Connecting face hitting sets in planar graphs

We show that any face hitting set of size n of a connected planar graph with a minimum degree of at least 3 is contained in a connected subgraph of size 5n−6. Furthermore we show that this bound is tight by providing a lower bound in the form of a family of graphs. This improves the previously known upper and lower bound of 11n−18 and 3n respectively by Grigoriev and Sitters. Our proof is valid for simple graphs with loops and generalizes to graphs embedded in surfaces of arbitrary genus.     

HPLC sugar profiles of Algerian honeys

Sugar profiles of fifty honey samples from different regions of Algeria are analysed by HPLC with pulsed amperometric detection. These samples consisted of 25 multifloral and 25 unifloral honeys. Eleven sugars (two monosaccharides, nine oligosaccharides) are quantified. The mean values of fructose and glucose are in the range 35.99–42.57% and 24.63–35.06%, respectively. These monosaccharides are the main sugars of all honey samples. The sucrose, maltose, isomaltose, turanose and erlose are present nearly in all the samples, while raffinose and melezitose are detected in few samples. Furthermore, trehalose is present only in two samples and none of the samples contain melibiose. Low amounts of melezitose, raffinose and erlose are present in the range of 0.03–2.14%, 0.03–0.35% and 0.01–2.35%, respectively. PCA (Principal Component Analysis) showed that the cumulative variance was approximately 40% and Apiaceae honeys are correctly classified using FDA (Factorial Discriminant Analysis).     

Distribution,sources, and behavior of trace elements in the Clinton River Watershed,Michigan

The Clinton River watershed near Detroit, Michigan, USA was separated in six different land uses: agricultural, residential, mixed industrial and residential, downstream industrial, Clinton River Spillway, and Lake St. Clair, utilizing As, Cd, Cu, Ni, Pb, and Zn contents of the sediment that has median values of 3, 0.3, 15, 14, 13, and 57 mg kg^− 1, respectively. However, trace element concentrations in the lower Clinton River rivaled those in the most contaminated watersheds of the world. Enrichment factors and principal component analysis (PCA) separated trace elements into 2 categories: anthropogenic (Cd, Cu, Ni, Pb, and Zn) and geogenic (Al, As, Ca, Fe, K, Mg, TOC) sources. PCA linked agricultural, residential, and mixed industrial and residential land uses to anthropogenic Cd, Cu, Ni, Pb, and Zn, and lake sediments to geogenic elements, organic matter and clay contents. The downstream industrial zone has a unique source signature. Trace element concentrations varied with land use. The upper Clinton River (> 20 km from mouth; residential land use; median concentrations up to 25 mg kg^− 1) appeared to meet delisting criteria. Partitioning was also land use and element specific with: (1) exchangeable fraction (up to 94% of total) related to road salt and mobile chloride complex formation; (2) carbonate-bound fraction (up to 100%) resulting from Ca substitution or adsorption; (3) presence of immobile (hydr)oxide-bound fraction (up to 90%) instead of potentially mobile organic matter and sulphide-bound fraction (up to 20%); and (4) residual fraction (up to 65%) originating from geogenic and/or anthropogenic sources.     

Thermal runaway analysis of a three-phase reactor for LCO hydrotreatment

Safety is a high-priority topic for the chemical industry to minimize the frequency and severity of accidents while keeping the productivity and quality of the production. The processes that may undergo thermal runaways due to exothermic reactions are at the heart of the risks of accidents. The study of such highly reactive systems is essential to achieve a safe and productive operation of existing processes and to ensure inherently safe new designs. It is well known that the stationary analysis with the van Heerden criterion must be satisfied, however, this is not sufficient to ensure reactor stability. Only dynamic analysis can provide an accurate answer concerning the safe operation of the reactor. Most of the reported stability studies are carried out for relatively simple systems (pseudo-homogeneous models, simple reaction schemes). This work presents the dynamic thermal stability study of a refining process (hydrotreatment of light cycle oils) carried out with real gasoils at industrial operating conditions. A 1D dynamic model that accurately represents the reactive system (gas–liquid–solid) was developed and validated with experimental pilot plant data. This mathematical model was used to perform the thermal stability analysis of the dynamic system using a perturbation method. The effect of the variation of the heat transfer coefficient on the thermal stability is presented. The spectral analysis of the eigenvalues indicating the stable/unstable behavior of the reactive system was compared with dynamic simulations. An excellent agreement was found between the simulations and the stability analysis. The case of oscillating behavior is also described. The frequencies of oscillation determined by the stability analysis are compared to the frequencies calculated by Fourier transform applied to the simulated signal. The reactor behavior and the oscillations features are accurately predicted with this stability analysis method.     

Moving recommender systems from on-line commerce to retail stores

The increasing diversity of consumers’ demand, as documented by the debate on the long tail of the distribution of sales volume across products, represents a challenge for retail stores. Recommender systems offer a tool to cope with this challenge. The recent developments in information technology and ubiquitous computing makes it feasible to move recommender systems from the on-line commerce, where they are widely used, to retail stores. In this paper, we aim to bridge the management literature and the computer science literature by analysing a number of issues that arise when applying recommender systems to retail stores: these range from the format of the stores that would benefit most from recommender systems to the impact of coverage and control of recommender systems on customer loyalty and competition among retail stores.     

In vivo measurement of the oxygen saturation of retinal vessels in healthy volunteers

A new method for the spatially resolved measurement of the oxygen saturation of retinal vessels is described. Imaging spectrometry was used for both measurements of transmission and reflectance spectra of whole blood in cuvettes as well as for fundus reflectance spectra. A model was developed for the calculation of the oxygen saturation, valid in the wavelength range between 510 nm and 586 nm, in that the internal reflectance is constant and only the transmitted light depends on layer thickness and hematocrit. Altogether 265 measurements were performed in different number at 30 eyes. In each measurement, the oxygen saturation was simultaneously determined for 193 locations along a line of 1.5 mm at the fundus. The mean oxygen saturation in retinal arteries was (92.2 +/- 4.1)% and (57.9 +/- 9.9)% in retinal veins. The mean retinal arterio-venous difference of the oxygen saturation was (35.1 +/- 9.5)%. The venous oxygen saturation depended on distance from the optic disc. The measured mean of the arterio-venous difference of the oxygen saturation corresponded well to the value of the brain (34%). The utilization of oxygen in the temporal quadrants (inferior: 39.4 +/- 10.4%) is significantly (p = 0.05) higher than in the nasal quadrants (inferior: 31.3 +/- 6.7%).     

Stability of systems of plane reflecting surfaces

A general rule for the stability of plane reflecting surface systems is derived by use of the features of the reflection matrix. It is proved that only two directions can be stable: the forward direction and the backward direction (retroreflection). Examples for the application of this rule in the design of stable reflecting systems for optical communication are given.     

Using the incompressibility method to obtain local lemma results for Ramsey-type problems

We reveal a connection between the incompressibility method and the Lovász local lemma in the context of Ramsey theory. We obtain bounds by repeatedly encoding objects of interest and thereby compressing strings. The method is demonstrated on the example of van der Waerden numbers. In particular we reprove that . The method is applicable to obtain lower bounds of Ramsey numbers, large transitive subtournaments and other Ramsey phenomena as well.