@unpublished{GalstianYagdjian1997,
  author    = {Galstian, Anahit and Yagdjian, Karen},
  title     = {Exponential function of pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24982},
  year      = {1997},
  abstract  = {The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Nonstationary problems for equations of Borel-Fuchs type},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24973},
  year      = {1997},
  abstract  = {In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On the index of differential operators on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24965},
  year      = {1997},
  abstract  = {The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.},
  language  = {en}
}
@unpublished{RabinovichSchulzeTarkhanov1997,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A calculus of boundary value problems in domains with Non-Lipschitz Singular Points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24957},
  year      = {1997},
  abstract  = {The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Lefschetz theory on manifolds with edges : introduction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24948},
  year      = {1997},
  abstract  = {The aim of this book is to develop the Lefschetz fixed point theory for elliptic complexes of pseudodifferential operators on manifolds with edges. The general Lefschetz theory contains the index theory as a special case, while the case to be studied is much more easier than the index problem. The main topics are: - The calculus of pseudodifferential operators on manifolds with edges, especially symbol structures (inner as well as edge symbols). - The concept of ellipticity, parametrix constructions, elliptic regularity in Sobolev spaces. - Hodge theory for elliptic complexes of pseudodifferential operators on manifolds with edges. - Development of the algebraic constructions for these complexes, such as homotopy, tensor products, duality. - A generalization of the fixed point formula of Atiyah and Bott for the case of simple fixed points. - Development of the fixed point formula also in the case of non-simple fixed points, provided that the complex consists of diferential operarators only. - Investigation of geometric complexes (such as, for instance, the de Rham complex and the Dolbeault complex). Results in this direction are desirable because of both purely mathe matical reasons and applications in natural sciences.},
  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}
}
@misc{Reich1994,
  author    = {Reich, Sebastian},
  title     = {Momentum conserving symplectic integrators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-16824},
  year      = {1994},
  abstract  = {In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n).},
  language  = {en}
}
@misc{AscherChinPetzoldetal.1994,
  author    = {Ascher, Uri M. and Chin, Hongsheng and Petzold, Linda R. and Reich, Sebastian},
  title     = {Stabilization of constrained mechanical systems with DAEs and invariant manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15698},
  year      = {1994},
  abstract  = {Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.},
  language  = {en}
}
@misc{LeimkuhlerReich1994,
  author    = {Leimkuhler, Benedict and Reich, Sebastian},
  title     = {Symplectic integration of constrained Hamiltonian systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15653},
  year      = {1994},
  abstract  = {A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.},
  language  = {en}
}
@misc{Reich1995,
  author    = {Reich, Sebastian},
  title     = {Smoothed dynamics of highly oscillatory Hamiltonian systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15639},
  year      = {1995},
  abstract  = {We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.},
  language  = {en}
}