9,419 research outputs found

    Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse-square potentials

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    Let \La be a Schr\"odinger operator with inverse square potential ax2a|x|^{-2} on \Rd, d\geq 3. The main aim of this paper is to prove weighted estimates for fractional powers of \La. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to \La. As an application, we obtain smoothing estimates regarding the propagator e^{it\La}

    Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse-square potentials

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    Let \La be a Schr\"odinger operator with inverse square potential ax2a|x|^{-2} on \Rd, d\geq 3. The main aim of this paper is to prove weighted estimates for fractional powers of \La. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to \La. As an application, we obtain smoothing estimates regarding the propagator e^{it\La}

    Experimental and theoretical analyses of three-dimensional surface crack propagation

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    2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

    Clinical features and risk factors of cognitive impairment after stroke in Hong Kong Chinese

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    Electronic structure of the vortex lattice of d-, d+is-, and dx2-y2+idxy-wave superconductors

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    On the basis of the self-consistent Bogoliubov-de Gennes equations and a tight-binding lattice model, we investigate the quasiparticle spectrum of vortex-lattice state in pure d-, mixed d+is, and dx2-y2+idxy-wave superconductors. For a d-wave case, the local density of states (LDOS) at the vortex core shows a multipeak structure, and the positions of peaks as well as the width of splitting between peaks are sensitively dependent on both the magnetic-field strength and the orientation of the vortex lattice. For the mixed d+is- and dx2-y2+idxy-wave pairing states, we observe a double-peak structure of the local density of states at vortex center, where the two peaks are asymmetrically situated around the Fermi energy. By taking into account the matrix-element effect, the local density of states appears to be qualitatively consistent with the scanning-tunneling-microscopy experimental data.published_or_final_versio

    Heuristic Approach for a Combined Transfer Line Balancing and Buffer Allocation Problem Considering Uncertain Demand

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    Featured Application This research was initiated by an industrial project. The problem was the design and configuration of machining lines for engine blocks. The proposed approach was validated using four real cases provided by the industrial partners of the project. The proposed approach could easily be applied to the design and configuration of any machining line for the production of a single complex mechanical component. In this paper, we refer to a real case study of an industrial partner recently committed to its project on the design of a multi-unit and multi-product manufacturing system. Although the considered problem refers to an actual complex manufacturing system, it can be theoretically classified as a union of two key problems that need to be solved during the transfer line design stage: the transfer line balancing problem (TLBP) and the buffer allocation problem (BAP). As two closely related problems, TLBP and BAP usually have similar optimizing directions and share the same purpose: finding a balance between the performance of the transfer line system as well as minimizing investment costs. These problems are usually solved sequentially, but this leads to solutions close to a local optimum in the solution space and not to the global optimum of the overall problem. This paper presents a multi-objective optimization for concurrently solving transfer line balancing and buffer allocation problems. The new approach is based on a combination of evolutionary and heuristic-based algorithms and takes into account the uncertainty of market demand. To validate the proposed approach, an industrial case study in a multi-unit manufacturing system producing multiple products (four engine blocks) is discussed
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