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The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matriz is superregular if all of its minors that are not trivially zero are nonzero. Given a a × b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients,(More)
n≤x φ(n) n − 6 π 2 x. Motivé par une conjecture de Erdös, Lau a développé une nouvelle méthode et il a démontré que #{n ≤ T : H(n)H(n + 1) < 0} T. Nous consi-dérons des fonctions arithmétiques f (n) = d|n b d d dont l'addition peutêtre exprimée comme n≤x f (n) = αx + P (log(x)) + E(x). Ici P (x) est un polynôme, E(x) = − n≤y(x) bn n ψ x n + o(1) avec ψ(x) =(More)
The key factors that influence the population growth rate can be identified with sensitivity analysis. Caswell presented an algorithm based on vector calculus that speeds up, and improves the practicality of the application of the sensitivity analysis, by calculating the derivatives of the explicit elements from the population Leslie matrix. Despite the(More)
This paper deals with the problem of constructing superregular matrices that lead to MDP convolutional codes. These matrices are a type of lower block triangular Toeplitz matrices with the property that all the square submatrices that can possibly be nonsingular due to the lower block triangular structure are nonsingular. We present a new class of matrices(More)
In this paper, we describe compact laser sources based on high-power amplification in Yb-doped silica fibers of ultra-stable mode-locked pulses from an all-fiber oscillator. The interplay between third-order nonlinearity, gain and chromatic dispersion in the polarization-maintaining fiber amplifier is engineered to produce high-quality, high-energy pulses(More)
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