Existence and global attractivity of solutions of a nonlinear functional integral equation

In this paper we prove a result on the existence and global attractivity of solutions of a nonlinear functional integral equations with deviating arguments. The investigations are placed in the Banach space of real functions defined, continuous and bounded on the real half-axis. The main tool used in consideration is a fixed point theorem of Krasnosel’skii type. A few examples illustrating the obtained results are also included.     

High-resolution wavelength-dispersive spectroscopy of K-shell transitions in hydrogen-like gold

We present a measurement of K-shell transitions in H-like gold (Au⁷⁸⁺) using specially developed transmission type crystal spectrometers combined with Ge(i) microstrip detectors. The experiment has been carried out at the Experimental Storage Ring at GSI in Darmstadt. This is a first high-resolution wavelength-dispersive measurement of a K-shell transition in a high-Z H-like ion, thus representing an important milestone in this field. Ideas on possible future improvements are discussed as well.     

Distribution of selected elements in atherosclerotic plaques of apoE/LDLR‐double knockout mice assessed by synchrotron radiation‐induced micro‐XRF spectrometry

Apolipoprotein E and LDL receptor double‐knockout (apoE/LDLR^?/?) mice represent a reliable experimental model of atherosclerosis. The aim of the present study was to examine the elemental content of atherosclerotic plaques using synchrotron radiation‐induced micro x‐ray fluorescence (XRF) spectrometry. Numerous essential and trace elements were detected in cross‐sections of aortic roots collected from 6‐month‐old apoE/LDLR^?/? mice fed with chow diet. Two‐dimensional maps of the elemental distribution and point recordings were compared with images of consecutive sections stained histologically, allowing precise localization of the analyzed elements in morphologically defined areas of aortic lesion. The sulphur was detected in areas occupied by macrophages and smooth muscle cells. Iron was observed in high concentrations in cardiac and smooth muscle, blood clots and in adjacent coronary vessels. Lower concentrations of iron were seen in the regions of plaques rich in macrophages and lipids. Copper was detected in higher amounts only in cardiac muscle and its concentration in plaques was very low. There was a quite high content of calcium in aortic plaque areas containing lipids and macrophages. Much higher concentrations of calcium were observed in mineral deposits, mostly located in the aortic media. Similar distribution was also characteristic for phosphorus. Zinc was observed in moderately low concentrations in atheromas. Higher content of zinc was seen in smooth musculature, in cardiac muscle and in mineral concretions. The presented results provide a substantial morphological and physicochemical background for further investigations aiming to evaluate pharmacological and dietary treatment of atherosclerosis in an apoE/LDLR^?/? mouse model. Copyright © 2008 John Wiley & Sons, Ltd.     

Electrochemical behaviour of p-Si in methanol solutions of chlorides

The mechanism of anodic dissolutions of p-Si single crystals in CH₃OH–LiCl and CH₃OH–LiCl–HCl solutions was investigated by means of the following electrochemical methods: linear sweep voltammetry, the potentiostatic transient technique and XPS surface analysis. The dissolution of p-Si proceeds by a two-step mechanism with the creation of a Si(II) surface intermediate. At low anodic overvoltage the dissolution proceeds with the formation of porous silicon, probably through the reaction: 2Si(II)Si+Si(IV). Structural etching of the single crystals surface was observed at high anodic overvoltage (E>2 V). At this potential range, silicon dissolves with the formation of a Si(IV) soluble product. Electrolysis of the methanol solvent containing Si(IV) in the cell p-Si|CH₃OH–LiCl–Si(IV)|M, where M=Pt, Cu or 18/8 stainless steel, leads to the deposition of an amorphous organosilicon layer on the cathode. The analysis of the deposit performed by means of XPS, FTIR and SEM allows determination of the morphology and composition of the film. The layer consists of Si–OCH₃ compounds and can be created only in methanol solvent. The film is unstable in a humid atmosphere and undergoes transformation into a Si–OH layer.Contribution to the 3rd Baltic Conference on Electrochemistry, Gdansk-Sobieszewo, Poland, 23–26 April 2003Dedicated to the memory of Harry B. Mark, Jr. (28 February 1934–3 March 2003)     

Electrochemical synthesis of magnetic iron oxide nanoparticles with controlled size

We present a novel and facile method enabling synthesis of iron oxide nanoparticles, which are composed mainly of maghemite according to X-ray diffraction (XRD) and Mössbauer spectroscopy studies. The proposed process is realized by anodic iron polarization in deaerated LiCl solutions containing both water and ethanol. Water seems to play an important role in the synthesis. Morphology of the product was studied by means of transmission electron microscopy and XRD. In the solution containing almost 100% of water a black suspension of round shaped maghemite nanoparticles of 20–40 nm size is obtained. Regulating water concentration allows to control nanoparticle size, which is reduced to 4–6 nm for 5% of water with a possibility to reach intermediate sizes. For 3% or lower water concentration nanoparticles are of a needle-like shape and form a reddish suspension. In this case phase determination is problematic due to a small particle size with the thickness of roughly 3 nm. However, XRD studies indicate the presence of ferrihydrite. Coercivities of the materials are similar to those reported for nanoparticle magnetite powders, whereas the saturation magnetization values are considerably smaller.     

A note on portfolios with risk-free internal gains

In this paper we show that if a not-necessarily-self-financing portfolio has instantaneously riskless internal gains, then on an infinitesimal time-interval, the increase in the internal gains on the portfolio is the same as the change in the price of that amount of bonds which has the same wealth as the portfolio has. As an application of this result, we derive the Black–Scholes PDE by using the original derivation of Black and Scholes, and we show that it can be made completely rigorous.     

Integral operators of Urysohn-Stieltjes type

Summary We investigate some properties of nonlinear integral operators of Urysohn--Stieltjes type with kernels depending on two variables. Results concerning the continuity and compactness of these operators are obtained. The solvability of nonlinear Urysohn--Stieltjes integral equations is also studied.     

On Free Products and Amalgams of Pomonoids

The study of amalgamation in the category of partially ordered monoids was initiated by Fakhuruddin in the 1980s. In 1986 he proved that, in the category of commutative pomonoids, every absolutely flat commutative pomonoid is a weak amalgmation base and every commutative pogroup is a strong amalgamation base. Some twenty years later, Bulman-Fleming and Sohail in 2011 extended this work to what they referred to as pomonoid amalgams. In particular, they proved that pogroups are poamalgmation bases in the category of pomonoids. Sohail, also in 2011, proved that absolutely poflat commutative pomonoids are poamalgmation bases in the category of commutative pomonoids. In the present article, we extend the work on pomonoid amalgams by generalizing the work of Renshaw on amalgams of monoids and extension properties of acts over monoids.     

Depth profiling of dopants implanted in Si using the synchrotron radiation based high‐resolution grazing emission technique

We report on the surface‐sensitive grazing emission X‐ray fluorescence technique combined with synchrotron radiation excitation and high‐resolution detection to realize depth‐profile measurements of Al‐implanted Si wafers. The principles of grazing emission measurements as well as the benefits offered by synchrotron sources and wavelength‐dispersive detection setups are presented. It is shown that the depth distribution of implanted ions can be extracted from the dependence of the X‐ray fluorescence intensity on the grazing emission angle with nanometer‐scale precision provided that an analytical function describing the shape of the depth distribution is assumed beforehand. If no a priori assumption is made, except a bell shaped form for the dopant distribution, the profile derived from the measured angular distribution is found to reproduce quite satisfactorily the depth distribution of the implanted ions. Copyright © 2012 John Wiley & Sons, Ltd.     

A multi-criteria model for auditing a Predictive Maintenance Programme

Auditing tools can play a key role in the continuous improvement of maintenance policies, in particular to enhance predictive maintenance (PM). This paper proposes a multi-criteria model for auditing a Predictive Maintenance Programme (PMP) developed and implemented in the General Hospital of Ciudad Real (GHCR) in Spain. The model has a two-level structure, with top level auditing areas specified by second level auditing criteria on which the performance of the PMP should be appraised. This structure resulted from the analysis and discussion of an internal questionnaire to the management, technical and consulting staff of GHCR. This also guided the association of a performance scale with each criterion, describing several reference levels of accomplishment. Using the MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) approach, a hierarchical additive value model was constructed, with criteria weights and value scales derived from staff judgments of comparison of different reference levels and profiles of performance. This model enables managers to measure the performance of the PMP and its added value for the hospital, not only against each audit criterion individually, but also on each area and in overall terms. Integrated in a management “tableau de bord”, the model outputs permit the identification of PMP deficiencies requiring urgent intervention and corrective measures for its continuous improvement.