Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations

In the first part of this paper, we give a survey on convergence rates analysis of quasi-Newton methods in infinite Hilbert spaces for nonlinear equations. Then, in the second part we apply quasi-Newton methods in their Hilbert formulation to solve matrix equations. So, we prove, under natural assumptions, that quasi-Newton methods converge locally and superlinearly; the global convergence is also studied. For numerical calculations, we propose new formulations of these methods based on the matrix representation of the dyadic operator and the vectorization of matrices. Finally, we apply our results to algebraic Riccati equations.     

Electrocatalytic performance of cobalt microparticles film-modified platinum disk electrode for amperometric detection of ascorbic acid

Deposited cobalt microparticales (Co-MPs) film onto the platinum disk electrode has been successfully used as a new amperometric sensor for the determination of ascorbic acid (AA). AA is detected by surface catalyzed oxidation involving cobalt(III) oxyhydroxides in alkaline solution. The Co-MPs/Pt electrode exhibits a high electrocatalytic activity toward the AA oxidation. The diffusion coefficient of AA (6.09 × 10⁵ cm²/s) and the catalytic rate constant (k _cat = 6.27 × 10³ M^–1s^–1) have been determined using electrochemical approaches. The amperometric response of the modified electrode is linear against the AA concentration in the range (0.01?0.48 mM). The sensor displays the best activity with a high response signal, a good sensitivity of 74.3 μA/mM, a low detection limit of 2.5 μM (signal/noise = 3) and a fast response time (<3 s). Moreover, the reproducibility, selectivity and applicability of this biosensor are satisfactorily evaluated.     

A Facile Strategy for Construction of Sensor for Detection of Ondansetron and Investigation of its Redox Behavior and Thermodynamic Parameters

A sodium dodecylsulfate‐doped polypyrrole (SDS‐PPy) film was elaborated on glassy carbon electrode (GCE) by an electrodeposition method in phosphate buffer solution (pH 2.0) containing pyrrole (Py) and sodium dodecyl sulfate (SDS). SDS‐PPy/GCE was used for the construction of sensor, which showed excellent electrochemical response for the detection of ondansetron (OND) compared to conventional PPy. The application of the square wave (SW), with the adsorptive accumulation, indicates a maximum response at 1.33 V in H₂SO₄ (0.5 M). The influence of experimental parameters on determination of OND is discussed. The adsorptive stripping technique showed to be more sensitive, giving responses twice as big as those of non‐accumulated OND. The substantial improvement of response permits the development of an electroanalytical technique with a linear concentration in the range (1.0–80 μM), low detection (0.09 μM), and quantification limits (0.3 μM), and acceptable relative standard deviations of repeatability (0.59 %), and reproducibility (1.51 %). Consequently, this electrode is promising candidate for an accurate electroanalytical determination of OND in pharmaceutical samples with high sensitivity and selectivity, good accuracy and precision. The electrooxidation of OND at SDS‐PPy/GCE at various temperatures were studied by cyclic voltammetry to evaluate both the kinetic (k_s and E_a) and thermodynamic (ΔG*, ΔH* and ΔS*) parameters.     

Square wave voltammetry for analytical determination of paracetamol using cobalt microparticles film modified platinum electrode

Cobalt microparticles (Co MPs) modified Pt electrode is simply and conveniently fabricated. The electrochemical properties of paracetamol (PCT) at the prepared modified electrode are investigated using cyclic voltammetry (CV) and square wave voltammetry (SWV) measurements. Based on these techniques, a sensitive and rapid electrochemical method is developed for the determination of PCT. The result indicates that the oxidation of PCT is strongly improved at the Co MPs/Pt electrode as compared with the bare Pt electrode, with relatively high sensitivity, stability and life time. The determination of PCT on the Co MPs/Pt with square wave voltammetry displays a high sensitivity of 101 μA/mM and a low detection limit of 0.42 μM (S/N = 3) in the range (0.5–100 μM). The sensitivity of the modified electrode for the detection of PCT is almost 17 times greater than on the bare Pt electrode. The proposed method is successfully applied to the PCT determination in tablets.     

Analysis of a Class of Frictional Contact Problems for the Bingham Fluid

We consider a mathematical model which describes the stationary flow of a Bingham fluid with friction. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive a weak formulation of the model which consists in a variational inequality for the velocity field. We establish the existence and uniqueness of the weak solution as well as its continuous dependence with respect to the contact condition. Finally, we describe a number of concrete friction conditions which may be set in this general framework and for which our results apply.     

Fixed point theorem in ordered Banach spaces and applications to matrix equations

In this paper, we give an important generalization of Lakshmikantham’s theorem (Theorem 2.1 in Nonlinear Anal Theory Methods Appl 3448–3458, 2009). Our main result asserts the existence of fixed point for a class of nonlinear operators defined in an ordered Banach space, and gives a new monotone Newton-like method to compute this fixed point. We also apply our new result to some important matrix equations.