An infinite family of subcubic graphs with unbounded packing chromatic number

Recently, Balogh et al. (2018) answered in negative the question that was posed in several earlier papers whether the packing chromatic number is bounded in the class of graphs with maximum degree 3. In this note, we present an explicit infinite family of subcubic graphs with unbounded packing chromatic number.     

Kinetic Modeling of Ethylene Glycol Monoesterification

The monoesterification of ethylene glycol under isothermal conditions was conducted using benzoic acid in methane‐sulfonic acid/Al₂O₃ as a catalyst. Using this reagent, glycol was selectively monoesterified with high yield. The reactions were performed within an automated batch reactor under equimolar conditions, constant rotational frequency of the stirrer, and within the temperature range from 65 to 85°C. The rate constant related to this reaction and to the corresponding reverse reaction, activation energy, and preexponential factor was derived from experimental data. It has been concluded that under these conditions the formation of dibenzoate was successfully prevented.     

Evaluation of calcium carbonate in eggshells using thermal analysis

The eggshell of the hen is an important structure which provides protection for the developing chick, and also a container for the egg in the food industry. Egg breakage can reach up to 10% of total egg production, causing considerable economic losses. The eggshell consists of membranes, composed mainly of proteins, and the mineral shell composed mainly of the calcite polymorph of CaCO₃. The average CaCO₃ content of a chicken eggshell is between 93 and 97%, depending on animal genotype, age, housing system of laying hens and mineral nutrition. In the present study, eggs of the same breed and approximately same age were collected from four different production systems: organic farming, free-range production, deep litter system and battery cage system. The CaCO₃ content was determined by the standard titration method and by atomic absorption spectroscopy. Thermal properties of dried eggshell powder were measured by thermogravimetric measurements between 30 and 900 °C in air, showing a significant mass loss of?≈?43% between 600 and 850 °C corresponding to the decomposition of CaCO₃ to CaO and CO₂. The relations between the thermal mass loss and CaCO₃ content determined by the titration method/atomic absorption spectroscopy were studied using predictive models fitted by the linear regression method. A good prediction ability with an average prediction error of 0.01% was obtained between CaCO₃ determined by titration and the thermal mass loss, indicating that TG could provide a reliable method for evaluation of CaCO₃ content in eggshells.

     

Partition distance in graphs

If G is a graph and \(\mathcal{P}\) is a partition of V(G), then the partition distance of G is the sum of the distance between all pairs of vertices that lie in the same part of \(\mathcal{P}\). This concept generalizes several metric concepts and is dual to the concept of the colored distance due to Dankelmann, Goddard, and Slater. It is proved that the partition distance of a graph can be obtained from the Wiener index of weighted quotient graphs induced by the transitive closure of the Djokovi?–Winkler relation as well as by any partition coarser than it. It is demonstrated that earlier results follow from the obtained theorems. Applying the main results, upper bounds on the partition distance of trees with prescribed order and radius are proved and corresponding extremal trees characterized.     

Analysis of the Thermal Stability of Very Thin Surface Layers of Corrosion Inhibitors by Time-of-Flight Secondary Ion Mass Spectrometry

The powerful nature of the secondary ion mass spectrometry (SIMS) technique was explored in order to analyse very thin surface layers that were self-assembled on steel material from acidic solution. These surface layers are adsorbed corrosion inhibitors. The SIMS technique proved useful to characterise the molecular structure and homogeneity of thin surface layers in the nanometre range of specific analytes on the metallic substrate. Using SIMS, the thermal stability of these layers was further investigated and the desorption energy at a certain temperature was determined, where special attention was devoted to the method’s static limit. In order to compare, and for certain cases emphasise, the benefits gained by using SIMS in such surface analysis compared with the X-ray photoelectron spectroscopy (XPS) method, the same samples were also analysed by means of the latter. XPS is usually considered to be the most powerful analytical tool in surface analysis studies, but, as shown herein, it has certain limitations compared to SIMS. Finally, the surface topography was investigated by employing atomic force microscopy (AFM) in order to carry out a comprehensive surface analysis.

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Graphical Abstract ?

     

Continuous multiplicative mappings on

Let and be compact Hausdorff topological spaces, and let and be real Banach algebras of all real-valued continuous functions on and , respectively. The general form of continuous multiplicative mappings is given.

     

Open cellular reactive porous membranes from high internal phase emulsions

High internal phase emulsions (HIPEs) incorporating styrene, 4-vinylbenzyl chloride, divinylbenzene and ethylhexyl acrylate were applied to prepare reactive, cross-linked porous membranes with open cellular architecture and thicknesses between 30 and 500 mum.