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Abstract  In this paper exact, analytical solutions are derived for another highly popular benchmark problem, namely, L-shaped domains having a horizontal line support and one or several point loads. The optimal topologies are obtained in the context of Michell structures, i.e., least-weight, stress, or compliance-controlled trusses with a single load condition. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we show that any graph map without periodic points has only one minimal set. We describe a class of graph maps without periodic points. Our main result is to give a structure theorem of graph maps without periodic points, which states that any graph map without periodic points must be topologically conjugate to one of the described class. In addition, we give some applications of the structure theorem. [Copyright &y& Elsevier]

Abstract: Cantor rings are rotational symmetric pupils that are generated from a Cantor set of a given level of growth. These pupils have certain fractal properties. For example, it is known that when illuminated by a general spherical wavefront they provide self-similar patterns at transverse planes in the Fraunhofer region. In this paper, we study the response of Cantor rings when illuminated by a Bessel light beam conforming what we call fractal axicons. It is shown that, with this kind of illumination a close replica of the radial profile of the pupil is obtained along the optical axis, i.e., we show that the axial behaviour of these pupils has self-similarity properties that can be correlated to those of the diffracting aperture. The influence of several construction parameters is numerically investigated. [Copyright &y& Elsevier]

In this paper, we prove the following: Let Y be a perfect paracompact (hereditarily Lindelöf) space and {Xn: n∈ω} be a countable collection of Čech-scattered paracompact (Lindelöf) spaces, then the product Y×∏n∈ωXn is paracompact (Lindelöf). [Copyright &y& Elsevier]

The motivation of this paper is to develop a local scheme of constructing G1 smooth B-spline surfaces with single interior knots over arbitrary topology. In this paper, we obtain the conditions of G1 continuity between two adjacent biquintic B-spline surfaces with interior single knots. These conditions are directly represented by the relevant control points of the two B-spline surfaces. By utilizing these G1 conditions, we develop the first local scheme of constructing G1 smooth biquintic B-spline surfaces with interior single knots for arbitrary topological type. The high complexity of deriving the local G1 scheme is well overwhelmed. The biquintic is the lowest degree for which there exists a local scheme of constructing G1 smooth B-spline surfaces with interior single knots over arbitrary topology. [Copyright &y& Elsevier]