2,130 research outputs found

    Electron Redistribution of Aromatic Ligands in (Arene)Cr(CO)\u3csub\u3e3\u3c/sub\u3e Complexes. Structural (Bond-Length) Changes as Quantitative Measures

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    Arene ligands experience significant ring expansion upon coordination with chromium tricarbonyl, as established by precise X-ray crystallographic analyses of various (η6-arene)Cr(CO)3 complexes. Such changes in ligand structures result from the charge (electron) redistribution, Ar+−Cr-, upon arene coordination, since they are closely related to those found in the intermolecular 1:1 complexes of the corresponding series of arenes with nitrosonium cation (NO+). The latter are prototypical examples of charge-transfer complexes as described by Mulliken. As such, they show enhanced degrees of charge (electron) transfer that approach unity, which is confirmed by quantitative comparison with the structural changes measured in the one-electron (oxidative) transformation of electron-rich arene donors (Ar) to the cation-radicals (Ar•+). Such a charge redistribution thus readily accounts for the enhanced reactivity to nucleophilic attack of the arene ligand in various ArCr(CO)3 complexes and related transition-metal/arene analogues

    On the arithmetic of crossratios and generalised Mertens' formulas

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    We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension up to 5. We prove generalisations of Mertens' formula for quadratic imaginary number fields and definite quaternion algebras over the rational numbers, counting results of quadratic irrationals with respect to two different natural complexities, and counting results of representations of (algebraic) integers by binary quadratic, Hermitian and Hamiltonian forms with error bounds. For each such statement, we prove an equidistribution result of the corresponding arithmetically defined points. Furthermore, we study the asymptotic properties of crossratios of such points, and expand Pollicott's recent results on the Schottky-Klein prime functions.Comment: 44 page

    Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and 9 families of 4-qubit entangled states

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    Three entanglement concentration protocols (ECPs) are proposed. The first ECP and a modified version of that are shown to be useful for the creation of maximally entangled cat and GHZ-like states from their non-maximally entangled counterparts. The last two ECPs are designed for the creation of maximally entangled (n+1)(n+1)-qubit state 12(∣Ψ0⟩∣0⟩+∣Ψ1⟩∣1⟩)\frac{1}{\sqrt{2}}\left(|\Psi_{0}\rangle|0\rangle+|\Psi_{1}\rangle|1\rangle\right) from the partially entangled (n+1)(n+1)-qubit normalized state α∣Ψ0⟩∣0⟩+β∣Ψ1⟩∣1⟩\alpha|\Psi_{0}\rangle|0\rangle+\beta|\Psi_{1}\rangle|1\rangle, where ⟨Ψ1∣Ψ0⟩=0\langle\Psi_{1}|\Psi_{0}\rangle=0 and ∣α∣≠12|\alpha|\neq\frac{1}{\sqrt{2}}. It is also shown that W, GHZ, GHZ-like, Bell and cat states and specific states from the 9 SLOCC-nonequivalent families of 4-qubit entangled states can be expressed as 12(∣Ψ0⟩∣0⟩+∣Ψ1⟩∣1⟩)\frac{1}{\sqrt{2}}\left(|\Psi_{0}\rangle|0\rangle+|\Psi_{1}\rangle|1\rangle\right) and consequently the last two ECPs proposed here are applicable to all these states. Quantum circuits for implementation of the proposed ECPs are provided and it is shown that the proposed ECPs can be realized using linear optics. Efficiency of the ECPs are studied using a recently introduced quantitative measure (Phys. Rev. A 85\textbf{85}, 012307 (2012)). Limitations of the measure are also reported.Comment: 11 pages 7 figure

    Fractal Spectrum of a Quasi_periodically Driven Spin System

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    We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time behaviour of various dynamical quantities, such as the moments of the distribution of the wave packet. Our data suggest a close similarity between the information dimension of the spectrum and the exponent ruling the algebraic growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from [email protected]

    Cycle Equivalence of Graph Dynamical Systems

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    Graph dynamical systems (GDSs) can be used to describe a wide range of distributed, nonlinear phenomena. In this paper we characterize cycle equivalence of a class of finite GDSs called sequential dynamical systems SDSs. In general, two finite GDSs are cycle equivalent if their periodic orbits are isomorphic as directed graphs. Sequential dynamical systems may be thought of as generalized cellular automata, and use an update order to construct the dynamical system map. The main result of this paper is a characterization of cycle equivalence in terms of shifts and reflections of the SDS update order. We construct two graphs C(Y) and D(Y) whose components describe update orders that give rise to cycle equivalent SDSs. The number of components in C(Y) and D(Y) is an upper bound for the number of cycle equivalence classes one can obtain, and we enumerate these quantities through a recursion relation for several graph classes. The components of these graphs encode dynamical neutrality, the component sizes represent periodic orbit structural stability, and the number of components can be viewed as a system complexity measure

    Measuring Coverage of Prolog Programs Using Mutation Testing

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    Testing is an important aspect in professional software development, both to avoid and identify bugs as well as to increase maintainability. However, increasing the number of tests beyond a reasonable amount hinders development progress. To decide on the completeness of a test suite, many approaches to assert test coverage have been suggested. Yet, frameworks for logic programs remain scarce. In this paper, we introduce a framework for Prolog programs measuring test coverage using mutations. We elaborate the main ideas of mutation testing and transfer them to logic programs. To do so, we discuss the usefulness of different mutations in the context of Prolog and empirically evaluate them in a new mutation testing framework on different examples.Comment: 16 pages, Accepted for presentation in WFLP 201
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