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

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