Partitioning a graph into convex sets

Let G be a finite simple graph. Let S⊆V(G), its closed interval I[S] is the set of all vertices lying on shortest paths between any pair of vertices of S. The set S is convex if I[S]=S. In this work we define the concept of a convex partition of graphs. If there exists a partition of V(G) into p convex sets we say that G is p-convex. We prove that it is NP-complete to decide whether a graph G is p-convex for a fixed integer p≥2. We show that every connected chordal graph is p-convex, for 1≤p≤n. We also establish conditions on n and k to decide if the k-th power of a cycle C_n is p-convex. Finally, we develop a linear-time algorithm to decide if a cograph is p-convex.     

On the forbidden induced subgraph sandwich problem

We consider the sandwich problem, a generalization of the recognition problem introduced by Golumbic et al. (1995) [15], with respect to classes of graphs defined by excluding induced subgraphs. We prove that the sandwich problem corresponding to excluding a chordless cycle of fixed length k is NP-complete. We prove that the sandwich problem corresponding to excluding K_r?e for fixed r is polynomial. We prove that the sandwich problem corresponding to 3PC(⋅,⋅)-free graphs is NP-complete. These complexity results are related to the classification of a long-standing open problem: the sandwich problem corresponding to perfect graphs.     

Thermal characterization of oil and biodiesel from oiticica (<Emphasis Type="Italic">Licania rigida</Emphasis> Benth)

Searching for other alternative sources, which are not part of the food chain, and which are able to supply the biofuel market is a promising option. In this context, it has been searched to investigate the oiticica oil, approaching its availability to the biodiesel synthesis, as well as its thermal stability. Few works retreat parameters such as: the optimization of the biodiesel synthesis, its physical–chemical properties, and thermal parameters etc. The characterization results revealed that the oil showed very high kinematic viscosity, and acidity value around 13 mg KOH/g, requiring a pre-treatment. To reduce the acid in the oil, it has been done the esterification of oil, which was studied in different molar ratios oiticica oil/ethanol (1:9) and 2.0% catalyst, in order to get the best reduction the index of acidity. The lowest level of acidity of the oil obtained after the esterification was 4.4 mg KOH/g. The reaction rate for the synthesis of biodiesel, compared to the initial mass of oiticica oil ester was 85%. This income can be overcome by pursuing an even smaller reduction of acid value of biodiesel oiticica. The acid value of biodiesel was 1.8 mg KOH/g. The results have revealed that the oiticica oil and biodiesel are stable at 224 and 179 °C, respectively.     

Rheology and MT-DSC studies of the flow properties of ethyl and methyl babassu biodiesel and blends

The synthesis of pigments from the system Ce_1−x O₂–M _x O (M = Cu, Co) was achieved via a polymeric precursors method, Pechini method. Differential scanning calorimetry (DSC) and thermogravimetry (TG) techniques were used to accurately characterize the distinct thermal events occurring during synthesis. The TG and DSC results revealed a series of decomposition temperatures due to different exothermal events, which were identified as H₂O elimination, organic compounds degradation, and phase formation. X-Ray diffraction patterns show the presence of pure cubic CeO₂ phase for the samples with low Cu and Co loading. A decrease of the specific surface area with increasing copper and cobalt content was observed. The UV–visible diffuse reflectance technique was employed to study the optical properties in the 200–800 nm range. Colorimetric coordinates L*, a*, b* were calculated for the pigment powders. The powders presented a variety of colors from yellow for pure CeO₂, to brown for the ones loaded with copper and gray for the ones with cobalt.     

Judd−Ofelt Parameters via Bayesian Inference

Bayesian inference was used as a new approach to calculate of rare earth (RE) ion spectroscopic parameters within the Judd?Ofelt theory using the Li₂O-B₂O₃-Al₂O₃ glass system doped with Nd₂O₃ and TiO₂. This system was synthesized by the fusion method, and the physical properties of the as-synthesized material were investigated. Optical absorption, photoluminescence, micro-Raman, mass density, refractive index, and radiative lifetime calcuations were performed. We investigated the effects of crystal field changes on Nd³⁺-ions caused due to co-doping with increasing TiO₂ content. We observed that co-doping with TiO₂ altered the radiative transition rates A(J,J^′), favored symmetry enhancement around the Nd³⁺-ions, and promoted the onset of vibrational modes, contributed to the attenuation of O-H bonds, and substantially increased the spectroscopic quality, χ.     

Structural and magnetic properties of ZnO and Zn1−xMnxO nanocrystals

Chemical precipitation of metal-ions from aqueous solution has been successfully used to produce Zn_1?xMn_xO nanocrystals, in the form of nano-powder. X-ray diffraction (XRD) measurements reveal that the as-prepared samples are single-phase materials and their lattice constant changes with the variation of Mn-concentration, which indicates the incorporation of Mn²⁺ into the hosting ZnO. These findings are corroborated by the observation of the well defined six hyperfine lines of Mn²⁺ ion in the electron paramagnetic resonance (EPR) spectra of the samples with a low Mn-concentration, and of a broad EPR line, which manifests the onset of Mn–Mn exchange interaction, in the samples with an elevated value of x.     

Self-similarity of some soluble relatively free groups

In this paper, we prove that a free nilpotent group of finite rank is transitive self-similar. In contrast, we prove that a free metabelian group of rank \(r \ge 2\) is not transitive self-similar.