Counting flags in triangle-free digraphs

Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle. This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in Combinatoric

A scanning electron microscopic study of hypercementosis

The purpose of this study was to evaluate morphological characteristics of teeth with hypercementosis that are relevant to endodontic practice. Twenty-eight extracted teeth with hypercementosis had their root apexes analyzed by scanning electron microscopy (SEM). The teeth were divided according to tooth groups and type of hypercementosis. The following aspects were examined under SEM: the contour and regularity of the root surface; presence of resorption; presence and number of apical foramina, and the diameter of the main foramen. The progression of club shape hypercementosis was directly associated with the presence of foramina and apical foramen obstruction. Cases of focal hypercementosis presented foramina on the surface, even when sidelong located in the root. Circular cementum hyperplasia form was present in 2 out of 3 residual roots, which was the highest proportion among the tooth types. The detection of a large number of foramina in the apical third of teeth with hypercementosis or even the possible existence of apical foramen obliteration contributes to understand the difficulties faced during endodontic treatment of these cases

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Effect of cooling methods on dimensional accuracy and surface finish of a turned titanium part

In metal cutting, the choice of cooling method influences the deformation mechanism, which is related to the dimensional accuracy and surface finish of the parts. The deformation mechanism of titanium alloys under machining conditions is known to be very different from that of commonly used industrial materials. Therefore, the effect of cooling methods on dimensional accuracy and surface finish in machining titanium is of particular interest. This paper investigates experimentally and analytically the influence of cooling method and cutting parameters on two major dimensional accuracy characteristics of a turned titanium part—diameter error and circularity, and surface finish. Data were analyzed via three methods: traditional analysis, Pareto ANOVA, and Taguchi method. The findings indicate that the cooling method has significant effect on circularity error (contribution ratio 76.75 %), moderate effect on diameter error (contribution ratio 25.00 %), and negligible effect on surface finish (contribution ratio 0.16 %)

Age-Related Adaptation of Bone-PDL-Tooth Complex: Rattus-Norvegicus as a Model System

Functional loads on an organ induce tissue adaptations by converting mechanical energy into chemical energy at a cell-level. The transducing capacity of cells alters physico-chemical properties of tissues, developing a positive feedback commonly recognized as the form-function relationship. In this study, organ and tissue adaptations were mapped in the bone-tooth complex by identifying and correlating biomolecular expressions to physico-chemical properties in rats from 1.5 to 15 months. However, future research using hard and soft chow over relevant age groups would decouple the function related effects from aging affects. Progressive curvature in the distal root with increased root resorption was observed using micro X-ray computed tomography. Resorption was correlated to the increased activity of multinucleated osteoclasts on the distal side of the molars until 6 months using tartrate resistant acid phosphatase (TRAP). Interestingly, mononucleated TRAP positive cells within PDL vasculature were observed in older rats. Higher levels of glycosaminoglycans were identified at PDL-bone and PDL-cementum entheses using alcian blue stain. Decreasing biochemical gradients from coronal to apical zones, specifically biomolecules that can induce osteogenic (biglycan) and fibrogenic (fibromodulin, decorin) phenotypes, and PDL-specific negative regulator of mineralization (asporin) were observed using immunohistochemistry. Heterogeneous distribution of Ca and P in alveolar bone, and relatively lower contents at the entheses, were observed using energy dispersive X-ray analysis. No correlation between age and microhardness of alveolar bone (0.7±0.1 to 0.9±0.2 GPa) and cementum (0.6±0.1 to 0.8±0.3 GPa) was observed using a microindenter. However, hardness of cementum and alveolar bone at any given age were significantly different (P<0.05). These observations should be taken into account as baseline parameters, during development (1.5 to 4 months), growth (4 to 10 months), followed by a senescent phase (10 to 15 months), from which deviations due to experimentally induced perturbations can be effectively investigated

Numerical Modelling and Measurements of Temperature for Tests of Structural Transformations in Steels under Welding Conditions

This paper presents the way in which temperature is measured in tests concerning structural transformations in various types of steel under welding conditions. In the test methodology, a small-sized steel specimen was subjected to simulated welding thermal cycles, during which the temperature of the specimen, changes in magnetic permeability and thermal expansion were measured simultaneously. The measurements of those parameters required the non-contact heating of the specimen, which involved the use of heating lamps. The temperature measurement was of key importance because the subsequent analysis of the remaining parameters was performed in the function of temperature. The tests of structural transformations resulted in the development of Continuous Cooling Transformation under welding conditions (CCT) diagrams, enabling the determination of steel weldability and constituting the source of information needed to determine the effect of welding thermal cycles on the structure and properties of the material subjected to the tests. Related numerical models to be used as the basis for the analysis of temperature distribution in the test specimen have been developed. These tests involved the analysis of the values and the distribution of temperature in relation to various model parameters, i.e. thermocouple types, geometrical features of a thermocouple junction and the diameter of thermocouple wires. The results of FEM calculations have been compared to the experiments