The automorphism group of a free-by-cyclic group in rank 2

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Maximal compactness, min- imal Hausdor ness and reversibility of frames and a study on automorphism group of frames

One can do research in pointfree topology in two ways. The rst is the contravariant way where research is done in the category Frm but the ultimate objective is to obtain results in Loc. The other way is the covariant way to carry out research in the category Loc itself directly. According to Johnstone [23], \frame theory is lattice theory applied to topology whereas locale theory is topology itself". The most part of this thesis is written according to the rst view. In this thesis, we make an attempt to study about 1. the frame counterparts of maximal compactness, minimal Hausdor - ness and reversibility, 2. the automorphism groups of a nite frame and its relation with the subgroups of the permutation group on the generator set of the frame

On the Closure of the Tame Automorphism Group of Affine Three-Space

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.

On the automorphism group of a reduced automaton /

"Supported in part jointly by the Atomic Energy Commission and the Advanced Research Projects Agency under AEC Contract AT(11-1)-1018."

The automorphism group of a strongly connected automaton and its quotient automata /

"February 14, 1966."

The Automorphism Group of the Free Algebra of Rank Two

The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group of linear automorphisms.

New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10

∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995.

Novel techniques for automorphism group computation

Graph automorphism (GA) is a classical problem, in which the objective is to compute the automorphism group of an input graph. In this work we propose four novel techniques to speed up algorithms that solve the GA problem by exploring a search tree. They increase the performance of the algorithm by allowing to reduce the depth of the search tree, and by effectively pruning it. We formally prove that a GA algorithm that uses these techniques correctly computes the automorphism group of the input graph. We also describe how the techniques have been incorporated into the GA algorithm conauto, as conauto-2.03, with at most an additive polynomial increase in its asymptotic time complexity. We have experimentally evaluated the impact of each of the above techniques with several graph families. We have observed that each of the techniques by itself significantly reduces the number of processed nodes of the search tree in some subset of graphs, which justifies the use of each of them. Then, when they are applied together, their effect is combined, leading to reductions in the number of processed nodes in most graphs. This is also reflected in a reduction of the running time, which is substantial in some graph families.

Risk factors for dental erosion in a group of 12- and 16-year-old Brazilian schoolchildren

Background. Dental erosion is a multifactorial disease and is associated with dietary habits in infancy and adolescence. Aim. To investigate possible associations among dental erosion and diet, medical history and lifestyle habits in Brazilian schoolchildren. Design. The sample consisted of a random single centre cluster of 414 adolescents (12- and 16-years old) of both genders from private and public schools in Bauru (Brazil). The O`Brien [Children`s Dental Health in the United Kingdom, 1993 (1994) HMSO, London] index was used for dental erosion assessment. Data on medical history, rate and frequency of food and drinks consumption, and lifestyle habits were collected by a self-reported questionnaire. Odds ratios with 95% confidence intervals were used to assess the univariate relationships between variables. Analysis of questionnaire items was performed by multiple logistic regression analysis. The statistical significance level was set at 5%. Results. The erosion present group comprised 83 subjects and the erosion absent group 331. There were no statistically significant correlations among dental erosion and the consumption of food and drinks, medical history, or lifestyle habits. Conclusion. The results indicate that there was no correlation between dental erosion and the risk factors analysed among adolescents in Bauru/Brazil and further investigations are necessary to clarify the multifactorial etiology of this condition.

The Effect of Framework Design on Fracture Resistance of Metal-Ceramic Implant-Supported Single Crowns

This study evaluated the effect of framework design on the fracture resistance of metal-ceramic implant-supported crowns. Screw-retained molar crowns with a screw access hole composed of metal or porcelain were compared to a cement-retained crown (control). For each group (n = 10), five crowns were subjected to dynamic loading (1,200,000 x 100 N x 2 Hz at 37 degrees C). Afterward, all specimens were loaded to failure using a universal testing machine. Significant differences could be established between the cement-and screw-retained groups (P <= .05), but no difference was found between the screw-retained groups and the specimens subjected to dynamic loading. Occlusal discontinuity of screw-retained crowns affects their resistance, and the metallic support on the screw access hole did not reinforce the crowns. Int J Prosthodont 2010;23:350-352.

Effect of framework design on crown failure

This study evaluated the effect of core-design modification on the characteristic strength and failure modes of glass-infiltrated alumina (In-Ceram) (ICA) compared with porcelain fused to metal (PFM). Premolar crowns of a standard design (PFMs and ICAs) or with a modified framework design (PFMm and ICAm) were fabricated, cemented on dies, and loaded until failure. The crowns were loaded at 0.5 mm min(-1) using a 6.25 mm tungsten-carbide ball at the central fossa. Fracture load values were recorded and fracture analysis of representative samples were evaluated using scanning electron microscopy. Probability Weibull curves with two-sided 90% confidence limits were calculated for each group and a contour plot of the characteristic strength was obtained. Design modification showed an increase in the characteristic strength of the PFMm and ICAm groups, with PFM groups showing higher characteristic strength than ICA groups. The PFMm group showed the highest characteristic strength among all groups. Fracture modes of PFMs and of PFMm frequently reached the core interface at the lingual cusp, whereas ICA exhibited bulk fracture through the alumina core. Core-design modification significantly improved the characteristic strength for PFM and for ICA. The PFM groups demonstrated higher characteristic strength than both ICA groups combined.

Relationship of high energy expenditure and variation in dietary intake with reporting accuracy on 7 day food records and diet histories in a group of healthy adult volunteers

Objectives: To assess the accuracy of reporting from both a diet history and food record and identify some of the characteristics of more accurate reporters in a group of healthy adult volunteers for an energy balance study. Design: Prospective measurements in free-living people. Setting: Wollongong, Australia. Subjects: Fifteen healthy volunteers (seven male, eight female; aged 22 -59 y; body mass index (BMI) 19 - 33 kg/m(2)) from the local community in the city of Wollongong, Australia. Interventions: Measurement of energy intake via diet history interview and 7 day food records, total energy expenditure by the doubly labelled water technique over 14 days, physical activity by questionnaire, and body fat by dual-energy X-ray absorptiometry. Results: Increased misreporting of energy intake was associated with increased energy expenditure (r = 0.90, P < 0.0001, diet history; r(s)=0.79, P=0.0005, food records) but was not associated with age, sex, BMI or body fat. Range in number of recorded dinner foods correlated positively with energy expenditure (r(s)=0.63, P=0.01) and degree of misreporting (r(s)=0.71, P=0.003, diet history; r(s)=0.63, P=0.01, food records). Variation in energy intake at dinner and over the whole day identified by the food records correlated positively with energy expenditure (r=0.58, P = 0.02) and misreporting on the diet history (r=0.62, P=0.01). Conclusions: Subjects who are highly active or who have variable dietary and exercise behaviour may be less accurate in reporting dietary intake. Our findings indicate that it may be necessary to screen for these characteristics in studies where accuracy of reporting at an individual level is critical. Sponsorship: The study was supported in part by Australian Research Council funds made available through the University of Wollongong.

The influence of experience and training in a group of novice observers: a jackknife alternative free-response receiver operating characteristic analysis

Purpose - The study evaluates the pre- and post-training lesion localisation ability of a group of novice observers. Parallels are drawn with the performance of inexperienced radiographers taking part in preliminary clinical evaluation (PCE) and ‘red-dot’ systems, operating within radiography practice. Materials and methods - Thirty-four novice observers searched 92 images for simulated lesions. Pre-training and post-training evaluations were completed following the free-response the receiver operating characteristic (FROC) method. Training consisted of observer performance methodology, the characteristics of the simulated lesions and information on lesion frequency. Jackknife alternative FROC (JAFROC) and highest rating inferred ROC analyses were performed to evaluate performance difference on lesion-based and case-based decisions. The significance level of the test was set at 0.05 to control the probability of Type I error. Results - JAFROC analysis (F(3,33) = 26.34, p < 0.0001) and highest-rating inferred ROC analysis (F(3,33) = 10.65, p = 0.0026) revealed a statistically significant difference in lesion detection performance. The JAFROC figure-of-merit was 0.563 (95% CI 0.512,0.614) pre-training and 0.677 (95% CI 0.639,0.715) post-training. Highest rating inferred ROC figure-of-merit was 0.728 (95% CI 0.701,0.755) pre-training and 0.772 (95% CI 0.750,0.793) post-training. Conclusions - This study has demonstrated that novice observer performance can improve significantly. This study design may have relevance in the assessment of inexperienced radiographers taking part in PCE or commenting scheme for trauma.