13,127 research outputs found
Orientability of Fredholm families and topological degree
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
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Intellectual Property Topics in Open University Distance-Taught Courses
Patents lie at the heart of engineering as a permanent and ongoing record of invention. We have taught the subject for about 5 years in both UG and PG courses, written from scratch owing to the absence of textbooks aimed specifically at engineers. Most practising engineers develop patent skills on the job rather than through conventional courses. But there is a need to present such courses as early as possible in the engineering curriculum, so that graduates have a flying start in their first employment
On the covering dimension of the set of solutions of some nonlinear equations
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
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
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
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
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
Averaging technique applied to variational equations describing rotational motions of rigid triaxial body in elliptical orbi
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