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.     

Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory

We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.     

Tunneling time correction to the intersubband optical absorption in a THz laser-dressed GaAs/Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1-</Subscript><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As quantum well

Tunneling effect on the intersubband optical absorption in a GaAs/Al _x Ga_{1- x} As quantum well under simultaneous presence of intense non-resonant laser and static electric fields is theoretically investigated. Based on the shooting method the quasi-stationary energy levels and their corresponding linewidths are obtained. By considering the joint action of the two external fields the linear absorption coefficient is calculated by means of Fermi’s golden rule and taking into account the intersubband relaxation. We found that: (i) the linewidth broadening due to the electron tunneling has an appreciable effect on the absorption spectrum; (ii) a constant relaxation time adopted in the previous studies could not be justified even for moderate electric fields, especially in the laser dressed wells. Our model predicts that the number of absorption peaks can be controlled by the external applied fields. While in the high-electric fields the excited states become unbounded due to a significant tunneling of the electrons, for high laser intensities and low/moderate electric fields the absorption spectrum has a richer structure due to the laser-generated resonant states. The possibility of tuning the resonant absorption energies by using the combined effects of the static electric field and the THz coherent radiation field can be useful in designing new optoelectronic devices.     

Adaption of a diffractometer for time‐resolved X‐ray resonant magnetic scattering

A new set‐up is presented to measure element‐selective magnetization dynamics using the ALICE chamber [Grabis et al. (2003), Rev. Sci. Instrum. 74 , 4048–4051] at the BESSY II synchrotron at the Helmholtz‐Zentrum Berlin. A magnetic‐field pulse serves as excitation, and the magnetization precession is probed by element‐selective X‐ray resonant magnetic scattering. With the use of single‐bunch‐generated X‐rays a temporal resolution well below 100 ps is reached. The ALICE diffractometer environment enables investigations of thin films, described here, multilayers and laterally structured samples in reflection or diffuse scattering geometry. The combination of the time‐resolved set‐up with a cryostat in the ALICE chamber will allow temperature‐dependent studies of precessional magnetization dynamics and of damping constants to be conducted over a large temperature range and for a large variety of systems in reflection geometry.     

Vanishing evaluations of simple functors

The classification of simple biset functors is known, but the evaluation of a simple biset functor at a finite group G$G$ may be zero. We investigate various situations where this happens, as well as cases where this does not occur. We also prove a closed formula for such an evaluation under some restrictive conditions on  G$G$.     

Generalized Iterated Function Systems with Place Dependent Probabilities

In the present paper we introduce the concept of generalized iterated function system with place dependent probabilities (GIFSpdp). In this framework, we provide sufficient conditions under which the Markov operator associated to a GIFSpdp is Lipschitz. We also prove, under certain conditions, the existence of an analogue of Hutchinson measure associated to a GIFSpdp and study its properties.     

Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems

We deal with monotone inclusion problems of the form 0 ∈ A x + D x + N _C (x) in real Hilbert spaces, where A is a maximally monotone operator, D a cocoercive operator and C the nonempty set of zeros of another cocoercive operator. We propose a forward-backward penalty algorithm for solving this problem which extends the one proposed by Attouch et al. (SIAM J. Optim. 21(4): 1251-1274, 2011). The condition which guarantees the weak ergodic convergence of the sequence of iterates generated by the proposed scheme is formulated by means of the Fitzpatrick function associated to the maximally monotone operator that describes the set C. In the second part we introduce a forward-backward-forward algorithm for monotone inclusion problems having the same structure, but this time by replacing the cocoercivity hypotheses with Lipschitz continuity conditions. The latter penalty type algorithm opens the gate to handle monotone inclusion problems with more complicated structures, for instance, involving compositions of maximally monotone operators with linear continuous ones.