Normal forms for differentiable maps near a fixed point

We propose in this paper a significant refinement of normal forms for differentiable maps near a fixed point. We give a method to obtain further reduction of classical normal forms with concrete and interesting applications. Our method leads to unique normal forms either with respect to general diffeomorphisms in certain cases or with respect to near identity diffeomorphisms in other cases. Our approach is rational in the sense that if the coefficients of a map are in a field K, so is its normal form. This revised version was published online in June 2006 with corrections to the Cover Date.     

Desorption of Coffee Pulp Used as an Adsorbent Material for Cr(III and VI) Ions in Synthetic Wastewater: A Preliminary Study

Some of the diverse agro-industrial waste generated in primary or secondary stages have proved to be promising biomaterials for treating aqueous effluents contaminated, in this case, with heavy metals. Therefore, it is necessary to know their optimal operating conditions and the regeneration or reusability of the solid by-product, an aspect related to desorption. Considering the above, this article presents the findings of a preliminary study related to the desorption process of coffee pulp without physicochemical modification (Castilla variety), an agricultural waste used as a sorbent of Cr(III and VI) ions in synthetic wastewater. The desorption efficiency of four eluting agents at defined concentrations (0.10M)—HC1, HNO₃, H₂SO₄, and EDTA—was evaluated in a time interval of 1 to 9 days. Likewise, the proposals for the sorption and/or desorption mechanisms proposed and reported in the literature with respect to the use of biosorbents derived from the coffee crop are presented. With respect to the results, the coffee pulp used in previous studies of the adsorption of chromium species mentioned (optimal conditions in synthetic water of particle size 180 μm, dose 20 g·L⁻¹, agitation 100 RPM, room temperature, time of 90 to 105 min) showed efficiencies in the removal of Cr(III) and Cr(VI) of 93.26% and 74.80%, respectively. Regarding the extracting substances used, H₂SO₄ 0.10 M was the one that presented the highest desorption percentage in both chromic species, with a desorption of 45.75% Cr(VI) and 66.84% Cr(III) in periods of 5 and 9 days, respectively, with agitation of 100 RPM and room temperature. Finally, the dissemination of preliminary results on the desorption of coffee pulp contaminated with chromic species without physicochemical modification is novel in this study, as similar work with this specific material has not yet been reported in the literature. On the other hand, the limitations of the study and future research are related to the evaluation at different concentrations and of other extractor solutions that allow improving the efficiency of desorption of these chemical species in a shorter time from the coffee pulp (with and without modification) as well as the reuse cycles. As a result, the desorption of coffee pulp used as an adsorbent material in real water could help researchers identify the possible interfering factors that affect the process (foreign anions and cations, organic matter, environmental conditions, among others).     

Design and analysis of thermally tunable liquid crystal filled hybrid photonic crystal fiber coupler

We propose a novel tunable photonic crystal fiber (PCF) coupler scheme, that the light is coupled between a total internal reflection (TIR) guiding core and a photonic bandgap (PBG) guiding core. By introducing the thermo-optic responsive nematic liquid crystals (NLC) into the air holes around the PBG core, the hybrid PCF based coupler exhibits enhanced thermal tunability. The thermo-optical characteristics of the proposed coupler are numerically studied using finite element method (FEM) and beam propagation method (BPM). The proposed design can find promising applications in filtering and sensing devices.     

Working without accumulation membrane in flow field-flow fractionation. Effect of sample loading on retention

Membraneless hyperlayer flow field-flow fractionation (Hyp FIFFF) has shown improved performance with respect to Hyp FIFFF with membrane. The conditions for high recovery and recovery independent of sample loading in membraneless Hyp FIFFF have been previously determined. The effect of sample loading should be also investigated in order to optimize the form of the peaks for real samples. The effect of sample loading on peak retention parameters is of prime importance in applications such as the conversion of peaks into particle size distributions. In this paper, a systematic experimental work is performed in order to study the effect of sample loading on retention parameters. A procedure to regenerate the frit operating as accumulation wall is described. High reproducibility is obtained with low system conditioning time.     

1H and 13C NMR spectral assignment of N,N′‐disubstituted thiourea and urea derivatives active against nitric oxide synthase

The ¹H and ¹³C NMR resonances of seventeen N‐alkyl and aryl‐N′‐[3‐hydroxy‐3‐(2‐nitro‐5‐substitutedphenyl)propyl]‐thioureas and ureas ( 1–17 ), and seventeen N‐alkyl or aryl‐N′‐[3‐(2‐amino‐5‐substitutedphenyl)‐3‐hydroxypropyl]‐thioureas and ureas ( 18–34 ), designed as NOS inhibitors, were assigned completely using the concerted application of one‐ and two‐dimensional experiments (DEPT, HSQC and HMBC). NOESY studies confirm the preferred conformation of these compounds. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear stochastic differential equations containing generalized delta processes

In this paper, some classes of nonlinear stochastic differential equations involving the generalized delta process and its derivatives are considered in the framework of the Colombeau generalized stochastic process theory. All initial problems considered are proven to have a unique unbiased solution. Several examples are exposed that provide more insight into the assumptions made in the theorems.     

Characterization of 4,5‐Dihydro‐1H‐Pyrazole Derivatives by 13C NMR Spectroscopy

The ¹³ C NMR resonances of 19 1‐acyl‐3‐(2‐nitro‐5‐substitutedphenyl)‐4,5‐dihydro‐1H‐pyrazoles, and 19 1‐acyl‐3‐(2‐amino‐5‐substituted)‐4,5‐dihydro‐1H‐pyrazoles, were completely assigned using the concerted application of one‐ and two‐dimensional NMR experiments (DEPT, gs‐HSQC and gs‐HMBC). Copyright © 2012 John Wiley & Sons, Ltd.     

The static microreactor technique a new, simple method for determination of kinetic parameters of gas-phase heterogeneous catalytic reactions

The dehydrogenation of methanol on a silver catalyst was studied in a static microreactor at 376–457°C, with initial methanol partial pressures of 60–90 Torr. The apparent activation energy agrees well with literature data. The experimental data suggest that the static microreactor is a suitable means for the rapid acquisition of preliminary kinetic data.

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376–457°C, 60–90 . . , .