher singularities}, series = {Journal of pseudo-differential operators and applications}, volume = {8}, journal = {Journal of pseudo-differential operators and applications}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-016-0180-x}, pages = {585 -- 622}, year = {2017}, abstract = {We establish extensions of the standard pseudo-differential calculus to specific classes of operators with operator-valued symbols occurring in symbolic hierarchies motivated by manifolds with higher singularities or stratified spaces.}, language = {en} } @article{ChangViahmoudiSchulze2016, author = {Chang, D. -C. and Viahmoudi, M. Hedayat and Schulze, Bert-Wolfgang}, title = {PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE}, series = {Journal of nonlinear and convex analysis : an international journal}, volume = {17}, journal = {Journal of nonlinear and convex analysis : an international journal}, publisher = {Yokohama Publishers}, address = {Yokohama}, issn = {1345-4773}, pages = {1889 -- 1937}, year = {2016}, abstract = {This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.}, language = {en} } @article{ChangHabalSchulze2014, author = {Chang, Der-Chen and Habal, Nadia and Schulze, Bert-Wolfgang}, title = {The edge algebra structure of the Zaremba problem}, series = {Journal of pseudo-differential operators and applications}, volume = {5}, journal = {Journal of pseudo-differential operators and applications}, number = {1}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-013-0088-7}, pages = {69 -- 155}, year = {2014}, abstract = {We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.}, language = {en} } @article{ChangHedayatMahmoudiSchulze2017, author = {Chang, Der-Chen and Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {Singular degenerate operators}, series = {Applicable analysis : an international journal}, volume = {96}, journal = {Applicable analysis : an international journal}, number = {14}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {0003-6811}, doi = {10.1080/00036811.2017.1336546}, pages = {2434 -- 2456}, year = {2017}, abstract = {We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.}, language = {en} } @article{ChangKhalilSchulze2021, author = {Chang, Der-Chen and Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Analysis on regular corner spaces}, series = {The journal of geometric analysis}, volume = {31}, journal = {The journal of geometric analysis}, number = {9}, publisher = {Springer}, address = {New York}, issn = {1050-6926}, doi = {10.1007/s12220-021-00614-3}, pages = {9199 -- 9240}, year = {2021}, abstract = {We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.}, language = {en} } @article{ChangMahmoudiSchulze2018, author = {Chang, Der-Chen and Mahmoudi, Mahdi Hedayat and Schulze, Bert-Wolfgang}, title = {Volterra operators in the edge-calculus}, series = {Analysis and Mathematical Physics}, volume = {8}, journal = {Analysis and Mathematical Physics}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {1664-2368}, doi = {10.1007/s13324-018-0238-4}, pages = {551 -- 570}, year = {2018}, abstract = {We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).}, language = {en} } @article{ChangQianSchulze2015, author = {Chang, Der-Chen and Qian, Tao and Schulze, Bert-Wolfgang}, title = {Corner Boundary Value Problems}, series = {Complex analysis and operator theory}, volume = {9}, journal = {Complex analysis and operator theory}, number = {5}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-014-0424-9}, pages = {1157 -- 1210}, year = {2015}, abstract = {Boundary value problems on a manifold with smooth boundary are closely related to the edge calculus where the boundary plays the role of an edge. The problem of expressing parametrices of Shapiro-Lopatinskij elliptic boundary value problems for differential operators gives rise to pseudo-differential operators with the transmission property at the boundary. However, there are interesting pseudo-differential operators without the transmission property, for instance, the Dirichlet-to-Neumann operator. In this case the symbols become edge-degenerate under a suitable quantisation, cf. Chang et al. (J Pseudo-Differ Oper Appl 5(2014):69-155, 2014). If the boundary itself has singularities, e.g., conical points or edges, then the symbols are corner-degenerate. In the present paper we study elements of the corresponding corner pseudo-differential calculus.}, language = {en} } @article{ChangSchulze2018, author = {Chang, Der-Chen and Schulze, Bert-Wolfgang}, title = {Corner spaces and Mellin quantization}, series = {Journal of nonlinear and convex analysis : an international journal}, volume = {19}, journal = {Journal of nonlinear and convex analysis : an international journal}, number = {2}, publisher = {Yokohama Publishers}, address = {Yokohama}, issn = {1345-4773}, pages = {179 -- 195}, year = {2018}, abstract = {Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones.}, language = {en} } @article{ChangSchulze2017, author = {Chang, Der-Chen and Schulze, Bert-Wolfgang}, title = {Ellipticity on spaces with higher singularities}, series = {Science China Mathematics}, volume = {60}, journal = {Science China Mathematics}, number = {11}, publisher = {Science China Press}, address = {Beijing}, issn = {1674-7283}, doi = {10.1007/s11425-016-0519-9}, pages = {2053 -- 2076}, year = {2017}, abstract = {We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.}, language = {en} } @phdthesis{Changphas2004, author = {Changphas, Thawhat}, title = {Monoids of Hypersubstitutions}, address = {Potsdam}, pages = {vii, 88 S.}, year = {2004}, language = {en} } @article{Changphas2006, author = {Changphas, Thawhat}, title = {The order of hypersubstitutions of type tau = (3)}, issn = {1005-3867}, year = {2006}, abstract = {Hypersubstitutions were introduced in [3] as a way of making precise the concepts of hyperidentity and M- hyperidentity. The monoid of hypersubstitutions has been widely studied by many authors. Knowledge of the monoid of hypersubstitutions can be applied to the concept of M-hyperidentities. In this paper, we show that the order of hypersubstitutions of type tau = (3) is 1, 2, 3 or infinite}, language = {en} } @article{ChangphasDenecke2005, author = {Changphas, Thawhat and Denecke, Klaus-Dieter}, title = {Green's relation R on the monoid of clone endomorphisms}, issn = {1005-3867}, year = {2005}, abstract = {A hypersubstitution is a map which takes n-ary operation symbols to n-ary terms. Any such map can be uniquely extended to a map defined on the set W-tau(X) of all terms of type tau, and any two such extensions can be composed in a natural way. Thus, the set Hyp(tau) of all hypersubstitutions of type tau forms a monoid. In this paper, we characterize Green's relation R on the monoid Hyp(tau) for the type tau = (n, n). In this case, the monoid of all hypersubstitutions is isomorphic with the monoid of all Clone endomorphisms. The results can be applied to mutually derived varieties}, language = {en} } @article{ChangphasDenecke2003, author = {Changphas, Thawhat and Denecke, Klaus-Dieter}, title = {Green's Relations on the Seminearring of Full Hypersubstitutions of Type (n)}, year = {2003}, language = {en} } @article{ChangphasDenecke2003, author = {Changphas, Thawhat and Denecke, Klaus-Dieter}, title = {Complexity of Hypersubstitutions and Lattices of Varieties}, year = {2003}, language = {en} } @article{ChelkakKargaevKorotyaev2004, author = {Chelkak, D. and Kargaev, P. and Korotyaev, Evgeni}, title = {Inverse problem for harmonic oscillator perturbed by potential, characterization}, issn = {0010-3616}, year = {2004}, abstract = {Consider the perturbed harmonic oscillator Ty=-y''+x(2)y+q(x)y in L-2(R), where the real potential q belongs to the Hilbert space H={q', xq is an element of L-2(R)}. The spectrum of T is an increasing sequence of simple eigenvalues lambda(n)(q)=1+2n+mu(n), ngreater than or equal to0, such that mu(n)-->0 as n-->infinity. Let psi(n)(x,q) be the corresponding eigenfunctions. Define the norming constants nu(n)(q)=lim(xup arrowinfinity)log |psi(n) (x,q)/psi(n) (-x,q)|. We show that {mu(n)}(0)(infinity) is an element of H {nu(n)}(0)(infinity) is an element of H-0 for some real Hilbert space and some subspace H-0 subset of H. Furthermore, the mapping Psi:q-- >Psi(q)=({lambda(n)(q)}(0)(infinity), {nu(n)(q)}(0)(infinity)) is a real analytic isomorphism between H and S x H-0, where S is the set of all strictly increasing sequences s={s(n)}(0)(infinity) such that s(n)=1+2n+h(n), {h(n)}(0)(infinity) is an element of H. The proof is based on nonlinear functional analysis combined with sharp asymptotics of spectral data in the high energy limit for complex potentials. We use ideas from the analysis of the inverse problem for the operator -y"py, p is an element of L-2(0,1), with Dirichlet boundary conditions on the unit interval. There is no literature about the spaces H,H-0. We obtain their basic properties, using their representation as spaces of analytic functions in the disk}, language = {en} } @article{ChelkhLyTarkhanov2020, author = {Chelkh, W. and Ly, Ibrahim and Tarkhanov, Nikolai}, title = {A remark on the Laplace transform}, series = {Siberian Mathematical Journal}, volume = {61}, journal = {Siberian Mathematical Journal}, number = {4}, publisher = {Consultants Bureau, Springer}, address = {New York}, issn = {0037-4466}, doi = {10.1134/S0037446620040151}, pages = {755 -- 762}, year = {2020}, abstract = {The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.}, language = {en} } @unpublished{ChenHidetoshi1998, author = {Chen, Hua and Hidetoshi, Tahara}, title = {On the holomorphic solution of non-linear totally characteristic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25333}, year = {1998}, abstract = {The paper deals with a non-linear singular partial differential equation: (E) t∂/∂t = F(t, x, u, ∂u/∂x) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by G{\´e}rard-Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case.}, language = {en} } @unpublished{ChenLiLiu2008, author = {Chen, Hua and Li, Jun-Feng and Liu, Wei-An}, title = {Behavior of the solution to a chemotaxis model with reproduction term}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30304}, year = {2008}, abstract = {Contents: 1 Introduction 2 Global existence and blow-up or quenching of the solution 3 Detailed asymptotical behavior of the solution}, language = {en} } @article{ChenLi2007, author = {Chen, Hua and Li, Ke}, title = {The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations}, 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 = {23 S.}, year = {2007}, language = {en} }