Common multiples of complete graphs

A graph H is said to divide a graph G if there exists a set S of subgraphs of G, all isomorphic to H, such that the edge set of G is partitioned by the edge sets of the subgraphs in S. Thus, a graph G is a common multiple of two graphs if each of the two graphs divides G.

Maximal sets of Hamilton cycles in Kn,n

In this article, we prove that there exists a maximal set of m Hamilton cycles in K-n,K-n if and only if n/4 < m less than or equal to n/2. (C) 2000 John Wiley & Sons, Inc.

Reference distribution of the bioelectrical impedance vector in healthy term newborns

Bioelectrical impedance vector analysis (BIVA) is a new method that is used for the routine monitoring of the variation in body fluids and nutritional status with assumptions regarding body composition values. The aim of the present study was to determine bivariate tolerance intervals of the whole-body impedance vector and to describe phase angle (PA) values for healthy term newborns aged 7-28 d. This descriptive cross-sectional study was conducted on healthy term neonates born at a low-risk public maternity. General and anthropometric neonatal data and bioelectrical impedance data (800 mu A-50 kHz) were obtained. Bivariate vector analysis was conducted with the resistance-reactance (RXc) graph method. The BIVA software was used to construct the graphs. The study was conducted on 109 neonates (52.3% females) who were born at term, adequate for gestational age, exclusively breast-fed and aged 13 (SD 3.6) d. We constructed one standard, reference, RXc-score graph and RXc-tolerance ellipses (50, 75 and 95 %) that can be used with any analyser. Mean PA was 3.14 (SD 0.43)degrees (3.12 (SD 0.39)degrees for males and 3.17 (SD 0.48)degrees for females). Considering the overlapping of ellipses of males and females with the general distribution, a graph for newborns aged 7-28 d with the same reference tolerance ellipse was defined for boys and girls. The results differ from those reported in the literature probably, in part, due to the ethnic differences in body composition. BIVA and PA permit an assessment without the need to know body weight and the prediction error of conventional impedance formulas.

Cephalometric evaluation in different phases of Jasper jumper therapy

Introduction: The aim of this study was to evaluate the dentoskeletal and soft-tissue effects of Class II malocclusion treatment with the Jasper jumper followed by Class II elastics at the different stages of therapy. Methods: The sample comprised 24 patients of both sexes (11 boys, 13 girls) with an initial age of 12.58 years, treated for a mean period of 2.15 years. Four lateral cephalograms were obtained of each patient in these stages of orthodontic treatment: at pretreatment (T1), after leveling and alignment (T2), after the use of the Jasper jumper appliance and before the use of Class II intermaxillary elastics (T3), and at posttreatment (T4). Thus, 3 treatment phases could be evaluated: leveling and alignment (T1-T2), use of the Jasper jumper (T2-T3), and use of Class II elastics (T3-T4). Dependent analysis of variance (ANOVA) and Tukey tests were used to compare the durations of the 3 treatment phases and for intragroup comparisons of the 4 treatment stages. Results: The alignment phase showed correction of the anteroposterior relationship, protrusion and labial inclination of the maxillary incisors, and reduction of overbite. The Jasper jumper phase demonstrated labial inclination, protrusion and intrusion of the mandibular incisors, mesialization and extrusion of the mandibular molars, reduction of overjet and overbite, molar relationship improvement, and reduction in facial convexity. The Class II elastics phase showed labial inclination of the maxillary incisors; retrusion, uprighting, and extrusion of the mandibular incisors; and overjet and overbite increases. Conclusions: The greatest amount of the Class II malocclusion anteroposterior discrepancy was corrected with the Jasper jumper appliance. Part of the correction was lost during Class II intermaxillary elastics use after use of the Jasper jumper appliance. (Am J Orthod Dentofacial Orthop 2011;140:e77-e84)

Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.

Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.

Strongly regular graphs from differences of quadrics

In this note strongly regular graphs with new parameters are constructed using nested "blown up" quadrics in projective spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

Variation in articulatory timing of three English consonants: An electropalatographic investigation

Increasingly, electropalatography (EPG) is being used in speech pathology research to identify and describe speech disorders of neurological origin. However, limited data currently exists that describes normal articulatory segment timing and the degree of variability exhibited by normal speakers when assessed with EPG. Therefore, the purpose of the current investigation was to use the Reading EPG3 system to quantify segmental timing values and examine articulatory timing variability for three English consonants. Ten normal subjects repeated ten repetitions of CV words containing the target consonants /t/, /l/, and /s/ while wearing an artificial palate. The target consonants were followed by the /i/ vowel and were contained in the carrier phrase 'I saw a __'. Mean duration of the approach, closure/constriction, and release phases of consonant articulation were calculated. In addition, inter-subject articulatory timing variability was investigated using descriptive graphs and intra-subject articulatory timing variability was investigated using a coefficient of variation. Results revealed the existence of intersubject variability for mean segment timing values. This could be attributed to individual differences in the suprasegmental features of speech and individual differences in oral cavity size and structure. No significant differences were reported for degree of intra-subject variability between the three sounds for these same phases of articulation. However, when this data set was collapsed, results revealed that the closure/constriction phase of consonant articulation exhibited significantly less intra-subject variability than both the approach and release phases. The stabilization of the tongue against the fixed structure of the hard palate during the closure phase of articulation may have reduced the levels of intra-subject variability.

The importance of quality in the consolidation of textile in Minho

The textile industry has a long tradition in Portugal and it is one of the most important sectors, despite the current economic crisis. It has always assumed a prominent role in terms of employment and a relevant position within the Portuguese economy. The lack of quality and the lower prices that other countries offer causes the loss of clients. Quality is a main tool to survive nowadays in the textile sector. To undertake our analysis, we made use of an existing database where 55 firms belonged to the textile industry, namely to the manufacturing sector. A new survey was created based on the original survey and was sent to 5 firms. Besides the survey, we also sent a few questions to the firms in order to retract more information about the actually situation in our country, concerning the textile industry. Several tables, graphs and pie charts were made to help shed light on our findings. This research was conducted in order to determine the importance of quality in the consolidation of textile firms in the north of Portugal. Most firms in our sample feel that quality improvement, business benefits, mobilizing employees’ knowledge and business image were important and that competition is very intense and is mainly by price and not by differentiation of product or service. The quality program has contributed to improve their competitive position and the improvement of their overall performance. The majority of the firms in our sample undertake TQM measures for quality purposes to meet customer expectations and prevent errors. Of all firms surveyed, the quality is certainly very important for its survival.

Open-source software in operations research in engineering teaching

ENEGI 2013: Atas do 2º Encontro Nacional de Engenharia e Gestão Industrial, Universidade de Aveiro, 17 e 18 de maio de 2013, Aveiro, Portugal.

Difficulties in the Learning of Statistics by the Students of the Primary Education

The present study, covering students from public schools and a private school on the island of São Miguel (Azores, Portugal), aims to meet the difficulties of the students of the 3rd and 4th years of the primary education in solving tasks involving construction, reading and interpreting tables and statistical graphs, in the context of Organization and Data Handling (ODH). We present the main results obtained from statistical methods, among which we highlight some non-parametric hypothesis tests and the Categorical Principal Component Analysis (CatPCA), given the nature of the variables included in the questionnaire (mostly nominal and ordinal variables).

Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

Periodic paths on nonautonomous graphs

We define nonautonomous graphs as a class of dynamic graphs in discrete time whose time-dependence consists in connecting or disconnecting edges. We study periodic paths in these graphs, and the associated zeta functions. Based on the analytic properties of these zeta functions we obtain explicit formulae for the number of n-periodic paths, as the sum of the nth powers of some specific algebraic numbers.

Behaviour and fate of metals in urban wastewater treatment plants: a review

The concerns on metals in urban wastewater treatment plants (WWTPs) are mainly related to its contents in discharges to environment, namely in the final effluent and in the sludge produced. In the near future, more restrictive limits will be imposed to final effluents, due to the recent guidelines of the European Water Framework Directive (EUWFD). Concerning the sludge, at least seven metals (Cd, Cr, Cu, Hg, Ni, Pb and Zn) have been regulated in different countries, four of which were classified by EUWFD as priority substances and two of which were also classified as hazardous substances. Although WWTPs are not designed to remove metals, the study of metals behaviour in these systems is a crucial issue to develop predictive models that can help more effectively the regulation of pre-treatment requirements and contribute to optimize the systems to get more acceptable metal concentrations in its discharges. Relevant data have been published in the literature in recent decades concerning the occurrence/fate/behaviour of metals in WWTPs. However, the information is dispersed and not standardized in terms of parameters for comparing results. This work provides a critical review on this issue through a careful systematization, in tables and graphs, of the results reported in the literature, which allows its comparison and so its analysis, in order to conclude about the state of the art in this field. A summary of the main consensus, divergences and constraints found, as well as some recommendations, is presented as conclusions, aiming to contribute to a more concerted action of future research. © 2015, Islamic Azad University (IAU).

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.