A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel

This work is concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation. Owing to the singular behavior of the solution near the origin, the global convergence order of product integration and collocation methods is not optimal. In order to recover the optimal orders a hybrid collocation method is used which combines a non-polynomial approximation on the first subinterval followed by piecewise polynomial collocation on a graded mesh. Some numerical examples are presented which illustrate the theoretical results and the performance of the method. A comparison is made with the standard graded collocation method.     

Metabisulfite interference in biosensing and Folin-Ciocalteu analysis of polyphenols

Sodium metabisulfite is one of the forms of sulphurous compounds which are added as preservative in food and beverage processing industries. Its interference with different methods of analysis of polyphenols was investigated in the present work. Studies involved the reaction of metabisulfite at platinum electrodes either at a constant applied potential of +100 mV vs. Ag/AgCl electrode with amperometric detection, or at linear potential sweep in cyclic voltammetry experiments. In a second stage, its effect on the analysis of polyphenols that are oxidised by enzymes was examined by the inhibition that metabisulfite caused on caffeic acid oxidation in the presence of free and immobilized laccase. It was found that immobilized laccase was less inhibited than free laccase. A confirmation of the influence of metabisulfite on the Folin-Ciocalteu analysis was also done.     

On-off scheduling schemes for power-constrained electric vehicle charging

In this paper, we study the problem of establishing a dynamic charging schedule of electric vehicles (EVs) at a charging station, assuming that limited power implies that only a limited number of EVs can charge simultaneously. The only control we assume to be available to the charging station is the ability to (at any given time) turn on or off the power supply to any EV, with this tool we want to develop a charging schedule that will satisfy the energy demands of the EVs in their intended deadlines. We propose two distinct approaches to this problem: a discretized time version, based on a greedy-like algorithm, and a continuous time version, based on linear programming. We compare these two approaches and numerically study the improvement they yield in the efficiency of the charging procedure, when applied to simulated data based on real parking data. Finally, we illustrate the flexibility of the models by sketching several possible extensions.     

Discrete Orbits,Recurrence and Solvable Subgroups of $${{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}$$

We discuss the local dynamics of a subgroup of \({{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}\) possessing locally discrete orbits as well as the structure of the recurrent set for more general groups. It is proved, in particular, that a subgroup of \({{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}\) possessing locally discrete orbits must be virtually solvable. These results are of considerable interest in problems concerning integrable systems.     

Aqueous biphasic systems involving alkylsulfate-based ionic liquids

The specific effects of K₃PO₄, K₂CO₃, Na₂CO₃, and (NH₄)₂SO₄, as high charge-density inorganic salts and thus inducers of the formation of aqueous biphasic systems (ABS) containing several ethyl-methylimidazolium alkylsulfate ionic liquids, C₂MIM C_nSO₄ (n = 2, 4, 6, or 8), have been assessed at T = 298.15 K. The results are analyzed in the light of the Hofmeister series. The influence of different alkyl chain lengths in the anion, together with the ability of the selected inorganic salts to induce the formation of ABS, is discussed. Phase diagrams have been determined through turbidimetry, including tie lines assignments from mass phase ratios according to the lever – arm rule. The Merchuck equation was satisfactorily used to correlate the solubility curve.     

Fibrations of Genus Two on Complex Surfaces

This work is devoted to the study of fibrations of genus 2 by using as its main tool the theory of singular holomorphic foliations. In particular we obtain a sharp differentiable version of Matsumoto–Montesinos theory. In the case of isotrivial fibrations, these methods are powerful enough to provide a detailed global picture of the both the ambient surface and of the structure of the fibrations itself.     

On the approximate solution to an initial boundary valued problem for the Cahn–Hilliard equation

The particular approximate solution of the initial boundary valued problem to the Cahn–Hilliard equation is provided. The Fourier Method is combined with the Adomian’s decomposition method in order to provide an approximate solution that satisfy the initial and the boundary conditions. The approximate solution also satisfies the mass conservation principle.     

A pointwise constrained version of the Liapunov convexity theorem for single integrals

Given any AC solution ${\overline{x} : [a,b] \rightarrow \mathbb{R}^{n}}$ to the convex ordinary differential inclusion $$x^{\prime} ( t) \in co\{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e. on [ a,b], \qquad \qquad (^{*})$$ we aim at solving the associated nonconvex inclusion $$x^{\prime} ( t) \in \{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e.,x( a) = \overline{x} ( a), x( b) = \overline{x} ( b), \qquad \qquad (^{**})$$ under an extra pointwise constraint (e.g. on the first coordinate): $$x_{1} ( t) \leq \overline{x}_{1} ( t) \qquad \forall t \in [ a,b]. \qquad \qquad \qquad (^{***})$$ While the unconstrained inclusion (**) had been solved already in 1940 by Liapunov, its constrained version, with (***), was solved in 1994 by Amar and Cellina in the scalar n = 1 case. In this paper we add an extra geometrical hypothesis which is necessary and sufficient, in the vector n > 1 case, for it existence of solution to the constrained inclusion (**) and (***). We also present many examples and counterexamples to the 2 × 2 case.     

FTIR Spectroscopy as a Tool to Study Age-Related Changes in Cardiac and Skeletal Muscle of Female C57BL/6J Mice

Studying aging is important to further understand the molecular mechanisms underlying this physiological process and, ideally, to identify a panel of aging biomarkers. Animals, in particular mice, are often used in aging studies, since they mimic important features of human aging, age quickly, and are easy to manipulate. The present work describes the use of Fourier Transform Infrared (FTIR) spectroscopy to identify an age-related spectroscopic profile of the cardiac and skeletal muscle tissues of C57BL/6J female mice. We acquired ATR-FTIR spectra of cardiac and skeletal muscle at four different ages: 6; 12; 17 and 24 months (10 samples at each age) and analyzed the data using multivariate statistical tools (PCA and PLS) and peak intensity analyses. The results suggest deep changes in protein secondary structure in 24-month-old mice compared to both tissues in 6-month-old mice. Oligomeric structures decreased with age in both tissues, while intermolecular β-sheet structures increased with aging in cardiac muscle but not in skeletal muscle. Despite FTIR spectroscopy being unable to identify the proteins responsible for these conformational changes, this study gives insights into the potential of FTIR to monitor the aging process and identify an age-specific spectroscopic signature.