Generalizations and error analysis of the iterative operator splitting method

The properties of iterative splitting with two bounded linear operators have been analyzed by Faragó et al. For more than two operators, iterative splitting can be defined in many different ways. A large class of the possible extensions to this case is presented in this paper and the order of accuracy of these methods are examined. A separate section is devoted to the discussion of two of these methods to illustrate how this class of possible methods can be classified with respect to the order of accuracy.     

On the equilibria of finely discretized curves and surfaces

Our goal is to identify the type and number of static equilibrium points of solids arising from fine, equidistant n-discretizations of smooth, convex surfaces. We assume uniform gravity and a frictionless, horizontal, planar support. We show that as n approaches infinity these numbers fluctuate around specific values which we call the imaginary equilibrium indices associated with the approximated smooth surface. We derive simple formulae for these numbers in terms of the principal curvatures and the radial distances of the equilibrium points of the solid from its center of gravity. Our results are illustrated on a discretized ellipsoid and match well the observations on natural pebble surfaces.     

Gamma radiation effects on physical properties of parchment documents: Assessment of Dmax

Parchments are important documents that give testimony for History; therefore these materials should be respected and preserved. Considering incremental biodeterioration problems that have to be faced daily, the Archive of the University of Coimbra (AUC) is involved in different scientific projects in order to evaluate and determine new methods for document decontamination and preservation.The aim of this study was to evaluate gamma radiation effects on the colour and texture of the AUC parchment documents. The assessment of these effects was used to estimate the maximum gamma radiation dose (D_max) that could guarantee parchment documents′ decontamination treatment, without significant alteration of their physical properties. Parchment samples were exposed to gamma radiation doses ranging from 10 to 30 kGy. The texture and colour of samples were assessed before and after the irradiation procedure, using a texture analyser and an electronic colorimeter. Hardness and springiness were determined based on texture spectra. Lightness (L?), Chroma (C), greenness vs. redness (a*) and yellowness vs. blueness (b*) values were obtained from colorimetric measures. Results indicate no significant effects of gamma radiation on the texture and colour of parchment for the studied doses.     

How different are ranking methods for fuzzy numbers? A numerical study

Ranking fuzzy numbers is often a necessary step in many mathematical models, and a large number of ranking methods have been proposed to perform this task. However, few comparative studies exist and nowadays it is still unknown how similar ranking methods are in practice, i.e., how likely they are to induce the same ranking. In this study, by means of numerical simulations, we try to answer this question. We shall discover that there are some very similar methods as well as some outliers. We end the paper interpreting the results and giving some recommendations on the use of ranking methods.     

Influence of the metal loading on the electrocatalytic activity of carbon-supported (100) Pt nanoparticles

Journal of Solid State Electrochemistry - The influence of the metal loading (i.e. interparticle distance) of shape-controlled Pt nanoparticles on their electrocatalytic properties is evaluated for...     

Quantum similarity matrices column set as holograms of DF molecular point clouds

A simple argument proves that quantum similarity measures, performed on any density function (DF) tag set of a given quantum object set, create a hologram of such DF tag set.     

Mass Spectrometry of Some Benzylidene Imidazolidinediones and Thiazolidinediones. II- chlorobenzyl imidazolidinedione and Fluoro or Chlorobenzyl Thiazolidinedione Compounds

In the present investigation, a study of the electron impact mass spectrometry data is reported for seven compounds of a series of some 3-(4-chlorobenzyl)-5-benzylidene-imidazolidine-2, 4-diones and 3-(4-fluoro or chlorobenzyl)-5-benzylidene-thiazolidine-2, 4-diones previously synthesized.     

Two Methods for Retrieving UV Index for All Cloud Conditions from Sky Imager Products or Total SW Radiation Measurements

Cloud effects on UV Index (UVI) and total solar radiation (TR) as a function of cloud cover and sunny conditions (from sky images) as well as of solar zenith angle (SZA) are assessed. These analyses are undertaken for a southern‐hemisphere mid‐latitude site where a 10‐years dataset is available. It is confirmed that clouds reduce TR more than UV, in particular for obscured Sun conditions, low cloud fraction (<60%) and large SZA (>60°). Similarly, local short‐time enhancement effects are stronger for TR than for UV, mainly for visible Sun conditions, large cloud fraction and large SZA. Two methods to estimate UVI are developed: (1) from sky imaging cloud cover and sunny conditions, and (2) from TR measurements. Both methods may be used in practical applications, although Method 2 shows overall the best performance, as TR allows considering cloud optical properties. The mean absolute (relative) differences of Method 2 estimations with respect to measured values are 0.17 UVI units (6.7%, for 1 min data) and 0.79 Standard Erythemal Dose (SED) units (3.9%, for daily integrations). Method 1 shows less accurate results but it is still suitable to estimate UVI: mean absolute differences are 0.37 UVI units (15%) and 1.6 SED (8.0%).