9,996 research outputs found

    Asymptotics of orthogonal polynomials and point perturbation on the unit circle

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    In the first five sections, we deal with the class of probability measures with asymptotically periodic Verblunsky coefficients of p-type bounded variation. The goal is to investigate the perturbation of the Verblunsky coefficients when we add a pure point to a gap of the essential spectrum. For the asymptotically constant case, we give an asymptotic formula for the orthonormal polynomials in the gap, prove that the perturbation term converges and show the limit explicitly. Furthermore, we prove that the perturbation is of bounded variation. Then we generalize the method to the asymptotically periodic case and prove similar results. In the last two sections, we show that the bounded variation condition can be removed if a certain symmetry condition is satisfied. Finally, we consider the special case when the Verblunsky coefficients are real with the rate of convergence being c_n . We prove that the rate of convergence of the perturbation is in fact O(c_n). In particular, the special case c_n = 1/n will serve as a counterexample to the possibility that the convergence of the perturbed Verblunsky coefficients should be exponentially fast when a point is added to a gap.Comment: Published in the Journal of Approximation Theor

    Porous calcium phosphate ceramics prepared by coating polyurethane foams with calcium phosphate cements

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    Porous calcium phosphates have important biomedical applications such as bone defect fillers, tissue engineering scaffolds, and drug delivery systems. While a number of methods to produce the porous calcium phosphate ceramics have been reported, this study aimed to develop a new fabrication method. The new method involved the use of polyurethane foams to produce highly porous calcium phosphate cements (CPCs). By firing the porous CPCs at 1200 degrees Celsius, the polyurethane foams were burnt off and the CPCs prepared at room temperature were converted into sintered porous hydroxyapatite-based calcium phosphate ceramics. The sintered porous calcium phosphate ceramics could then be coated with a layer of the CPC at room temperature, resulting in high porosity, high pore interconnectivity, and controlled pores size

    Photonic quantum memory in two-level ensembles based on modulating the refractive index in time: equivalence to gradient echo memory

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    We present a quantum memory protocol that allows to store light in ensembles of two-level atoms, e.g. rare-earth ions doped into a crystal, by modulating the refractive index of the host medium of the atoms linearly in time. We show that under certain conditions the resulting dynamics is equivalent to that underlying the gradient echo memory protocol, which relies on a spatial gradient of the atomic resonance frequencies. We discuss the prospects for an experimental implementation.Comment: 5 pages, 2 figure

    Exploring The Influences on Cyber Education in a Bilingual Higher Institution

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    This paper presents the research study which explores the variables influencing the learning effectiveness of the students taking an online introductory information technology course in cyber education in a bilingual higher education institution in Hong Kong. These variables are: (1) student's English proficiency, (2) instructor's guidance in an online discussion forum and (3) peer students' collaboration in an online discussion forum. Correlation analysis was adopted to identify whether any of these variables could be potential factors on the students 'learning performance while multiple regression analysis was performed to explore the combined effect of these variables on the students' learning performance. Validity and reliability of this research study are highlighted in this paper. Finally, the research findings are discussed

    Implementation of an intelligent control system

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    A laboratory testbed facility which was constructed at NASA LeRC for the development of an Intelligent Control System (ICS) for reusable rocket engines is described. The framework of the ICS consists of a hierarchy of various control and diagnostic functions. The traditional high speed, closed-loop controller resides at the lowest level of the ICS hierarchy. Above this level resides the diagnostic functions which identify engine faults. The ICS top level consists of the coordination function which manages the interaction between an expert system and a traditional control system. The purpose of the testbed is to demonstrate the feasibility of the OCS concept by implementing the ICS as the primary controller in a simulation of the Space Shuttle Main Engine (SSME). The functions of the ICS which are implemented in the testbed are as follows: an SSME dynamic simulation with selected fault mode models, a reconfigurable controller, a neural network for sensor validation, a model-based failure detection algorithm, a rule based failure detection algorithm, a diagnostic expert system, an intelligent coordinator, and a user interface which provides a graphical representation of the event occurring within the testbed. The diverse nature of the ICS has led to the development of a distributed architecture consisting of specialized hardware and software for the implementation of the various functions. This testbed is made up of five different computer systems. These individual computers are discussed along with the schemes used to implement the various ICS components. The communication between computers and the timing and synchronization between components are also addressed

    Grimoires: Grid Registry with Metadata Oriented Interface: Robustness, Efficiency, Security --- Work-in-Progress

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    Grid registries allow users to discover resources made available by Grid resource providers. In this paper, we present our on-going work on a next-generation registry, initially designed as part of the myGrid project and to be part of the OMII Grid software release. Specifically, we discuss the support of semantic service descriptions and task/user-specific metadata, along with related performance and security considerations
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