Approximation of Solutions of Fractional-Order Delayed Cellular Neural Network on $$\varvec{[0,\infty )}$$

In this paper, we study a class of fractional-order cellular neural network containing delay. We prove the existence and uniqueness of the equilibrium solution followed by boundedness. Based on the theory of fractional calculus, we approximate the solution of the corresponding neural network model over the interval \([0,\infty )\) using discretization method with piecewise constant arguments and variation of constants formula for fractional differential equations. Furthermore, we conclude that the solution of the fractional-delayed system can be approximated for large t by the solution of the equation with piecewise constant arguments, if the corresponding linear system is exponentially stable. At the end, we give two numerical examples to validate our theoretical findings.     

Pseudo–almost‐periodic solutions for delayed differential equations with integrable dichotomies and bi–almost‐periodic Green functions

Using the existence of integrable bi–almost‐periodic Green functions of linear homogeneous differential equations and the contraction fixed point, we are able to prove the existence of almost and pseudo–almost‐periodic mild solutions under quite general hypotheses for the differential equation with constant delay in a Banach space X, where τ>0 is a fixed constant. The results extend the corresponding ones in the case of exponential dichotomy. Some examples illustrate the importance of the concepts.     

Within‐host and synaptic transmissions: contributions to the spread of HIV infection

We study the contributions of within‐host (virus‐to‐cell) and synaptic (cell‐to‐cell) transmissions in a mathematical model for human immunodeficiency virus epidemics. The model also includes drug resistance. We prove the local and global stability of the disease‐free equilibrium and the local stability of the endemic equilibrium. We analyse the effect of the cell‐to‐cell transmission rate on the value of the reproduction number, R₀. Moreover, we show evidence of a qualitative change in the models' dynamics, subjected to the value of the drug efficacy. In the end, important inferences are drawn. Copyright © 2016 John Wiley & Sons, Ltd.     

L p-Perturbations of Invariant Subbundles for Linear Systems

We use Riccati's equations and the ordinary and exponential dichotomies to get simple recurrent formulae for the asymptotic integration of linear systems subjected to L _p -perturbations with arbitrary p 1. Moreover, we establish conditions which are necessary and sufficient for the persistence of one-dimensional invariant subbundles for the linear system under L _p -perturbations. In this way, we prove the sharp nature of the well known Levinson and Hartman–Wintner asymptotic theorems.     

Cellulose-based liquid crystalline photoresponsive films with tunable surface wettability

We report on a new type of liquid crystalline cellulosic films with light controllable reversible wettability. The films are prepared from a thermotropic cellulose derivative functionalized with azo-containing groups. These groups exhibit dynamic changes in interfacial properties in response to UV irradiation. The UV irradiation induces trans-to-cis isomerization in the azobenzene moiety, which causes a conformational change in the upper molecular layers of the thin films. These changes originate a hydrophobic to comparatively hydrophilic transformation of the surface. The reversible wettability of the surface results from the cis/trans photo and thermal isomerization. The UV-vis absorption spectra, as well as contact angle measurements with UV irradiation, clearly support the understanding of the phenomenon. This type of surface design enables the amplification of molecular level conformational transitions to macroscopic changes in interface properties using the means of isomerism. This opens new opportunities in surface engineering using eco-friendly cellulose manipulation.     

Adsorptive stripping voltammetry of nickel with 1-nitroso-2-napthol using a bismuth film electrode

A sensitive procedure is presented for the voltammetric determination of nickel. The procedure involves an adsorptive accumulation of nickel 1-nitroso-2-napthol (NN) complex on a bismuth film electrode prepared ex situ by electrodeposition. The most suitable operating conditions and parameters such as pH, ligand concentration (C_NN), adsorptive potential (E_ads), adsorptive time (t_ads), scan rate and others were selected and the determination of nickel in aqueous solutions using the standard addition method was possible. The adsorbed Ni-NN complex gives a well defined cathodic stripping peak current at −0.70 V, which was used for the determination of nickel in the concentration range of 10.0-70.0 μg L⁻¹ (pH 7.5; C_NN 6.5 μmol L⁻¹; E_ads −0.30 V; t_ads 60 s) with a detection limit of 0.1 μg L⁻¹. The relative standard deviation for a solution containing 10.0 μg L⁻¹ of Ni(II) was 3.5% (n = 4). The proposed method was validated determining Ni(II) in certified reference waste water (SPS-WW1) and Certified Reference Water for Trace Elements (TMDA 51.3) with satisfactory results. Then lake water samples were analyzed.     

Synthesis and characterization of novel amino cellulose esters

The homogeneous conversion of cellulose dissolved in N-methyl-2-pyrrolidone/LiCl and 1-N-butyl-3-methylimidazolium chloride with N-methyl-2-pyrrolidone, ε-caprolactam, N-methyl-ε-caprolactam, and N-methyl-2-piperidone in the presence of p-toluenesulphonic acid chloride was studied. Depending on the reaction conditions, novel cellulose esters with degree of substitution (DS) values ranging from 0.12 to 1.17 could be prepared. The structure of the amino group containing cellulose esters was elucidated by elemental analysis, FTIR- and NMR spectroscopy. NMR spectroscopy revealed an almost complete esterification of position 6 of the anhydroglucose unit at DS of 1. The conversion can be conducted between room temperature and 40 °C, while side-reactions became predominant at 60 °C. Starting with DS of 0.24, the samples were soluble both in water and dimethyl sulphoxide. The derivatives described are capable of forming polyelectrolyte complexes. The samples were stable at room temperature in aqueous solution at pH 2 and 7. Lower viscosities were found for samples with higher DS in aqueous solution at comparable molar mass.     

A simplified Quick, Easy, Cheap, Effective, Rugged and Safe approach for the determination of trihalomethanes and benzene, toluene, ethylbenzene and xylenes in soil matrices by fast gas chromatography with mass spectrometry detection

A method based on simplified QuEChERS (Quick, Easy, Cheap, Effective, Rugged and Safe) extraction followed by large-injection volume-fast gas chromatography and mass spectrometry detection has been developed for the determination of trihalomethanes (chloroform, bromodichloromethane, dibromochloromethane and bromoform) and BTEX (benzene, toluene, ethylbenzene and xylenes) in soil samples.The simplified version of QuEChERS used meets the requirements of the “green chemistry” and provides reliable results with high sample throughput, low solvent consumption, little labour and the use of materials commonly employed in laboratories. The GC device used is equipped with a programmable temperature vaporizer (PTV), with a liner packed with Tenax-TA^®. Using the solvent-vent mode, the PTV allows the injection of large volumes of sample, affording an improvement in the sensitivity of the method. The chromatographic conditions used here allowed the separation of the compounds in less than 5.50 min. Good linearity was obtained for all the target compounds, with highly satisfactory repeatability and reproducibility values. The limits of detection were in the 0.2 to 15 μg kg⁻¹ range. The method was validated by the analysis of two certified reference materials.     

Enzyme based assays in a sequential injection format: a review

Sequential injection analysis systems have been extensively exploited in the last decades for the implementation of enzyme based assays aiming the evaluation of enzyme activity or the determination of specific analytes. The most prominent aspects of the automation of enzymatic assays in these systems are discussed in this review. Special attention is devoted to the mode of enzyme manipulation in homogeneous or heterogeneous media and to the comparison with batch and flow injection enzyme methodologies. The possibility of implementing strategies for the enhancement of selectivity in specific determinations is also addressed. The more recent trends in this field are discussed focusing mainly on the miniaturization resorting to the lab-on valve platform as well as on the bead injection concept.