TY - GEN A1 - Reich, Sebastian T1 - On a geometrical interpretation of differential-algebraic equations N2 - The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE. and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lowsr-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 157 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46683 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Congruences on maximal partial clones and strong regular varieties generated by preprimal partial algebras II Y1 - 1991 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Strong regular varieties of partial algebras I Y1 - 1991 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Minimal algebras and category equivalences Y1 - 1991 ER - TY - GEN A1 - Reich, Sebastian T1 - On an existence and uniqueness theory for nonlinear differential-algebraic equations N2 - An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure. A DAE is called regular if there is a unique nonautonomous vector field such that the solutions of the DAE and the solutions of the vector field are in one-to-one correspondence. Sufficient conditions for regularity of a DAE are derived in terms of constrained manifolds. Based on this differential-geometric characterization, existence and uniqueness results are stated for regular DAEs. Furthermore, our not ons are compared with techniques frequently used in the literature such as index and solvability. The results are illustrated in detail by means of a simple circuit example. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 158 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46706 ER - TY - GEN A1 - Reich, Sebastian T1 - Differential-algebraic equations and applications in circuit theory N2 - Technical and physical systems, especially electronic circuits, are frequently modeled as a system of differential and nonlinear implicit equations. In the literature such systems of equations are called differentialalgebraic equations (DAEs). It turns out that the numerical and analytical properties of a DAE depend on an integer called the index of the problem. For example, the well-known BDF method of Gear can be applied, in general, to a DAE only if the index does not exceed one. In this paper we give a geometric interpretation of higherindex DAEs and indicate problems arising in connection with such DAEs by means of several examples. N2 - Die mathematische Modellierung technisch physikalischer Systeme wie elektrische Netzwerke, führt häufig auf ein System von Differentialgleichungen und nichtlinearen impliziten Gleichungen sogenannten Algebrodifferentialgleichungen (ADGL). Es zeigt sich, daß die numerischen und analytischen Eigenschaften von ADGL durch den Index des Problems charakterisiert werden können. Insbesondere können die bekannten Integrationsformeln von Gear im allgemeinen nur auf ADGL mit dem Index eins angewendet werden. In diesem Beitrag wird eine geometrische Interpretation von ADGL mit einem höheren Index gegeben sowie auf Probleme im Zusammenhang mit derartigen ADGL an Hand verschiedener Beispiele hingewiesen. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 156 Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46646 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen A1 - Wang, Anzhong T1 - Plane domain walls when coupled with the Brans-Dicke scalar field T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 06 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Kasper, Uwe T1 - On the phenomenological description of particle and entropy creation T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 07 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Braunß, Hans-Andreas T1 - On holomorphic mappings of Schatten class type Y1 - 1992 ER - TY - BOOK A1 - Böckmann, Christine T1 - A modification of the Trust-Region Gauss-Newton method to solve separable nonlinear least squares problems T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 17 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Böckmann, Christine T1 - Curve fitting and identification of physical spectra T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 18 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - On inflation within closed Fiedmann universe models T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 02 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Scale-invariant gravity in two dimensions II T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 03 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Amendola, Luca A1 - Battaglia Mayer, Alexandra A1 - Capozziello, Salvatore A1 - Gottlöber, Stefan A1 - Müller, Volker A1 - Occhionero, Franco A1 - Schmidt, Hans-Jürgen T1 - Generalized sixth-order gravity and inflation JF - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 04 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Rainer, Martin T1 - Projective geometry for relativistic quantum physics T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 05 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Gottlöber, Stefan A1 - Schmidt, Hans-Jürgen A1 - Starobinsky, A. A. A1 - Müller, Volker T1 - Models of chaotic inflation JF - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 08 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - On the de Sitter space-time : the geometric foundation of infaltionary cosmology T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 10 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Reuter, Stefan A1 - Schmidt, Hans-Jürgen T1 - On the Wheeler-de Witt equation for homogeneous cosmological models T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 11 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Kasper, Uwe T1 - Particle and entropy creation in cosmology T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 13 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Junek, Heinz T1 - Factorization of operator ideals and boundes sets in tensor products of locally convex spaces T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 16 PB - Univ. CY - Potsdam ER - TY - BOOK ED - Denecke, Klaus-Dieter T1 - General algebra and applications T3 - Research and exposition in mathematics Y1 - 1993 SN - 3-88538-220-2 VL - 20 PB - Heldermann CY - Berlin ER - TY - BOOK A1 - Battaglia Mayer, Alexandra A1 - Schmidt, Hans-Jürgen T1 - The de Sitter space-time as attractor solution in eighth order gravity T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 05 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Jonas, Peter A1 - Langer, Heinz T1 - Selfadjoint extensions of a closed linear relation of defect one in a Krein space Y1 - 1993 ER - TY - JOUR A1 - Louis, Alfred K. A1 - Maaß, Peter T1 - Contour reconstructions for 3D X-Ray CT-Images Y1 - 1993 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Comment to a paper by J. Simon in Phys. Rev. D 45 (1992) 1953 T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 06 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Rainer, Martin T1 - Orientation duality of 4-dimensional real Lie algebras T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 08 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Some operatoralgebraic fundamentals of the algebraic quantum field theory T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 09 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Junek, Heinz T1 - Factorization of operator ideals and the BB-property Y1 - 1993 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - On the characterization of primal partial algebras by strong regular hyperidentities Y1 - 1994 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Halkowska, Katarzcyna T1 - P-compatible hybrid-identities and hyperidentities Y1 - 1994 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Malcev, I. A. T1 - Separation of clones by means of hyperidentities Y1 - 1994 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Wismath, Shelly T1 - Solid varieties of semigroups Y1 - 1994 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Hyperassociative semigroups Y1 - 1994 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Pre-solid varieties Y1 - 1994 ER - TY - GEN A1 - Ascher, Uri M. A1 - Chin, Hongsheng A1 - Reich, Sebastian T1 - Stabilization of DAEs and invariant manifolds N2 - Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 030 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15625 ER - TY - GEN A1 - Leimkuhler, Benedict A1 - Reich, Sebastian T1 - Symplectic integration of constrained Hamiltonian systems N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 032 KW - differential-algebraic equations KW - constrained Hamiltonian systems KW - canonical discretization schemes KW - symplectic methods Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15653 ER - TY - GEN A1 - Ascher, Uri M. A1 - Chin, Hongsheng A1 - Petzold, Linda R. A1 - Reich, Sebastian T1 - Stabilization of constrained mechanical systems with DAEs and invariant manifolds N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 033 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15698 ER - TY - GEN A1 - Reich, Sebastian T1 - Momentum conserving symplectic integrators N2 - 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). T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 044 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16824 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Why do all the curvature invariants of a gravitational wave vanish? T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 03 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Dahlke, Stephan A1 - Maaß, Peter T1 - The affine uncertainty principle in one and two dimensions T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1994 VL - 1994, 01 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Wollenberg, Manfred T1 - On an inverse problem in modular theory T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 07 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Dahlke, Stephan A1 - Maaß, Peter T1 - A continuous wavelet transform on tangent bundles of spheres T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 16 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Kasper, Uwe T1 - On first class sonstraints of simple cosmological models in Einstein's gravity theory T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 10 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Stability and Hamiltonian formulation of higher derivative theories T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 04 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Rainer, Martin T1 - Conformal minisuperspace quantization and equivalence of multidimensional classical and quantum models : lecuture presented at the International Conference on Multidimensional Cosmology, Jaroslavl, June 20-26, 1994 T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 09 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - A modified approach to the Doplicher-Roberts theorem on the construction of field algebra and the symmetry group in superselection theory T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1994 VL - 134 CY - Berlin ER - TY - BOOK A1 - Kasper, Uwe T1 - On the Hamilton formalism for cosmological models in fourth order gravity theories T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 11 CY - Potsdam ER - TY - BOOK A1 - Neidhardt, Hagen A1 - Zagrebnov, Valentin A. ED - Demuth, Michael ED - Exner, Pavel T1 - Mathematical results in quantum mechanics : international conference in Blossin (Germany), May 17 - 21, 1993 T3 - Operator Theory Y1 - 1994 VL - 70 PB - Birkhäuser CY - Basel ER - TY - JOUR A1 - Gähler, Siegfried A1 - Gähler, Werner T1 - Fuzzy real numbers Y1 - 1994 ER - TY - JOUR A1 - Louis, Alfred K. A1 - Maaß, Peter A1 - Rieder, Andreas A1 - Stark, H.-G. T1 - Wavelets and digital image processing Y1 - 1994 ER - TY - JOUR A1 - Jaksic, V. A1 - Jung, K. A1 - Klein, Markus A1 - Seiler, R. T1 - Corrections to quantized charge transport in quantum hall systems Y1 - 1994 ER - TY - BOOK A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - A remark on covariant and causal nets of CAR-resp.CCR-type local algebras assigned to the irreducible unitary representation of the poincare group labeled by (m>0, s, +) T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1994 VL - 120 CY - Berlin ER - TY - JOUR A1 - Klein, Markus T1 - Hall conductance of Riemann surfaces Y1 - 1994 ER - TY - GEN A1 - Klotzek, Benno T1 - Falkner, N., A characterization of inner product spaces Y1 - 1994 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - An alternate Hamiltonian formulation of fourth-order theories T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 12 PB - Univ. CY - Potsdam ER - TY - THES A1 - Rainer, Martin T1 - The topology of the space of real LIE algebras up to dimension 4 with applications to homogeneous cosmological models Y1 - 1994 PB - Univ. ER - TY - JOUR A1 - Maaß, Peter T1 - Wavelet galerkin methods for inverse problems Y1 - 1994 ER - TY - JOUR A1 - Neidhardt, Hagen A1 - Zagrebnov, Valentin A. T1 - Singular perturbations, regularization and extension theory Y1 - 1994 ER - TY - GEN A1 - Quaisser, Erhard T1 - Kuperberg, W., Discrete and Computational Geometry, 12 (1994), S. 83 - 90 BT - Discrete and Computational Geometry Y1 - 1994 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Comment on stability of the semiclassical Einstein equation Y1 - 1994 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Stability and Hamiltonian formulation of higher derivative theories Y1 - 1994 ER - TY - BOOK ED - Läuter, Henning T1 - Statistics : a journal of theoretical and applied statistics Y1 - 1994 SN - 0233-1888 PB - Gordon & Breach Science Publ. CY - Reading Berkshire [u.a.] ER - TY - JOUR A1 - Brasche, Johannes F. A1 - Neidhardt, Hagen T1 - Some remarks to Krein's extension theory Y1 - 1994 ER - TY - JOUR A1 - Brasche, Johannes F. A1 - Koshmanenko, V. D. A1 - Neidhardt, Hagen T1 - Some new aspects of Krein's extension theory Y1 - 1994 ER - TY - JOUR A1 - Schrohe, Elmar A1 - Schulze, Bert-Wolfgang T1 - Boundary value problems in Boutet de Monvelïs algebra for manifolds with conical singularities I Y1 - 1994 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Resurgent analysis and differential equations with singularities Y1 - 1994 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang T1 - The variable discrete asymptotics in pseudo-differential boundary value problems Y1 - 1994 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang T1 - Pseudo-differential operators, ellipticity and asymptotics on manifolds with edges Y1 - 1994 ER - TY - JOUR A1 - Dorschfeldt, Christoph A1 - Schulze, Bert-Wolfgang T1 - Pseudo-differential operators with operator-valued symbols in the Mellin-edge-approach Y1 - 1994 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang T1 - Pseudo-differential boundary value problems, conical singularities, and asymptotics T3 - Mathematical topics Y1 - 1994 SN - 3-05-501597-5 VL - 4 PB - Akad.-Verl. CY - Berlin ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Plonka, J. T1 - Regularization and normalization of solid varieties Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Reichel, Mario T1 - Monoids of hypersubstitutions and m-solid varieties Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Plonka, J. T1 - Edge-solid varieties Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Malcev, I. A. A1 - Reschke, M. T1 - On separation of Boolean clones by means of hyperidentities Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Pre-solid varieties of commutative semigroups Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - M-solid varieties of semigroups Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Pre-solid varieties of semigroups Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Hybrid identities and hybrid equational logic Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Clones and hyperidentities Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Lüders, Otfried T1 - Category equivalences of clones Y1 - 1995 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Lau, Dietlinde A1 - Pöschel, Reinhard A1 - Schweigert, D. T1 - Free clones and solid varieties Y1 - 1995 ER - TY - GEN A1 - Reich, Sebastian T1 - Smoothed dynamics of highly oscillatory Hamiltonian systems N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 031 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15639 ER - TY - GEN A1 - Reich, Sebastian T1 - On the local qualitative behavior of differential-algebraic equations N2 - A theoretical famework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equili Drium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for vector fields, to DAEs that are regular locally around a g: ven equilibrium point (e.g. Local Stable and Unstable Manifold Theorem, Hopf theorem). It is important that ihese theorems are stated in terms of the given problem and not in terms of the corresponding vector field. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 159 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46739 ER - TY - BOOK A1 - Konakov, Valentin S. A1 - Läuter, Henning A1 - Liero, Hannelore T1 - Nonparametric versus parametric goodness of fit T3 - Discussion Paper / Humboldt-Universität zu Berlin, Institut für Mathematik, SFB 373 Y1 - 1995 VL - 49 CY - Berlin ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - An alternate Hamiltonian formulation of fourth-order theories Y1 - 1995 CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Comment on conformal transformations single out a unique measure of distance Y1 - 1995 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - How to measure spatial distances? T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1995 VL - 1995, 10 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Gähler, Werner A1 - Bayoumi, Fatma A1 - Kandil, Anwar A1 - Nouh, Ali T1 - The theory of general fuzzy neighborhood structures, part I Y1 - 1995 ER - TY - JOUR A1 - Schrohe, Elmar T1 - Schulze, B.-W., Pseudo-Differential Boundary Value Problems, Conical Singularities, and Asymptotics; Berlin, Akademie-Verl., 1995 BT - Pseudo-Differential Boundary Value Problems, Conical Singularities and Asymptotics Y1 - 1995 ER - TY - JOUR A1 - Brasche, Johannes F. A1 - Neidhardt, Hagen T1 - On the point spectrum of selfadjoint extensions Y1 - 1995 ER - TY - BOOK A1 - Junek, Heinz T1 - Closed ideals of polynomials T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1995 PB - Univ. CY - Potsdam ER - TY - THES A1 - Dorschfeldt, Christoph T1 - An algebra of mellin pseudo-differential operators near corner singularities Y1 - 1995 CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Kasper, Uwe A1 - Kluske, Sabine A1 - Rainer, Martin A1 - Reuter, Stefan T1 - Stability properties of the Starobinsky cosmological model Y1 - 1995 ER - TY - THES A1 - Behm, Sebastian T1 - Pseudo-differential operators with parameters on manifolds with edges Y1 - 1995 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Operatoralgebraic methods in quantum field theory : a series of lectures Y1 - 1995 PB - Akademie Verl. CY - Berlin ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Fourier transformation of Hilbert C*-systems, with compact groups, by their regular representation Y1 - 1995 ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - On free nets over Minkowski space Y1 - 1995 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - On Haag dual nets over compact spaces Y1 - 1995 ER - TY - JOUR A1 - Böckmann, Christine T1 - A modification of the trust-region Gauss-Newton method to solve separable nonlinear least squares problems Y1 - 1995 ER - TY - JOUR A1 - Brasche, Johannes F. A1 - Neidhardt, Hagen T1 - On the absolutely continuous spectrum of self-adjoint extensions Y1 - 1995 ER -