10,901 research outputs found
Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules
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
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 and the space of 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
Let \cP_n be the complex vector space of all polynomials of degree at most
. We give several characterizations of the linear operators T\in\cL(\cP_n)
for which there exists a constant such that for all nonconstant
p\in\cP_n there exist a root of and a root of with
. We prove that such perturbations leave the degree unchanged and,
for a suitable pairing of the roots of and , the roots are never
displaced by more than a uniform constant independent on . We show that such
``good'' operators are exactly the invertible elements of the commutative
algebra generated by the differentiation operator. We provide upper bounds in
terms of for the relevant constants.Comment: 23 page
HYMAD: Hybrid DTN-MANET Routing for Dense and Highly Dynamic Wireless Networks
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
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Unions: Rent Extractors or Creators?
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Towards automated knowledge-based mapping between individual conceptualisations to empower personalisation of Geospatial Semantic Web
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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