69,516 research outputs found

    Comment on "Revision of Bubble Bursting: Universal Scaling Laws of Top Jet Drop Size and Speed"

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    Comment on "Revision of Bubble Bursting: Universal Scaling Laws of Top Jet Drop Size and Speed"Comment: Accepted for publication in Physical Review Letters (2018

    Estimation of the modulation index of cpm signals using hos

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    Three simple methods are proposed for the estimation of the modulation index of continuous phase modulated signals in noise. These methods employ the estimated autocorrelation and fourth-order cumulant sequences of the received signal after sampling at the symbol rate. Analytic expressions are derived for the asymptotic mean and variance of the estimated parameters which are corroborated by means of Monte Carlo simulations. The performance of the methods is illustrated graphically and numerically. It is concluded that, under significant noise degradation, only the scheme based on the fourth-order cumulant sequence can be used to estimate consistently the modulation index h in the range 0(h(1.Peer ReviewedPostprint (published version

    Blind multiuser deconvolution in fading and dispersive channels

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    An adaptive near-far resistant technique for the blind joint multiuser identification and detection in asynchronous CDMA systems is analyzed in fading and dispersive GSM channels.Peer ReviewedPostprint (published version

    A relationship between the ideals of Fq[x,y,x1,y1]\mathbb{F}_q\left[x, y, x^{-1}, y^{-1} \right] and the Fibonacci numbers

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    Let Cn(q)C_n(q) be the number of ideals of codimension nn of Fq[x,y,x1,y1]\mathbb{F}_q\left[x, y, x^{-1}, y^{-1} \right], where Fq\mathbb{F}_q is the finite field with qq elements. Kassel and Reutenauer [KasselReutenauer2015A] proved that Cn(q)C_n(q) is a polynomial in qq for any fixed value of n1n \geq 1. For q=3+52q = \frac{3+\sqrt{5}}{2}, this combinatorial interpretation of Cn(q)C_n(q) is lost. Nevertheless, an unexpected connexion with Fibonacci numbers appears. Let fnf_n be the nn-th Fibonacci number (following the convention f0=0f_0 = 0, f1=1f_1 = 1). Define the series F(t)=n1f2ntn. F(t) = \sum_{n \geq 1} f_{2n}\,t^n. We will prove that for each n1n \geq 1, Cn(3+52)=λn(f2n3+52f2n2), C_n\left( \frac{3+\sqrt{5}}{2}\right) = \lambda_n \, \left(f_{2n} \frac{3+\sqrt{5}}{2} - f_{2n-2} \right) , where the integers λn0\lambda_n \geq 0 are given by the following generating function \prod_{m \geq 1} \left(1+F\left( t^m\right)\right) = 1 + \sum_{n \geq 1} \lambda_n\,t^n. $

    On prime numbers of the form 2n±k2^n \pm k

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    Consider the set K\mathcal{K} of integers kk for which there are infinitely many primes pp such that p+kp+k is a power of 22. The aim of this paper is to show a relationship between K\mathcal{K} and the limits points of some set rational numbers related to a sequence of polynomials Cn(q)C_n(q) introduced by Kassel and Reutenauer [KasselReutenauer]

    Middle divisors and σ\sigma-palindromic Dyck words

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    Given a real number λ>1\lambda > 1, we say that dnd|n is a λ\lambda-middle divisor of nn if nλ<dλn. \sqrt{\frac{n}{\lambda}} < d \leq \sqrt{\lambda n}. We will prove that there are integers having an arbitrarily large number of λ\lambda-middle divisors. Consider the word  ⁣n ⁣λ:=w1w2...wk{a,b}, \langle\! \langle n \rangle\! \rangle_{\lambda} := w_1 w_2 ... w_k \in \{a,b\}^{\ast}, given by wi:={aif uiDn\(λDn),bif ui(λDn)\Dn, w_i := \left\{ \begin{array}{c l} a & \textrm{if } u_i \in D_n \backslash \left(\lambda D_n\right), \\ b & \textrm{if } u_i \in \left(\lambda D_n\right)\backslash D_n, \end{array} \right. where DnD_n is the set of divisors of nn, λDn:={λd:dDn}\lambda D_n := \{\lambda d: \quad d \in D_n\} and u1,u2,...,uku_1, u_2, ..., u_k are the elements of the symmetric difference DnλDnD_n \triangle \lambda D_n written in increasing order. We will prove that the language Lλ:={ ⁣n ⁣λ:nZ1} \mathcal{L}_{\lambda} := \left\{\langle\! \langle n \rangle\! \rangle_{\lambda} : \quad n \in \mathbb{Z}_{\geq 1} \right\} contains Dyck words having an arbitrarily large number of centered tunnels. We will show a connection between both results
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