@unpublished{AlsaedyTarkhanov2012,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {The method of Fischer-Riesz equations for elliptic boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-61792},
  year      = {2012},
  abstract  = {We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.},
  language  = {en}
}
@unpublished{Eckstein2012,
  author    = {Eckstein, Lars},
  title     = {'We're destroyed if we mix. And we're destroyed if we don't'},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85529},
  pages     = {11},
  year      = {2012},
  language  = {en}
}
@unpublished{KleinLeonardRosenberger2012,
  author    = {Klein, Markus and L{\´e}onard, Christian and Rosenberger, Elke},
  title     = {Agmon-type estimates for a class of jump processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56995},
  year      = {2012},
  abstract  = {In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.},
  language  = {en}
}
@unpublished{BlanchardMathe2012,
  author    = {Blanchard, Gilles and Math{\´e}, Peter},
  title     = {Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57117},
  year      = {2012},
  abstract  = {The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.},
  language  = {en}
}
@unpublished{KiselevTarkhanov2012,
  author    = {Kiselev, Oleg M. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Scattering of autoresonance trajectories upon a separatrix},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56880},
  year      = {2012},
  abstract  = {We study asymptotic properties of solutions to the primary resonance equation with large amplitude on a long time interval.},
  language  = {en}
}
@unpublished{RattanaBoeckmann2012,
  author    = {Rattana, Amornrat and B{\"o}ckmann, Christine},
  title     = {Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59279},
  year      = {2012},
  abstract  = {This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.},
  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}
}
@unpublished{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {On gravity, torsion and the spectral action principle},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59989},
  year      = {2012},
  abstract  = {We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.},
  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}
}
@unpublished{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {The Holst action by the spectral action principle},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60032},
  year      = {2012},
  abstract  = {We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.},
  language  = {en}
}