Sequential optimality conditions for composed convex optimization problems

Using a general approach which provides sequential optimality conditions for a general convex optimization problem, we derive necessary and sufficient optimality conditions for composed convex optimization problems. Further, we give sequential characterizations for a subgradient of the precomposition of a K-increasing lower semicontinuous convex function with a K-convex and K-epi-closed (continuous) function, where K is a nonempty convex cone. We prove that several results from the literature dealing with sequential characterizations of subgradients are obtained as particular cases of our results. We also improve the above mentioned statements.     

On the stability of the additive Cauchy functional equation in random normed spaces

Some stability results for the functional equations of Cauchy and Jensen in probabilistic setting are proved by using the fixed point method.     

On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

An Application of the Bivariate Inf-Convolution Formula to Enlargements of Monotone Operators

Motivated by a classical result concerning the ε-subdifferential of the sum of two proper, convex and lower semicontinuous functions, we give in this paper a similar result for the enlargement of the sum of two maximal monotone operators defined on a Banach space. This is done by establishing a necessary and sufficient condition for a bivariate inf-convolution formula.     

Carbon and diamond paste microelectrodes based on Mn(III) porphyrins for the determination of dopamine

Three Mn(III) porphyrins were used for the design of carbon paste and diamond paste based microelectrodes, which were employed for the determination of dopamine in pharmaceutical and biological samples using differential pulse voltammetry (DPV). The limits of detection lie between 1.6 × 10⁻¹³ and 2.0 × 10⁻⁶ mol L⁻¹ while the sensitivities were between 230 pA μmol L⁻¹ and 3.24 μA mol L⁻¹. Dopamine was recovered reliable from pharmaceutical and biological samples in percentages higher than 91.00% and 92.00%, respectively. The surface of the microelectrodes can easily be renewed by simple polishing, obtaining a fresh surface ready for use in a new assay.     

Optimization of acetylcholinesterase immobilization on microelectrodes based on nitrophenyl diazonium for sensitive organophosphate insecticides detection

The immobilization of acetylcholinesterase on platinum microelectrodes modified with p-nitrobenzenediazonium is optimized. In the first step, a layer of p-nitrophenyl groups was deposited on the surface and then reduced to p-aminophenyl groups. Finally, the enzyme was linked to the amino groups on the surface using glutaraldehyde. Each step of the electrode modification was characterized by cyclic voltammetry and electrochemical impedance spectroscopy (EIS) at acidic and neutral pH to modify the electric charges of different bound moieties. The deposition of diazonium groups was attempted by potentiometry, amperometry or CV, but only potentiometry proceeded without passivation of the surface. The use of microelectrodes improved the limit of detection of ethylparaoxon measurements to 20 nM (compared to 100 nM in case of screen-printed electrodes based on the same method of immobilization). The method allowed the production of stable and reproducible amperometric microbiosensors and may be adapted to other enzymes and electrode materials.