13,127 research outputs found

    Orientability of Fredholm families and topological degree

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    We construct a degree theory for oriented Fredholm mappings of index zero between open subsets of Banach spaces and between Banach manifolds. Our approach is based on the orientation of Fredholm mappings: it does not use Fredholm structures on the domain and target spaces. We provide a computable formula for the change in degree through an admissible homotopy that is necessary for applications to global bifurcation. The notion of orientation enables us to establish rather precise relationships between our degree and many other degree theories for particular classes of Fredholm maps, including the Elworthy-Tromba degree, which have appeared in the literature in a seemingly unrelated manner

    On the covering dimension of the set of solutions of some nonlinear equations

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    We prove an abstract theorem whose sole hypothesis is that the degree of a certain map is nonzero and whose parametric equations are studied using cohomological mconclusions imply sharp, multidimensional continuation results. Applications are given to nonlinear partial differential equations

    Complementing maps, continuation and global bifurcation

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    We state, and indicate some of the consequences of, a theorem whose sole assumption is the nonvanishing of the Leray- Schauder degree of a compact vector field, and whose conclusions yield multidimensional existence, continuation and bifurcation result

    Application of the methods of celestial mechanics to the rigid body problem Final report, 1 Jul. 1965 - 1 Jun. 1966

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    Celestial mechanics perturbation methods applied to problem of describing motion of rigid artificial earth satellite about its center of mas

    Limit Theorems For Quantum Walks Associated with Hadamard Matrices

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    We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given

    Media Coverage of EPA\u27s Draft Dioxin Reassessment Report

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    Using content analysis, the authors examine the utility of news media in democratic decision making

    Certain comments on the application of the method of averaging to the study of the rotational motions of a triaxial rigid body

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    Averaging technique applied to variational equations describing rotational motions of rigid triaxial body in elliptical orbi
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