10,901 research outputs found

    Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

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    We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case where the electronic Hamiltonian admits a local gap in its spectrum. In particular, we show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, we study the propagation of certain wave packets up to long time values of Ehrenfest order. (This work has been accepted for publication as part of the Memoirs of the American Mathematical Society and will be published in a future volume.)Comment: 73 page

    Roots and polynomials as homeomorphic spaces

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    We provide a unified, elementary, topological approach to the classical results stating the continuity of the complex roots of a polynomial with respect to its coefficients, and the continuity of the coefficients with respect to the roots. In fact, endowing the space of monic polynomials of a fixed degree nn and the space of nn roots with suitable topologies, we are able to formulate the classical theorems in the form of a homeomorphism. Related topological facts are also considered.Comment: 16 page

    Perturbations of roots under linear transformations of polynomials

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    Let \cP_n be the complex vector space of all polynomials of degree at most nn. We give several characterizations of the linear operators T\in\cL(\cP_n) for which there exists a constant C>0C > 0 such that for all nonconstant p\in\cP_n there exist a root uu of pp and a root vv of TpTp with ∣u−v∣≤C|u-v|\leq C. We prove that such perturbations leave the degree unchanged and, for a suitable pairing of the roots of pp and TpTp, the roots are never displaced by more than a uniform constant independent on pp. We show that such ``good'' operators TT are exactly the invertible elements of the commutative algebra generated by the differentiation operator. We provide upper bounds in terms of TT for the relevant constants.Comment: 23 page

    HYMAD: Hybrid DTN-MANET Routing for Dense and Highly Dynamic Wireless Networks

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    In this paper we propose HYMAD, a Hybrid DTN-MANET routing protocol which uses DTN between disjoint groups of nodes while using MANET routing within these groups. HYMAD is fully decentralized and only makes use of topological information exchanges between the nodes. We evaluate the scheme in simulation by replaying real life traces which exhibit this highly dynamic connectivity. The results show that HYMAD outperforms the multi-copy Spray-and-Wait DTN routing protocol it extends, both in terms of delivery ratio and delay, for any number of message copies. Our conclusion is that such a Hybrid DTN-MANET approach offers a promising venue for the delivery of elastic data in mobile ad-hoc networks as it retains the resilience of a pure DTN protocol while significantly improving performance.Comment: 7 pages, 6 figure

    Towards automated knowledge-based mapping between individual conceptualisations to empower personalisation of Geospatial Semantic Web

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    Geospatial domain is characterised by vagueness, especially in the semantic disambiguation of the concepts in the domain, which makes defining universally accepted geo- ontology an onerous task. This is compounded by the lack of appropriate methods and techniques where the individual semantic conceptualisations can be captured and compared to each other. With multiple user conceptualisations, efforts towards a reliable Geospatial Semantic Web, therefore, require personalisation where user diversity can be incorporated. The work presented in this paper is part of our ongoing research on applying commonsense reasoning to elicit and maintain models that represent users' conceptualisations. Such user models will enable taking into account the users' perspective of the real world and will empower personalisation algorithms for the Semantic Web. Intelligent information processing over the Semantic Web can be achieved if different conceptualisations can be integrated in a semantic environment and mismatches between different conceptualisations can be outlined. In this paper, a formal approach for detecting mismatches between a user's and an expert's conceptual model is outlined. The formalisation is used as the basis to develop algorithms to compare models defined in OWL. The algorithms are illustrated in a geographical domain using concepts from the SPACE ontology developed as part of the SWEET suite of ontologies for the Semantic Web by NASA, and are evaluated by comparing test cases of possible user misconceptions
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