Some reflections on the impact of globalization in the teaching and learning of English in socalled “expanding circle” countries

This article deals with the ongoing debate on the complex role of English as an International Language, be it understood as a homogeneous entity (one language with an international role [EIL]) or a heterogeneous one (different varieties (WE or ELF) grouped under one label, «English») as well as on the implications of this «globalising» status for its teaching in non-native settings. Given the complexity of this phenomenon, whose study is still in its infancy, we attempt neither to provide definitive answers nor adopt a prescriptive attitude, but simply contribute to the discussion and clarification of this, to some extent, emergent, controversial situation.

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials

In this paper we give a new characterization of the closure of the set of the real parts of the zeros of a particular class of Dirichlet polynomials that is associated with the set of dimensions of fractality of certain fractal strings. We show, for some representative cases of nonlattice Dirichlet polynomials, that the real parts of their zeros are dense in their associated critical intervals, confirming the conjecture and the numerical experiments made by M. Lapidus and M. van Frankenhuysen in several papers.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.

On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

The influence of promoters (Zr, La, Tb, Pr) on the catalytic performance of CuO-CeO2 systems for the preferential oxidation of CO in the presence of CO2 and H2O

CuO supported on CeO2 and Ce0.9X0.1O2, where X is Zr, La, Tb or Pr, were synthesized using nitrate precursors, giving rise ceria based materials with a small particle size which interact with CuO species generating a high amount of interfacial sites. The incorporation of cations to the ceria framework modifies the CeO2 lattice parameter, improving the redox behavior of the catalytic system. The catalysts were characterized by X-ray fluorescence spectrometry (XRFS), X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), Raman spectroscopy, thermoprogrammed reduction with H2 (H2-TPR) and X-ray photoelectron spectroscopy (XPS). The catalysts were tested in the preferential oxidation of CO under a H2-rich stream (CO-PROX), reaching conversion values higher than 95% between 115 and 140 °C and being the catalyst with 6 wt.% of Cu supported on Ce0.9Zr0.1O2 (sample 6CUZRCE) the most active catalyst. The influence of the presence of CO2 and H2O was also studied simulating a PROX unit, taking place a decrease of the catalytic activity due to the inhibitor effect both CO2 and H2O.