On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

We present two modified versions of the primal-dual splitting algorithm relying on forward–backward splitting proposed in V\(\tilde{\mathrm{u}}\) (Adv Comput Math 38(3):667–681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of \(\mathcal{{O}}(\frac{1}{n})\) and \(\mathcal{{O}}(\omega ^n)\), for \(\omega \in (0,1)\), respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.     

Photocatalytically-assisted electrochemical degradation of <Emphasis Type="Italic">p</Emphasis>-aminophenol in aqueous solutions using zeolite-supported TiO<Subscript>2</Subscript> catalyst

This paper reports the results of an investigation into enhancement of the electrochemical oxidation of p-aminophenol (4-AP) in an aqueous solution with a boron-doped diamond (BDD) electrode, assisted by photocatalysis using a zeolite-supported TiO₂ (Z-TiO₂) catalyst. The BDD electrode was characterised in 0.1 M Na₂SO₄-supporting electrolyte and the presence of 4-AP by open-circuit potential behaviour (OCP) and cyclic voltammetry (CV). The electrode behaviour was investigated in the dark and following UV irradiation and in the absence/presence of the Z-TiO₂ catalyst. The electro-oxidation process was carried out using chronoamperometry (CA) and multiple-pulsed amperometry (MPA) at the selected potential under potentiostatic conditions. The electrochemical degradation process of 4-AP on the BDD electrode was improved by the application of a pulsed potential, which allowed both in-situ electrochemical cleaning of the electrode and indirect oxidation of 4-AP by oxygen evolution. The application of photocatalysis using Z-TiO₂ in the 4-AP electrochemical degradation exhibited an enhanced effect when the anodic potential was set at +1.25 V vs. Ag/AgCl in the water stability region, close to the oxygen evolution potential.     

Sensitive detection of endocrine disrupters using ionic liquid--single walled carbon nanotubes modified screen-printed based biosensors

Simple and low cost biosensor based on screen-printed electrode for sensitive detection of some alkylphenols was developed, by entrapment of HRP in a nanocomposite gel based on single-walled carbon nanotubes (SWCNTs) and 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF₆]) ionic liquid. Raman and FTIR spectroscopy, CV and EIS studies demonstrate the interaction between SWCNTs and ionic liquid. The nanocomposite gel, SWCNT-[BMIM][PF₆] provides to the modified sensor a considerable enhanced electrocatalytic activity toward hydrogen peroxide reduction. The HRP based biosensor exhibits high sensitivity and good stability, allowing a detection of the alkylphenols at an applied potential of −0.2 V vs. Ag/AgCl, in linear range from 5.5 to 97.7 μM for 4-t-octylphenol and respectively, between 5.5 and 140 μM for 4-n-nonylphenol, with a response time of about 5 s. The detection limit was 1.1 μM for 4-t-octylphenol, and respectively 0.4 μM for 4-n-nonylphenol (S/N = 3).     

Existence for nonlinear evolution inclusions with nonlocal retarded initial conditions

In this paper, we prove a sufficient condition for the global existence of bounded C⁰-solutions for a class of nonlinear functional differential evolution equation of the form where X is a real Banach space, A is the infinitesimal generator of a nonlinear compact semigroup, is a nonempty, convex, weakly compact valued, and almost strongly–weakly u.s.c. multi-function, and is nonexpansive.     

Probing the Pore Size of Porous Ceramics with Controlled Amount of Magnetic Impurities via Diffusion Effects on the CPMG Technique

In our work, we will explore the possibility of implementing the well-known Carr–Purcell–Meiboom–Gill pulse sequence to determine the pore size of porous ceramics with magnetic impurities. The proposed approach exploits the diffusion dependence of the spin-echo signal in the presence of internal gradients occurring as a result of susceptibility contrast between the porous matrix and the confined liquid. For calibrating the technique, a comparison of the pore size data with those extracted from the so-called DDIF technique (DDIF, decay due to diffusion in the internal fields) is performed. This approach can be applied for nondestructive in situ characterization of soils, concrete, biological tissues or other structures with micrometer pore size.     

Unbounded divergence of simple quadrature formulas

Given a sequence of real or complex coefficients c_i and a sequence of distinct nodes t_i in a compact interval T, we prove the divergence and the unbounded divergence on superdense sets in the space C(T) of the simple quadrature formulas ∝_Tx(t)du(t) = Q_n(x) + R_n(x) and ∝_Tw(t)x(t)dt = Q_n(x) + R_n(x), where Q_n(x)=∑_i=1^m_n c_ix(t_i), ε C(T).The divergence (not certainly unbounded) for at most one continuous function of the first simple quadrature formula, with m_n = n and u(t) = t, was established by P. J. Davis in 1953.     

New polyphenylene‐g‐polystyrene and polyphenylene‐g‐polystyrene/poly(ε‐caprolactone) copolymers by combined controlled polymerization and cross‐coupling processes

1,4‐Dibromo‐2‐(bromomethyl)benzene and 1,3‐dibromo‐5‐(bromomethyl)benzene were used as initiators in the atom transfer radical polymerization of styrene in conjunction with CuBr/2,2′‐bipyridine as a catalyst. The resulting polystyrene (PSt)‐based macromonomers, possessing at one end a 2,5‐dibromophenylene or 3,5‐dibromophenylene moiety, were used in combination with 2,5‐dihexylbenzene‐1,4‐diboronic acid for Suzuki coupling in the presence of Pd(PPh₃)₄ as a catalyst or with the system NiCl₂/2,2′‐bipyridine/triphenylphosphine/Zn for Yamamoto polymerization. Polyphenylenes (PPs) with PSt chains as substitution groups were obtained. The same macromonomers were used in Yamamoto copolycondensation reactions, in combination with a poly(ε‐caprolactone) (PCL) macromonomer, and this resulted in PPs with PSt/PCL side chains. The obtained PPs had good solubility properties in common organic solvents at room temperature similar to those of the starting macromonomers. The new polymers were characterized with ¹H (¹³C) NMR, IR, and gel permeation chromatography. The optical properties of the polymers were monitored with UV and fluorescence spectroscopy. The thermal behaviors of the macromonomers and final PPs were investigated with differential scanning calorimetry and compared. The morphology of PPs containing PSt and PCL blocks was characterized with atomic force microscopy, and a microphase‐separated layered morphology was observed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 879–896, 2005     

Group VA effects on surfactant aggregation number and dye solubilization efficiency

The effects of changing the charge-bearing atom in the polar head of a surfactant ion on micelle size and dye solubilization efficiency were investigated. Replacement of nitrogen in decyltrimethylammonium bromide by phosphorus or arsenic increases the micellar aggregation number by at least 20% in 0.5 m NaBr solutions. The ability of the surfactants to solubilize the dye Orange-OT is only slightly affected by the substitution of phosphorus for nitrogen, but it is lowered appreciably by the substitution of arsenic.     

(E)-3-(2-Alkyl-10H-phenothiazin-3-yl)-1-arylprop-2-en-1-ones: Preparative, IR, NMR and DFT study on their substituent-dependent reactivity in hydrazinolysis and sonication-assisted oxidation with copper(II)nitrate

A series of novel 3(5)-aryl/ferrocenyl-5(3)-phenothiazinylpyrazoles and pyrazolines were obtained by substituent-dependent regioselective condensation of the corresponding (E)-3-(2-alkyl-10H-phenothiazin-3-yl)-1-aryl/ferrocenylprop-2-en-1-one with hydrazine or methylhydrazine in acetic acid. The different propensity of the primary formed beta-hydrazino adducts to undergo competitive retro-Mannich reaction was interpreted in terms of tautomerisation equilibrium constants calculated by DFT using a solvent model. The regioselectivity of the cyclisation reactions with methylhydrazine and the substituent-dependent redox properties of pyrazolines were also rationalized by comparative DFT calculations performed for simplified model molecules. On the effect of ultrasound-promoted oxidation with copper(II)nitrate phenothiazine-containing pyrazolines, enones and oxo-compounds were selectively transformed into sulfoxides. Only one sulfoxide enone was partially converted into an oxirane derivative. The structure of the novel products was determined by IR and NMR spectroscopy including COSY, HSQC, HMBC and DNOE measurements.