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A mean-square bound concerning the lattice discrepancy of a torus in ℝ3

Acta Mathematica Hungarica
Authors: V. Garcia and W. Nowak

Abstract

For positive constants a > b > 0, let P T (t) denote the lattice point discrepancy of the body tT a,b, where t is a large real parameter and T = T a,b is bounded by the surface

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\partial \tau _{a,b} :\left( {\begin{array}{*{20}c} x \\ y \\ z \\ \end{array} } \right) = \left( {\begin{array}{*{20}c} {(a + b\cos \alpha )\cos \beta } \\ {(a + b\cos \alpha )\sin \beta } \\ {b\sin \alpha } \\ \end{array} } \right), 0 \leqq \alpha ,\beta < 2\pi .$$ \end{document}
In a previous paper [12] it has been proved that
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$P_\tau (t) = \mathcal{F}_{a,b} (t)t^{3/2} + \Delta _\tau (t),$$ \end{document}
where F a,b(t) is an explicit continuous periodic function, and the remainder satisfies the (“pointwise”) estimate ΔT(t) ≪ t 11/8+ɛ. Here it will be shown that this error term is only ≪ t 1+ɛ in mean-square, i.e., that
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {(\Delta _\tau (t))^2 dt} \ll T^{3 + \varepsilon }$$ \end{document}
for any ɛ > 0.

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Thermal decomposition of ammonium monochloroacetate and ammonium monochloroacetate silicomolybdate

Journal of Thermal Analysis and Calorimetry
Authors: A. La Iglesia, V. García, and J. Pozas
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Paley Type Inequalities for Orthogonal Series with Vector-Valued Coefficients

Acta Mathematica Hungarica
Authors: J. Garcia-Cuerva, K. Kazarian, and V. Kolyada

Abstract

We investigate the extension to Banach-space-valued functions of the classical inequalities due to Paley for the Fourier coefficients with respect to a general orthonormal system Φ. This leads us to introduce the notions of Paley Φ-type and Φ-cotype for a Banach space and some related concepts. We study the relations between these notions of type and cotype and those previously defined. We also analyze how the interpolation spaces inherit these characteristics from the original spaces, and use them to obtain sharp coefficient estimates for functions taking values in Lorentz spaces.

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Phase transition in niobium pentoxide supported on silica-alumina

Journal of Thermal Analysis and Calorimetry
Authors: V. Braga, F. Garcia, J. Dias, and Sílvia Dias

Abstract

Nb2O5 supported on SiO2-Al2O3 were prepared with a wide loading range (2, 5, 10, 15, 20 and 25 mass%) and analyzed by simultaneous thermogravimetric (TG) and differential thermal analysis (DTA). The materials presented a phase transition close to 1364°C. This phase transition was studied by XRD, FTIR and Raman spectroscopy. Amixture of orthorhombic (T) andmonoclinic (H andM) crystalline phases was evidenced in the supported samples, which is coverage dependent, in contrast to the formation of only the monoclinic phase (H and M) when pure Nb2O5 is heated under the same conditions. These results indicate the stabilization of Nb2O5 on silica-alumina surface.

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Gasification in steam of a bituminous coal from Peñarroya (Cordoba, Spain) and of different samples prepared from it

Journal of Thermal Analysis and Calorimetry
Authors: C. Calahorro, A. Bernalte García, and V. Gómez Serrano
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Grain weight of durum wheat cultivars released in Italy and Spain during the 20 th century as affected by source-sink manipulations

Cereal Research Communications
Authors: Y. Rharrabti, D. Miralles, V. Martos, and L. García Del Moral

The present work analysed whether grain weight is affected by changes in source:sink ratio in twenty-four durum wheat cultivars from Italy and Spain released through the 20 th century grown under Mediterranean conditions. For this purpose, a field experiment was conducted during the 2002 growing-season in southeastern Spain. Sink strength was modified by removing half of the spikelets, of one side of the spike, one week after anthesis. Spikelet trimming had different effects on both average grain weight and individual grain weight at different positions within the spike. While old cultivars did not respond positively to spikelet trimming, and appear to be mainly sink-limited, intermediate and modern cultivars from Spain increased their grain weight in response to sink reductions, suggesting co-limitation by the sink and source. On the contrary, grain weight of intermediate and modern Italian cultivars remained relatively unchanged suggesting a sink-limitation to grain yield. The differential response to source-sink manipulations observed between Italian and Spanish cultivars could be attributed to their different genetic background, which determines their level of adaptation to harsh Mediterranean environments.

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Preliminary study of the thermally stimulated blue luminescence of ulexite

Journal of Thermal Analysis and Calorimetry
Authors: V Correcher, J Garcia-Guinea, and FJ Valle-Fuentes

Abstract

In this paper, novel results on the blue thermally stimulated luminescence (TSL) emission of ulexite (NaCaB5O6(OH)65H2O) have been studied. The four maxima appearing at 60, 110, 200 and 240C on the TSL glow curves of this borate could be respectively associated to: (i) the first dehydration (NaCaB5O6(OH)65H2O→NaCaB5O6(OH)63H2O), (ii) the creation-annihilation of the three-hydrated phase, (iii) the Na-coordinated chains dehydroxylation and the starting point of the alkali self-diffusion through the lattice and (iv) the amorphisation of the lattice. These results are fairly well correlated with the differential thermal analyses (DTA), in situ thermal observations under environmental scanning electron microscope (TESEM) and thermal X-ray diffraction (TXRD) techniques.

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Grain growth and yield formation of durum wheat grown at contrasting latitudes and water regimes in a Mediterranean environment

Cereal Research Communications
Authors: C. Royo, D. Villegas, Y. Rharrabti, R. Blanco, V. Martos, and L. García del Moral

A set of ten durum wheat genotypes was grown in experiments conducted under four contrasting Mediterranean conditions during three years to assess the effect of latitude and water regime on grain growth and grain yield formation. The relationship between grain weight and accumulated growing degree-days (GDD) from anthesis was described by a logistic equation and final grain weight ( W ) and maximum rate ( R ) and duration ( D ) of grain filling were calculated from the fitted curves. Thousand kernel weight (TKW) was positively related to grain yield at both latitudes and water regimes, although the contribution of the number of grains per m 2 to final yield was only significant in the south, where environmental constraints likely limited the achievement of a large grain set. Differences in final grain weight between latitudes could be mostly explained by differences in the grain filling rate, while changes on W between water regimes were due to altered grain filling durations. Under northern conditions grain yield was positively associated to grain filling duration but negatively related to the maximum rate of grain filling, while in the south the coefficients of the grain filling curves had little or no effect on final yield. Reductions in grain yield under rainfed conditions were due to the fall in the number of grains per m 2 since TKW was not significantly affected by drought.

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Ethylenediamine effect on Co2+ uptake by zeolite Y

Journal of Radioanalytical and Nuclear Chemistry
Authors: M. Solache-Ríos, I. García, V. Martínez-Miranda, P. Bosch, and S. Bulbulian

Abstract

Co2+ ion exchange, at room temperature, from aqueous cobalt — sodium chloride solutions with NaY zeolite has been studied. The effect of contact time on the shape of the sorption curves of Co2+ using zeolite Y dehydrated at 600°C is similar to the one found in our previous work with a zeolite dehydrated at 150 °C. A fast sorption uptake is observed in which 1.8 meq of Na+ ions/g of zeolite are replaced by cobalt ions followed by a desorption process where the uptake decreases to 1.2 meq/g zeolite. The Co2+ sorption using zeolite Y dehydrated at 600 °C is increased when ethylenediamine solution is passed through the zeolite. The Co2+ sorption uptake, initially 2.0 meq/g, incrases to 2.8 meq/g of zeolite. This behavior is explained by the location and coordination of cobalt in zeolite Y sites. It is suggested that the highest uptake process is due to the blocking of zeolite sites by a Co complex compound.

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