Electrochemical study of the corrosion behaviour of carbon steel in fracturing fluid

Corrosion behaviour of carbon steel (K-55) in fracturing fluid was studied with a rotation cylinder electrode, under static and rotation conditions by means of several electrochemical techniques which are as follows: open circuit potential (OCP) decay, potentiodynamic polarisation and electrochemical impedance spectroscopy (EIS). The corrosion rate was determined by weight loss measurements. The electrode surface after a prefixed immersion time was characterised by scanning electron microscopy (SEM) and X-ray diffraction (XRD). The results indicated that carbon steel showed anodic dissolution behaviour that increased under rotating condition. The cathodic polarisation current density also increased with the electrode rotation due to the increased oxygen diffusion on the electrode surface. Two different oxide layers were formed: a dark, thin layer of magnetite tightly adhering to the electrode surface, characterised by localised corrosion spots, and a porous reddish layer of poorly adhering hematite (Fe₂O₃) and maghemite (γ-Fe₂O₃). Under higher rotation rate, the developed oxide layer was not so stable, owing to the shear stress induced between the solution and the specimen surface, enhancing the corrosion rate.     

On existence and asymptotic behaviour of solutions of a functional integral equation

The paper contains a result on the existence and asymptotic behaviour of solutions of a functional integral equation. That result is proved under rather general hypotheses. The main tools used in our considerations are the concept of a measure of noncompactness and the classical Schauder fixed point principle. The investigations of the paper are placed in the space of continuous and tempered functions on the real half-line. We prove an existence result which generalizes several ones concerning functional integral equations and obtained earlier by other authors. The applicability of our result is illustrated by some examples.     

Quantum electrodynamics in strong electric fields: the ground-state Lamb shift in hydrogenlike uranium

X-ray spectra following radiative recombination of free electrons with bare uranium ions (U92+) were measured at the electron cooler of the ESR storage ring. The most intense lines observed in the spectra can be attributed to the characteristic Lyman ground-state transitions and to the recombination of free electrons into the K shell of the ions. Our experiment was carried out by utilizing the deceleration technique which leads to a considerable reduction of the uncertainties associated with Doppler corrections. This, in combination with the 0 degree observation geometry, allowed us to determine the ground-state Lamb shift in hydrogenlike uranium (U91+) from the observed x-ray lines with an accuracy of 1%. The present result is about 3 times more precise than the most accurate value available up to now and provides the most stringent test of bound-state quantum electrodynamics for one-electron systems in the strong-field regime.     

On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation

The existence of solutions of a nonlinear quadratic Volterra integral equation is studied. In our considerations we apply the technique of measures of noncompactness in conjunction with the classical Schauder fixed point principle. Such an approach allows us to obtain a result on the existence of solutions of an equation in question which are uniformly locally attractive or asymptotically stable.     

Proof of Kolmogorovian censorship

Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of classical probability theory are incompatible with quantum probabilities, and that this is the reason for the violation of Bell's inequalities. Szabó showed that, in fact, these inequalities are not violated by the experimentally observed frequencies if we consider the real, “effective” frequencies. We prove in this work a theorem which generalizes this results: “effective” frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected through different experimental setups, the choice of which obeys a classical distribution.     

A new approach to the theory of functional integral equations of fractional order

The aim of the paper is to present a new approach to the theory of functional integral equations of fractional order. That approach depends on converting of the mentioned equations to the form of functional integral equations of Volterra-Stieltjes type. It turns out that the study of functional integral equations of Volterra-Stieltjes type is more convenient and effective than the study of functional integral equations of fractional order. An example illustrating our approach is also discussed.