9,278 research outputs found

    Transmission eigenvalues and thermoacoustic tomography

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    The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimension greater than or equal to three, we prove that the transmission spectrum for a pair of radially symmetric non-trapping sound speeds is countable, and conclude that the ranges of the associated thermoacoustic maps have only trivial intersection

    Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions

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    We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for pxpamodq1/p\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p and, as a by-product, for the Meissel-Mertens constant defined as pamodq(log(11/p)+1/p)\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p), for q{3q \in \{3, ..., 100}100\} and (q,a)=1(q, a) = 1.Comment: 12 pages, 6 table

    The longest excursion of stochastic processes in nonequilibrium systems

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    We consider the excursions, i.e. the intervals between consecutive zeros, of stochastic processes that arise in a variety of nonequilibrium systems and study the temporal growth of the longest one l_{\max}(t) up to time t. For smooth processes, we find a universal linear growth \simeq Q_{\infty} t with a model dependent amplitude Q_\infty. In contrast, for non-smooth processes with a persistence exponent \theta, we show that < l_{\max}(t) > has a linear growth if \theta \sim t^{1-\psi} if \theta > \theta_c. The amplitude Q_{\infty} and the exponent \psi are novel quantities associated to nonequilibrium dynamics. These behaviors are obtained by exact analytical calculations for renewal and multiplicative processes and numerical simulations for other systems such as the coarsening dynamics in Ising model as well as the diffusion equation with random initial conditions.Comment: 4 pages,2 figure

    Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

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    The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure

    City Sanitation Problems

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    Grothendieck's constant and local models for noisy entangled quantum states

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    We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show that there is a local model for projective measurements if and only if p1/KG(3)p \le 1/K_G(3), where KG(3)K_G(3) is Grothendieck's constant of order 3. Known bounds on KG(3)K_G(3) prove the existence of this model at least for p0.66p \lesssim 0.66, quite close to the current region of Bell violation, p0.71p \sim 0.71. We generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur

    Secondary school admissions

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