180 research outputs found

    Bispecial factors in circular non-pushy D0L languages

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    We study bispecial factors in fixed points of morphisms. In particular, we propose a simple method of how to find all bispecial words of non-pushy circular D0L-systems. This method can be formulated as an algorithm. Moreover, we prove that non-pushy circular D0L-systems are exactly those with finite critical exponent.Comment: 18 pages, 5 figure

    Evolutionary influences on the structure of red-giant acoustic oscillation spectra from 600d of Kepler observations

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    Context: The Kepler space mission is reaching continuous observing times long enough to start studying the fine structure of the observed p-mode spectra. Aims: In this paper, we aim to study the signature of stellar evolution on the radial and p-dominated l=2 modes in an ensemble of red giants that show solar-type oscillations. Results: We find that the phase shift of the central radial mode (eps_c) is significantly different for red giants at a given large frequency separation (Dnu_c) but which burn only H in a shell (RGB) than those that have already ignited core He burning. Even though not directly probing the stellar core the pair of local seismic observables (Dnu_c, eps_c) can be used as an evolutionary stage discriminator that turned out to be as reliable as the period spacing of the mixed dipole modes. We find a tight correlation between eps_c and Dnu_c for RGB stars and no indication that eps_c depends on other properties of these stars. It appears that the difference in eps_c between the two populations becomes if we use an average of several radial orders, instead of a local, i.e. only around the central radial mode, Dnu to determine the phase shift. This indicates that the information on the evolutionary stage is encoded locally, in the shape of the radial mode sequence. This shape turns out to be approximately symmetric around the central radial mode for RGB stars but asymmetric for core He burning stars. We computed radial modes for a sequence of RG models and find them to qualitatively confirm our findings. We also find that, at least in our models, the local Dnu is an at least as good and mostly better proxy for both the asymptotic spacing and the large separation scaled from the model density than the average Dnu. Finally, we investigate the signature of the evolutionary stage on the small frequency separation and quantify the mass dependency of this seismic parameter.Comment: 12 pages, 9 figures, accepted for publication in A&

    A Geometric Approach to the stabilisation of certain sequences of Kronecker coefficients

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    We give another proof, using tools from Geometric Invariant Theory, of a result due to S. Sam and A. Snowden in 2014, concerning the stability of Kro-necker coefficients. This result states that some sequences of Kronecker coefficients eventually stabilise, and our method gives a nice geometric bound from which the stabilisation occurs. We perform the explicit computation of such a bound on two examples, one being the classical case of Murnaghan's stability. Moreover, we see that our techniques apply to other coefficients arising in Representation Theory: namely to some plethysm coefficients and in the case of the tensor product of representations of the hyperoctahedral group.Comment: Manuscripta mathematica, Springer Verlag, In press, \&\#x3008;https://doi.org/10.1007/s00229-018-1021-4\&\#x300

    Large Deviation Approach to the Randomly Forced Navier-Stokes Equation

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    The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure yields the dimensional scaling predicted by K41 theory at the lowest perturbative order, where the perturbation parameter is the inverse Reynolds number. Moreover, an explicit expression of the prefactor of the scaling law is obtained.Comment: 24 page

    Integrable systems and holomorphic curves

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    In this paper we attempt a self-contained approach to infinite dimensional Hamiltonian systems appearing from holomorphic curve counting in Gromov-Witten theory. It consists of two parts. The first one is basically a survey of Dubrovin's approach to bihamiltonian tau-symmetric systems and their relation with Frobenius manifolds. We will mainly focus on the dispersionless case, with just some hints on Dubrovin's reconstruction of the dispersive tail. The second part deals with the relation of such systems to rational Gromov-Witten and Symplectic Field Theory. We will use Symplectic Field theory of S1×MS^1\times M as a language for the Gromov-Witten theory of a closed symplectic manifold MM. Such language is more natural from the integrable systems viewpoint. We will show how the integrable system arising from Symplectic Field Theory of S1×MS^1\times M coincides with the one associated to the Frobenius structure of the quantum cohomology of MM.Comment: Partly material from a working group on integrable systems organized by O. Fabert, D. Zvonkine and the author at the MSRI - Berkeley in the Fall semester 2009. Corrected some mistake

    Morphic words and equidistributed sequences

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    The problem we consider is the following: Given an infinite word ww on an ordered alphabet, construct the sequence νw=(ν[n])n\nu_w=(\nu[n])_n, equidistributed on [0,1][0,1] and such that ν[m]<ν[n]\nu[m]<\nu[n] if and only if σm(w)<σn(w)\sigma^m(w)<\sigma^n(w), where σ\sigma is the shift operation, erasing the first symbol of ww. The sequence νw\nu_w exists and is unique for every word with well-defined positive uniform frequencies of every factor, or, in dynamical terms, for every element of a uniquely ergodic subshift. In this paper we describe the construction of νw\nu_w for the case when the subshift of ww is generated by a morphism of a special kind; then we overcome some technical difficulties to extend the result to all binary morphisms. The sequence νw\nu_w in this case is also constructed with a morphism. At last, we introduce a software tool which, given a binary morphism φ\varphi, computes the morphism on extended intervals and first elements of the equidistributed sequences associated with fixed points of φ\varphi

    On the critical exponent of generalized Thue-Morse words

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    For certain generalized Thue-Morse words t, we compute the "critical exponent", i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine exactly the occurrences of powers realizing it.Comment: 13 pages; to appear in Discrete Mathematics and Theoretical Computer Science (accepted October 15, 2007
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