@article{BoldrighiniFrigioMaponietal.2020,
  author    = {Boldrighini, Carlo and Frigio, Sandro and Maponi, Pierluigi and Pellegrinotti, Alessandro and Sinai, Yakov G.},
  title     = {3-D incompressible Navier-Stokes equations: Complex blow-up and related real flows},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47220},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472201},
  pages     = {185 -- 194},
  year      = {2020},
  language  = {en}
}
@article{BomansonJanhunenSchaubetal.2016,
  author    = {Bomanson, Jori and Janhunen, Tomi and Schaub, Torsten and Gebser, Martin and Kaufmann, Benjamin},
  title     = {Answer Set Programming Modulo Acyclicity},
  series = {Fundamenta informaticae},
  volume    = {147},
  journal   = {Fundamenta informaticae},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0169-2968},
  doi       = {10.3233/FI-2016-1398},
  pages     = {63 -- 91},
  year      = {2016},
  abstract  = {Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving.},
  language  = {en}
}
@article{BourneCushingLiuetal.2018,
  author    = {Bourne, D. P. and Cushing, D. and Liu, S. and M{\"u}nch, Florentin and Peyerimhoff, Norbert},
  title     = {Ollivier-Ricci idleness functions of graphs},
  series = {SIAM Journal on Discrete Mathematics},
  volume    = {32},
  journal   = {SIAM Journal on Discrete Mathematics},
  number    = {2},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {0895-4801},
  doi       = {10.1137/17M1134469},
  pages     = {1408 -- 1424},
  year      = {2018},
  abstract  = {We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.},
  language  = {en}
}
@article{BovierEckhoffGayrardetal.2004,
  author    = {Bovier, Anton and Eckhoff, Michael and Gayrard, Veronique and Klein, Markus},
  title     = {Metastability in reversible diffusion processes : I. Sharp asymptotics for capacities and exit times},
  issn      = {1435-9855},
  year      = {2004},
  abstract  = {We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form -epsilonDelta+ delF(.) del on R-d or subsets of R-d, where F is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of F can be related, up to multiplicative errors that tend to one as epsilon down arrow 0, to the capacities of suitably constructed sets. We show that these capacities can be computed, again up to multiplicative errors that tend to one, in terms of local characteristics of F at the starting minimum and the relevant saddle points. As a result, we are able to give the first rigorous proof of the classical Eyring - Kramers formula in dimension larger than 1. The estimates on capacities make use of their variational representation and monotonicity properties of Dirichlet forms. The methods developed here are extensions of our earlier work on discrete Markov chains to continuous diffusion processes},
  language  = {en}
}
@article{BovierEckhoffGayrardetal.2002,
  author    = {Bovier, Anton and Eckhoff, Michael and Gayrard, Veronique and Klein, Markus},
  title     = {Metastability and low-Lying spectra in reversible Markov chains},
  year      = {2002},
  language  = {en}
}
@article{BovierEckhoffGayrardetal.2001,
  author    = {Bovier, Anton and Eckhoff, Michael and Gayrard, Veronique and Klein, Markus},
  title     = {Metastability in stochastic dynamics of disordered mean-field models},
  issn      = {0178-8051},
  year      = {2001},
  language  = {en}
}
@article{BovierGayrardKlein2005,
  author    = {Bovier, Anton and Gayrard, Veronique and Klein, Markus},
  title     = {Metastability in reversible diffusion processes : II. Precise asymptotics for small eigenvalues},
  issn      = {1435-9855},
  year      = {2005},
  abstract  = {We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form -epsilonDelta + delF(.) del on R-d or subsets of Rd, where F is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum is given, up to multiplicative errors tending to one, by the eigenvalues of the classical capacity matrix of the array of capacitors made of balls of radius epsilon centered at the positions of the local minima of F. We also get very precise uniform control on the corresponding eigenfunctions. Moreover, these eigenvalues can be identified with the same precision with the inverse mean metastable exit times from each minimum. In [BEGK3] it was proven that these mean times are given, again up to multiplicative errors that tend to one, by the classical Eyring- Kramers formula},
  language  = {en}
}
@phdthesis{Branding2012,
  author    = {Branding, Volker},
  title     = {The evolution equations for Dirac-harmonic Maps},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64204},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {This thesis investigates the gradient flow of Dirac-harmonic maps. Dirac-harmonic maps are critical points of an energy functional that is motivated from supersymmetric field theories. The critical points of this energy functional couple the equation for harmonic maps with spinor fields. At present, many analytical properties of Dirac-harmonic maps are known, but a general existence result is still missing. In this thesis the existence question is studied using the evolution equations for a regularized version of Dirac-harmonic maps. Since the energy functional for Dirac-harmonic maps is unbounded from below the method of the gradient flow cannot be applied directly. Thus, we first of all consider a regularization prescription for Dirac-harmonic maps and then study the gradient flow. Chapter 1 gives some background material on harmonic maps/harmonic spinors and summarizes the current known results about Dirac-harmonic maps. Chapter 2 introduces the notion of Dirac-harmonic maps in detail and presents a regularization prescription for Dirac-harmonic maps. In Chapter 3 the evolution equations for regularized Dirac-harmonic maps are introduced. In addition, the evolution of certain energies is discussed. Moreover, the existence of a short-time solution to the evolution equations is established. Chapter 4 analyzes the evolution equations in the case that the domain manifold is a closed curve. Here, the existence of a smooth long-time solution is proven. Moreover, for the regularization being large enough, it is shown that the evolution equations converge to a regularized Dirac-harmonic map. Finally, it is discussed in which sense the regularization can be removed. In Chapter 5 the evolution equations are studied when the domain manifold is a closed Riemmannian spin surface. For the regularization being large enough, the existence of a global weak solution, which is smooth away from finitely many singularities is proven. It is shown that the evolution equations converge weakly to a regularized Dirac-harmonic map. In addition, it is discussed if the regularization can be removed in this case.},
  language  = {en}
}
@article{BrandingDrukker2009,
  author    = {Branding, Volker and Drukker, Nadav},
  title     = {BPS Wilson loops in N=4 supersymmetric Yang-Mills theory : examples on hyperbolic submanifolds of space-time},
  issn      = {1550-7998},
  doi       = {10.1103/Physrevd.79.106006},
  year      = {2009},
  abstract  = {In this paper we present a family of supersymmetric Wilson loops of N=4 supersymmetric Yang-Mills theory in Minkowski space. Our examples focus on curves restricted to hyperbolic submanifolds, H-3 and H-2, of space-time. Generically they preserve two supercharges, but in special cases more, including a case which has not been discussed before, of the hyperbolic line, conformal to the straight line and circle, which is 1/2 BPS. We discuss some general properties of these Wilson loops and their string duals and study special examples in more detail. Generically the string duals propagate on a complexification of AdS(5)xS(5) and in some specific examples the compact sphere is effectively replaced by a de Sitter space.},
  language  = {en}
}
@article{BrascheKoshmanenkoNeidhardt1994,
  author    = {Brasche, Johannes F. and Koshmanenko, V. D. and Neidhardt, Hagen},
  title     = {Some new aspects of Krein's extension theory},
  year      = {1994},
  language  = {en}
}
@article{BrascheNeidhardt1995,
  author    = {Brasche, Johannes F. and Neidhardt, Hagen},
  title     = {On the point spectrum of selfadjoint extensions},
  year      = {1995},
  language  = {en}
}
@article{BrascheNeidhardt1996,
  author    = {Brasche, Johannes F. and Neidhardt, Hagen},
  title     = {On the singular continuous spectrum of self-adjoint extensions},
  year      = {1996},
  language  = {en}
}
@article{BrascheNeidhardt1995,
  author    = {Brasche, Johannes F. and Neidhardt, Hagen},
  title     = {On the absolutely continuous spectrum of self-adjoint extensions},
  year      = {1995},
  language  = {en}
}
@article{BrascheNeidhardt1994,
  author    = {Brasche, Johannes F. and Neidhardt, Hagen},
  title     = {Some remarks to Krein's extension theory},
  year      = {1994},
  language  = {en}
}
@book{BrauerKarp2006,
  author    = {Brauer, Uwe and Karp, Lavi},
  title     = {Local existence of classical solutions for the Einstin-Euler system using weighted Sobolev spaces of fractional order},
  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     = {12 S.},
  year      = {2006},
  language  = {en}
}
@unpublished{BrauerKarp2006,
  author    = {Brauer, Uwe and Karp, Lavi},
  title     = {Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30175},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@unpublished{BrauerKarp2008,
  author    = {Brauer, Uwe and Karp, Lavi},
  title     = {Well-posedness of Einstein-Euler systems in asymptotically flat spacetimes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30347},
  year      = {2008},
  abstract  = {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.},
  language  = {en}
}
@book{Braunss1998,
  author    = {Braunß, Hans-Andreas},
  title     = {A note about ranks of m-homogeneous polynomials on Banach spaces},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 18a},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {4 Bl.},
  year      = {1998},
  language  = {en}
}
@article{Braunss1992,
  author    = {Braunß, Hans-Andreas},
  title     = {On holomorphic mappings of Schatten class type},
  year      = {1992},
  language  = {en}
}
@article{BraunssJunek2004,
  author    = {Braunß, Hans-Andreas and Junek, Heinz},
  title     = {Factorization of injective ideals by interpolation},
  issn      = {0022-247x},
  year      = {2004},
  abstract  = {We construct a factorization of certain multilinear mappings through linear operators belonging to closed, injective operator ideals using interpolation technique. An extension of the duality theorem for interpolation spaces is also obtained.},
  language  = {en}
}
@book{BronnikovKasperRainer1997,
  author    = {Bronnikov, K. A. and Kasper, Uwe and Rainer, Martin},
  title     = {Intersecting electric and magnetic p-branes: spherically symmetric solutions},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 21},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {[9] Bl.},
  year      = {1997},
  language  = {en}
}
@article{BronnikovKasperRainer1999,
  author    = {Bronnikov, K. A. and Kasper, Uwe and Rainer, Martin},
  title     = {Intersecting electric and magnetic p-brains : spherically symmetric solutions},
  year      = {1999},
  language  = {en}
}
@article{BrungsGraeter1996,
  author    = {Brungs, Hans and Gr{\"a}ter, Joachim},
  title     = {Orders of Higher Rank in Semisimple Artinian Rings},
  year      = {1996},
  language  = {en}
}
@article{BrungsGraeter2000,
  author    = {Brungs, Hans and Gr{\"a}ter, Joachim},
  title     = {Trees and Valuation Rings},
  year      = {2000},
  language  = {en}
}
@article{BrungsGraeter2017,
  author    = {Brungs, Hans H. and Gr{\"a}ter, Joachim},
  title     = {On central extensions of SL(2, F) admitting left-orderings},
  series = {Journal of Algebra},
  volume    = {486},
  journal   = {Journal of Algebra},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-8693},
  doi       = {10.1016/j.jalgebra.2017.05.025},
  pages     = {288 -- 327},
  year      = {2017},
  abstract  = {For an arbitrary euclidean field F we introduce a central extension (G(F), Phi) of SL(2, F) admitting a left-ordering and study its algebraic properties. The elements of G(F) are order preserving bijections of the convex hull of Q in F. If F = R then G(F) is isomorphic to the classical universal covering group of the Lie group SL(2, R). Among other results we show that G(F) is a perfect group which possesses a rank 1 cone of exceptional type. We also prove that its centre is an infinite cyclic group and investigate its normal subgroups.},
  language  = {en}
}
@article{Bubenzer2014,
  author    = {Bubenzer, Johannes},
  title     = {Cycle-aware minimization of acyclic deterministic finite-state automata},
  series = {Discrete applied mathematics},
  volume    = {163},
  journal   = {Discrete applied mathematics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0166-218X},
  doi       = {10.1016/j.dam.2013.08.003},
  pages     = {238 -- +},
  year      = {2014},
  abstract  = {In this paper a linear-time algorithm for the minimization of acyclic deterministic finite-state automata is presented. The algorithm runs significantly faster than previous algorithms for the same task. This is shown by a comparison of the running times of both algorithms. Additionally, a variation of the new algorithm is presented which handles cyclic automata as input. The new cycle-aware algorithm minimizes acyclic automata in the desired way. In case of cyclic input, the algorithm minimizes all acyclic suffixes of the input automaton.},
  language  = {en}
}
@unpublished{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231},
  year      = {1998},
  abstract  = {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.},
  language  = {en}
}
@article{BuchholzSchulze1997,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Anisotropic edges pseudo-differential operators withdiscrete asymptotics},
  year      = {1997},
  language  = {en}
}
@book{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 11},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {57 S.},
  year      = {1998},
  language  = {en}
}
@article{BurenkovSchulzeTarchanov1998,
  author    = {Burenkov, V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Extension operators for sobolev spaces commuting with a given transform},
  year      = {1998},
  language  = {en}
}
@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}
}