Let k be a positive integer and G be a k-connected graph. In 2009, Chartrand, Johns, McKeon, and Zhang introduced the rainbow k-connection number rc_k(G) of G. An edge-coloured path is rainbow if its edges have distinct colours. Then, rc_k(G) is the minimum number of colours required to colour the edges of G so that any two vertices of G are connected by k internally vertex-disjoint rainbow paths. The function rc_k(G) has since been studied by numerous researchers. An analogue of the function rc_k(G) involving vertex colourings, the rainbow vertex k-connection number rvc_k(G), was subsequently introduced. In this paper, we introduce a version which involves total colourings. A total-coloured path is total-rainbow if its edges and internal vertices have distinct colours. The total rainbow k-connection number of G, denoted by trc_k(G), is the minimum number of colours required to colour the edges and vertices of $G$, so that any two vertices of $G$ are connected by $k$ internally vertex-disjoint total-rainbow paths. We study the function trc_k(G) when G is a cycle, a wheel, and a complete multipartite graph. We also compare the functions rc_k(G), rvc_k(G), and trc_k(G), by considering how close and how far apart trc_k(G) can be from rc_k(G) and rvc_k(G).

A transparent Eu3 +-doped lithium aluminophosphate glass was prepared by melt-quenching technique. The thermal behavior of the glass was investigated by differential thermal analysis (DTA), the structure was studied by X-ray diffraction (XRD) and the morphology was observed by optical polarization microscopy and scanning electron microscopy (SEM). The activation energy of glass transition and the activation energy of crystallization and Avrami exponent have been evaluated under non-isothermal conditions from the data obtained by DTA at different heating rates. DTA curves exhibited an endothermic peak associated with the glass transition and two exothermic peaks. The mean value calculated for the activation energy of glass transition was 545 kJ mol- 1. The activation energy of crystallization was   400 kJ mol- 1 for the first exothermic peak and   170 kJ mol- 1 for the second peak. The Avrami exponent was   1 for both peaks indicating surface crystallization. XRD results showed that the main crystalline phase, aluminum metaphosphate, Al(PO3)3, and aluminum phosphate, AlPO4, were formed together with lithium barium phosphate, Li 3Ba(PO3)7, during the first exothermic peak and together with barium pyrophosphate, Ba2P2O7, during the second peak. Morphological study of heat-treated glass samples revealed microstructural features that confirmed a surface crystallization process. © 2014 Elsevier B.V.

The crystallization kinetics of a glass with a molar composition 40BaO-20ZnO-30B2O3-10SiO2 was investigated. The kinetic parameters, activation energy for crystallization (Ec) and Avrami exponent (n), were evaluated under non-isothermal conditions using the results obtained by differential thermal analysis (DTA) performed at different heating rates. DTA curves exhibited two overlapping exothermic peaks associated with the crystallization of the glass. Barium borate (BaB4O 7) was the first crystalline phase to be formed and it was followed by the formation of barium zinc silicate (BaZnSiO4), as identified by XRD. For the first exothermic peak, when the fraction of crystallization (χ) increased from 0.1 to 0.9, the local activation energy (E c(χ)) decreased from 700 to 500 kJ/mol, while for the second exothermic peak, Ec(χ) slightly increased from 490 to 570 kJ/mol. For the range of 0.1 < χ < 0.9, the local Avrami exponent (n(χ)) increased from ∼1 to 1.4 for the first exothermic peak and it decreased from ∼1.7 to 1.4 for the second exothermic peak. Observation by SEM of the microstructure of sintered glass samples revealed that crystallization started at the surface of glass particles, with growth of lamellar crystallites, that together with some quasi-spherical nano-sized crystallites progressed towards the inside of the glass at the highest sintering temperatures. The change of the local activation energy with the fraction of crystallization suggested that a multi-step kinetic reaction took place during sintering and crystallization of the glass. © 2013 Elsevier B.V. All rights reserved.

Two glass compositions were prepared from the system SiO2-Li2O-K2O-ZrO2-P2O5 with different SiO2/Li2O ratio (2.39 and 3.39) and the crystallization behavior was investigated by differential thermal analysis (DTA), X-ray diffraction (XRD) and scanning electron microscopy (SEM). The crystallization kinetic parameters (activation energy of crystallization and Avrami exponent) were evaluated by different methods from the data obtained by DTA performed at different heating rates. For both glasses, two exothermic peaks were observed in the DTA curves, and the crystallization peak temperatures increased with SiO2/Li2O ratio. XRD analysis revealed that the first peak corresponds to the crystallization of lithium metasilicate (Li2SiO3) and the second to the formation of lithium disilicate (Li2Si2O5). After heating the glasses at a temperature above the second crystallization peak (900 °C), both Li2Si2O5 and Li2SiO3 were found in samples having the lowest SiO2/Li2O ratio, whereas no Li2SiO3 was detected in samples with the highest SiO2/Li2O ratio. For both glasses, the value obtained by different methods for the activation energy of crystallization was in the range of 225-275 kJ mol-1 for the first exothermic peak and in the range of 425-500 kJ mol-1 for the second peak. The estimated Avrami exponent was close to 1 for the first exothermic peak, indicating surface crystallization, and close to 3 for the second exothermic peak, suggesting volume crystallization. This was confirmed by the morphological study made by SEM that showed needle-like crystals in the microstructure of samples with lithium metasilicate and granular crystals in the microstructure of samples having lithium disilicate. © 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Background Indoor air quality (IAQ) is considered an important determinant of human health. The association between exposure to volatile organic compounds, particulate matter, house dust mite, molds and bacteria in day care centers (DCC) is not completely clear. The aim of this project was to study these effects. Methods ? study design This study comprised two phases. Phase I included an evaluation of 45 DCCs (25 from Lisbon and 20 from Oporto, targeting 5161 children). In this phase, building characteristics, indoor CO2 and air temperature/relative humidity, were assessed. A children's respiratory health questionnaire derived from the ISAAC (International Study on Asthma and Allergies in Children) was also distributed. Phase II encompassed two evaluations and included 20 DCCs selected from phase I after a cluster analysis (11 from Lisbon and 9 from Oporto, targeting 2287 children). In this phase, data on ventilation, IAQ, thermal comfort parameters, respiratory and allergic health, airway inflammation biomarkers, respiratory virus infection patterns and parental and child stress were collected. Results In Phase I, building characteristics, occupant behavior and ventilation surrogates were collected from all DCCs. The response rate of the questionnaire was 61.7% (3186 children). Phase II included 1221 children. Association results between DCC characteristics, IAQ and health outcomes will be provided in order to support recommendations on IAQ and children's health. A building ventilation model will also be developed. Discussion This paper outlines methods that might be implemented by other investigators conducting studies on the association between respiratory health and indoor air quality at DCC.

The glass transition and crystallization kinetics of a glass with a molar composition 60BaO-30B2O3-10SiO2were investigated by differential scanning calorimetry (DSC) under non-isothermal conditions. DSC curves exhibited an endothermic peak associated with the glass transition and two partially overlapped exothermic peaks associated with the crystallization of the glass. The dependence of the glass transition temperature (Tg) and of the maximum crystallization temperature (Tp) on the heating rate was used to determine the activation energy associated with the glass transition (Eg), the activation energy for crystallization (Ec), and the Avrami exponent (n). X-ray diffraction (XRD) revealed that barium borate (β-BaB2O4) was the first crystalline phase to be formed followed by the formation of barium silicate (Ba5Si8O21). The variations of activation energy for crystallization and of Avrami exponent with the fraction of crystallization (χ) were also examined. When the crystallization fraction (χ) increased from 0.1 to 0.9, the value of local activation energy (Ec(χ)) decreased from 554 to 458 kJ/mol for the first exothermic peak and from 1104 to 831 kJ/mol for the second exothermic peak. The value determined for the Avrami exponent was near 2 indicating a similar one-dimensional crystallization mechanism for both crystalline phases. This was confirmed by the morphological studies performed by scanning electron microscopy (SEM) on glass samples heat-treated at the first and at the second crystallization temperatures. © 2014 AIP Publishing LLC.

The crystallization kinetics and phase transformation of a transparent Tb3+-doped lithium-aluminum phosphate glass, prepared by melt quenching, were investigated. The energy associated to the glass transition and the crystallization parameters (activation energy for crystallization and Avrami exponent) were evaluated by different methods using the experimental data obtained by differential thermal analysis performed at different heating rates. Using an isoconversional method to determine the change of the activation energy for crystallization with the fraction of crystallization, it was verified that with the increase in the fraction of crystallization from 0.1 to 0.9, the value of the activation energy decreased slightly from  370 to  310 kJ mol -1 and that the Avrami exponent varied from 0.8 to 1, suggesting a surface crystal growth mechanism. Observation of the microstructural evolution of heat-treated glass samples confirmed a surface crystallization process revealing spherulitic crystals constituted mainly by aluminum metaphosphate. © 2014 Springer Science+Business Media New York.