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 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 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.

Power line interference filtering on surface electromyography based on the stationary wavelet packet transform

Power line interference is one of the main problems in surface electromyogram signals (EMG) analysis. In this work, a new method based on the stationary wavelet packet transform is proposed to estimate and remove this kind of noise from EMG data records. The performance has been quantitatively evaluated with synthetic noisy signals, obtaining good results independently from the signal to noise ratio (SNR). For the analyzed cases, the obtained results show that the correlation coefficient is around 0.99, the energy respecting to the pure EMG signal is 98–104%, the SNR is between 16.64 and 20.40 dB and the mean absolute error (MAE) is in the range of −69.02 and −65.31 dB. It has been also applied on 18 real EMG signals, evaluating the percentage of energy respecting to the noisy signals. The proposed method adjusts the reduction level to the amplitude of each harmonic present in the analyzed noisy signals (synthetic and real), reducing the harmonics with no alteration of the desired signal.

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.

Practical experiences on a real pumping system emulated by a hardware model and used as a remote laboratory

Paper submitted to ACE 2013, 10th IFAC Symposium on Advances in Control Education, University of Sheffield, UK, August 28-30, 2013.

The imprint of the crustal magnetic field on the thermal spectra and pulse profiles of isolated neutron stars

Isolated neutron stars (NSs) show a bewildering variety of astrophysical manifestations, presumably shaped by the magnetic field strength and topology at birth. Here, using state-of-the-art calculations of the coupled magnetic and thermal evolution of NSs, we compute the thermal spectra and pulse profiles expected for a variety of initial magnetic field configurations. In particular, we contrast models with purely poloidal magnetic fields to models dominated by a strong internal toroidal component. We find that, while the former displays double-peaked profiles and very low pulsed fractions, in the latter, the anisotropy in the surface temperature produced by the toroidal field often results in a single pulse profile, with pulsed fractions that can exceed the 50–60 per cent level even for perfectly isotropic local emission. We further use our theoretical results to generate simulated ‘observed’ spectra, and show that blackbody (BB) fits result in inferred radii that can be significantly smaller than the actual NS radius, even as low as ∼1–2 km for old NSs with strong internal toroidal fields and a high absorption column density along their line of sight. We compute the size of the inferred BB radius for a few representative magnetic field configurations, NS ages and magnitudes of the column density. Our theoretical results are of direct relevance to the interpretation of X-ray observations of isolated NSs, as well as to the constraints on the equation of state of dense matter through radius measurements.

On the stability of Voronoi cells

Let T be a given subset of ℝ n , whose elements are called sites, and let s∈T. The Voronoi cell of s with respect to T consists of all points closer to s than to any other site. In many real applications, the position of some elements of T is uncertain due to either random external causes or to measurement errors. In this paper we analyze the effect on the Voronoi cell of small changes in s or in a given non-empty set P⊂T\{s}. Two types of perturbations of P are considered, one of them not increasing the cardinality of T. More in detail, the paper provides conditions for the corresponding Voronoi cell mappings to be closed, lower and upper semicontinuous. All the involved conditions are expressed in terms of the data.

Direct Nucleophilic Substitution of Free Allylic Alcohols in Water Catalyzed by FeCl3⋅6 H2O: Which is the Real Catalyst?

The allylic substitution reaction, and particularly the direct allylic amination reaction, of free allylic alcohols in water catalyzed by FeCl3⋅6 H2O is described. This novel environmentally-friendly methodology allows the use of a wide variety of nitrogenated nucleophiles such as sulfonamides, carbamates, benzamides, anilines, benzotriazoles, and azides, generally giving good yields of the corresponding substitution products. The synthetic applicability of the process is also demonstrated because the reaction can be performed on gram-scale. Additionally, carbon nucleophiles such as silylated nucleophiles, aromatic compounds, and malonates also proved to be suitable for this transformation. Finally, the nature of the catalytic species present in aqueous media is unveiled, pointing towards the formation of hexaaquo iron(III) complexes.

On the Radial Onset of Clumping in the Wind of the B0I Massive Star QV Nor

We present an analysis of a 78 ks Chandra high-energy transmission gratings observation of the B0I star QV Nor, the massive donor of the wind-accreting pulsar 4U1538−52. The neutron star (NS) orbits its companion in a very close orbit (r < 1.4R*, in units of the stellar radii), thereby allowing probing of the innermost wind regions. The flux of the Fe Kα line during eclipse reduces to only ∼30% of the flux measured out of eclipse. This indicates that the majority of Fe fluorescence must be produced in regions close to the NS, at distances smaller than 1R* from its surface. The fact that the flux of the continuum decreases to only ∼3% during eclipse allows for a high contrast of the Fe Kα line fluorescence during eclipse. The line is not resolved and centered at 1.9368 0.0018 l = 0.0032 - + Å. From the inferred plasma speed limit of v < c l < 800 l D km s−1 and range of ionization parameters of log 1, 2 x = [- ], together with the stellar density profile, we constrain the location of the cold, dense material in the stellar wind of QV Nor using simple geometrical considerations. We then use the Fe Kα line fluorescence as a tracer of wind clumps and determine that these clumps in the stellar wind of QV Nor (B0I) must already be present at radii r < 1.25R*, close to the photosphere of the star.

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.

On the forbidden gap of finite graphene nanoribbons

The electronic structure of isolated finite graphene nanoribbons is investigated by solving, at the Hartree-Fock (HF) level, the Pariser, Parr and Pople (PPP) many-body Hamiltonian. The study is mainly focused on 7-AGNR and 13-AGNR (Armchair Graphene Nano-Ribbons), whose electronic structures have been recently experimentally investigated. Only paramagnetic solutions are considered. The characteristics of the forbidden gap are studied as a function of the ribbon length. For a 7-AGNR, the gap monotonically decreases from a maximum value of ~6.5 eV for short nanoribbons to a very small value of ~0.12 eV for the longer calculated systems. Gap edges are defined by molecular orbitals that are spatially localized near the nanoribbon extremes, that is, near both zig-zag edges. On the other hand, two delocalized orbitals define a much larger gap of about 5 eV. Conductance measurements report a somewhat smaller gap of ~3 eV. The small real gap lies in the middle of the one given by extended states and has been observed by STM and reproduced by DFT calculations. On the other hand, the length dependence of the gap is not monotonous for a 13-AGNR. It decreases initially but sharply increases for lengths beyond 30 Å remaining almost constant thereafter at a value of ~2.1 eV. Two additional states localized at the nanoribbon extremes show up at energies 0.31 eV below the HOMO (Highest Occupied Molecular Orbital) and above the LUMO (Lowest Unoccupied Molecular Orbital). These numbers compare favorably with those recently obtained by means of STS for a 13-AGNR sustained by a gold surface, namely 1.4 eV for the energy gap and 0.4 eV for the position of localized band edges. We show that the important differences between 7- and 13-AGNR should be ascribed to the charge rearrangement near the zig-zag edges obtained in our calculations for ribbons longer than 30 Å, a feature that does not show up for a 7-AGNR no matter its length.

Vinasse application to sugar cane fields. Effect on the unsaturated zone and groundwater at Valle del Cauca (Colombia)

Extensive application of vinasse, a subproduct from sugar cane plantations for bioethanol production, is currently taking place as a source of nutrients that forms part of agricultural management in different agroclimatic regions. Liquid vinasse composition is characterised by high variability of organic compounds and major ions, acid pH (4.7), high TDS concentration (117,416–599,400 mg L− 1) and elevated EC (14,350–64,099 μS cm− 1). A large-scale sugar cane field application is taking place in Valle del Cauca (Colombia), where monitoring of soil, unsaturated zone and the aquifer underneath has been made since 2006 to evaluate possible impacts on three experimental plots. For this assessment, monitoring wells and piezometers were installed to determine groundwater flow and water samples were collected for chemical analysis. In the unsaturated zone, tensiometers were installed at different depths to determine flow patterns, while suction lysimeters were used for water sample chemical determinations. The findings show that in the sandy loam plot (Hacienda Real), the unsaturated zone is characterised by low water retention, showing a high transport capacity, while the other two plots of silty composition presented temporal saturation due to La Niña event (2010–2011). The strong La Niña effect on aquifer recharge which would dilute the infiltrated water during the monitoring period and, on the other hand dissolution of possible precipitated salts bringing them back into solution may occur. A slight increase in the concentration of major ions was observed in groundwater (~ 5% of TDS), which can be attributed to a combination of factors: vinasse dilution produced by water input and hydrochemical processes along with nutrient removal produced by sugar cane uptake. This fact may make the aquifer vulnerable to contamination.