A version of a theorem of R. Datko for nonuniform exponential contractions

We point out versions of a well-known theorem of R. Datko for nonuniform exponential contractions. More precisely, we obtain theorems that characterize the nonuniform exponential stability and the nonuniform exponential dichotomy for nonuniform exponential contractions. Thus, we generalize the results in Datko (1972) [8] and Preda and Megan (1985) [14].     

A new version of a theorem of Minh–Räbiger–Schnaubelt regarding nonautonomous evolution equations

We develop a new version of a known theorem obtained by Van Minh, Räbiger, Schnaubelt in [N. Van Minh, F. Räbiger and R. Schnaubelt, Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line, Integral Equ. Oper. Theory 32 (1998) pp. 332–353]. We rely completely on the classical ‘test functions’ method designed by Perron in 1930. The advantage of such a version is that is more readable since the classical method of Perron have been known for decades and that we do not involve a sophisticated mathematical machinery. Our approach is in contrast with the general philosophy of ‘autonomization’ the nonautonomous system, since we do not require to attach the evolution semigroup. Also we point out a discrete-time version of our approach extending some known results given by Li and Henry.     

Facile Polymer Functionalization of Hydrothermal‐Carbonization‐Derived Carbons

A simple and efficient polymer grafting onto hydrothermal carbonization (HTC)‐derived materials is described. The method pertains to the Diels–Alder cycloaddition reaction of furan moieties present on the surface of a HTC material with the maleimide groups stemming from a maleimide protected poly(ethylene glycol) (Me‐PEG‐MI) by a retro Diels‐Alder reaction. The precursor polymer, HTC material, and final product are characterized. Successful grafting is confirmed by elemental analysis, X‐ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, and dispersion studies.

     

Determination of ascorbic acid content of some fruit juices and wine by voltammetry performed at pt and carbon paste electrodes

A method was developed for assessing ascorbic acid concentration in fruit juices and wine by differential pulse voltammetry. The oxidation peak for ascorbic acid occurs at about 530 mV (versus SCE) on a Pt strip working electrode and at about 470 mV on a carbon paste working electrode. The influence of the operational parameters like the pulse amplitude and the pulse period on the analytical signal was investigated. The obtained calibration graph shows a linear dependence between the peak height and ascorbic acid concentration within the range 0.31-20 mM with a Pt working electrode, and within the range 0.07-20 mM with a carbon paste working electrode. The equation of the calibration graph was y = 21.839x + 35.726, r2 = 0.9940, when a Pt strip electrode was used (where y represents the value of the current intensity measured for the peak height, expressed as μA and x the analyte concentration, as mM). R.S.D. = 2.09%, n = 10, C(ascorbic acid) = 2.5 mM. The equation of the calibration graph was y = 3.4429x + 5.7334, r2 = 0.9971, when a carbon paste electrode was used (where y represents the value of intensity measured for the peak height, expressed as μA and x the analyte concentration, as mM). R.S.D. = 2.35%, n = 10, C(ascorbic acid) = 2.5 mM. The developed method was applied to ascorbic acid assessment in fruit juices and wine. The ascorbic acid content determined ranged between 6.83 mg/100 mL juice for soft drinks (Fanta Madness) and 54.74 mg/100 mL for citrus (lemon) juices obtained by squeezing fruit. Different ascorbic acid concentrations (from standard solutions) were added to the analysed samples, the degree of recovery being comprised between 94.74 and 104.97%. The results of ascorbic acid assessment by differential pulse voltammetry were compared with those obtained by cyclic voltammetry. The results obtained by the two methods were in good agreement.     

An extension of some theorems of L. Barreira and C. Valls for the nonuniform exponential dichotomous evolution operators

The aim of this paper is to study the connection between the (non)uniform exponential dichotomy of a non(uniform) exponentially bounded, strongly continuous evolution family and the admissibility of some function spaces. Thus, there are extended recent results established by L. Barreira and C. Valls (2010, 2011) in [10] and [11].     

Some remarks on the Clebsch's system

The almost Hamilton-Poisson realization, the stability problem, the existence of periodic solutions and the numerical integration via the Lie-Trotter integrator for the Clebsch system are discussed and some of their properties are pointed out.     

Schäffer spaces and uniform exponential stability of linear skew-product semiflows

We study the exponential stability of linear skew-product semiflows on locally compact metric space with Banach fibers. Our main tool is the admissibility of a pair of the so-called Schäffer spaces. This characterization is a very general one, it includes as particular cases many interesting situations among them we can mention some results due to Clark, Datko, Latushkin, van Minh, Montgomery-Smith, Randolph, Räbiger, Schnaubelt.     

Thermal behaviour and adsorption properties of some benzothiazole derivatives

The thermal stability and the adsorption properties have been investigated for three benzothiazole compounds: 2-mercaptobenzothiazole (MBT), N-cyclohexyl-2-benzothiazole sulfenamide (NCBSA), and 2,2′-dibenzothiazole disulphide (BTD), reported in our early studies as corrosion inhibitors for carbon steel in different media. The electrochemical results were used to calculate the degree of surface coverage (θ). The adsorption mechanism of the three inhibitors was discussed according to the free energy of adsorption ( \( \Delta G_{{\text{ads}}}^{\circ } \) ) value obtained from Temkin adsorption isotherm, this being the best way to quantitatively express the adsorption process of their molecules on carbon steel surface. Thus, a mixed type mechanism involving the synergism between physisorption and chemisorption was proposed. The thermal analysis curves showed that, for the occurred events up to 470 °C, mass losses take place with endothermic effects followed by the total oxidation of the residue with an exothermic effect around 520 °C. Consequently, their effectiveness follows the order: BTD > NCBSA ≥ MBT, while the thermal stability ranges as follows: NCBSA < BTD ≤ MBT.     

Iterative fixed point theorems in E-metric spaces

We present a multivalued nonlinear fixed point theorem in an E-metric space introducing the concept of strict positivity in a Riesz space. Our result extends some well-known fixed point theorems obtained by J. Matkowski, R. W?grzyk, R. Cristescu, and C. Çevik, I. Altun.