Turán numbers for odd wheels

The Turán number $\text{ex}(n,G)$ is the maximum number of edges in any $n$-vertex graph that does not contain a subgraph isomorphic to $G$. A wheel$W_n$ is a graph on $n$ vertices obtained from a $C_{n?1}$ by adding one vertex $w$ and making $w$ adjacent to all vertices of the $C_{n?1}$. We obtain two exact values for small wheels:

$\text{ex}(n,W_5)=?\frac{n^2}{4}+\frac{n}{2}?,$

$\text{ex}(n,W_7)=?\frac{n^2}{4}+\frac{n}{2}+1?.$

Given that $\text{ex}(n,W_6)$ is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound $\text{ex}(n,W_{2k+1})>?\frac{n^2}{4}?+?\frac{n}{2}?$ in general case.     

Probing interactions in exploratory teaching: a case study

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students’ competence in justifying an ellipse. We analyse the complex interactions between student, content, and teacher, and discuss explicit pedagogical strategies that help students develop a higher level of geometric reasoning. The findings indicate that students engaged in guided explorations by the teacher and in group discussions with peers were able to identify an ellipse and justify their reasoning.     

Comparative validation of amisulpride determination in pharmaceuticals by several chromatographic, electrophoretic and spectrophotometric methods

Depleted uranium (DU) is a by-product of the uranium enrichment process for nuclear fuel. According to the Commission Decision 2002/657/EC, a confirmatory method for the quantification of DU in freeze-dried fish was developed by isotope ratio dynamic reaction cell inductively coupled plasma-mass spectrometry (IR-DRC-ICP-MS). A preliminary study was performed to determine the following parameters: instrumental detection limit (IDL), isotopic ratio measurement limit (IRML), percentage of DU (P(DU)) in presence of natural uranium (NU) and limit of quantification (LoQ(DU)). The analyses were carried out by means of IR-DRC-ICP-MS. Ammonia was the reaction gas used for the dynamic reaction cell. In addition, a sector field inductively coupled plasma mass spectrometer (SF-ICP-MS) was employed to calculate the within-laboratory reproducibility. For the confirmatory method the following parameters were determined: (a) trueness; (b) precision; (c) critical concentrations alpha and beta (CC(alpha), CC(beta)); (d) specificity; (e) stability. Trueness was assessed by using the recovery tests. The recovery and within-laboratory reproducibility were determined by fortifying the blank digested solution of dogfish tissue: six aliquots were fortified at 1, 1.5 and 2 times the LOQ(DU) with 25.0, 37.5 and 50.0 ng L(-1) or 4.16, 6.24, 8.32 microg kg(-1) with a recovery of -8.2, +9.5 and +9.6%, respectively and a within-laboratory reproducibility (three analytical run) of 15.5, 8.0 and 11.0%, respectively. The results for the decision limit and the detection capability were: CC(alpha) = 11.69 ng L(-1) and CC(beta) = 19.8 ng L(-1). The digested solutions resulted to be stable during testing time (60 days) and the method can be considered highly specific as well.     

A structural investigation of the alkali metal site distribution within bioactive glass using neutron diffraction and multinuclear solid state NMR

The atomic-scale structure of Bioglass and the effect of substituting lithium for sodium within these glasses have been investigated using neutron diffraction and solid state magic angle spinning (MAS) NMR. Applying an effective isomorphic substitution difference function to the neutron diffraction data has enabled the Na-O and Li-O nearest-neighbour correlations to be isolated from the overlapping Ca-O, O-(P)-O and O-(Si)-O correlations. These results reveal that Na and Li behave in a similar manner within the glassy matrix and do not disrupt the short range order of the network former. Residual differences are attributed solely to the variation in ionic radius between the two species. Successful simplification of the 2 < r (?) < 3 region via the difference method has enabled all the nearest neighbour correlations to be deconvolved. The diffraction data provides the first direct experimental evidence of split Na-O nearest-neighbour correlations in these melt quench bioactive glasses, and an analogous splitting of the Li-O correlations. The observed correlations are attributed to the metal ions bonded either to bridging or to non-bridging oxygen atoms. (23)Na triple quantum MAS (3QMAS) NMR data corroborates the split Na-O correlations. The structural sites present will be intimately related to the release properties of the glass system in physiological fluids such as plasma and saliva, and hence to the bioactivity of the material. Detailed structural knowledge is therefore a prerequisite for optimizing material design.     

Evidence for an Iminium Cation Intermediate and its Non-Oxidative Decarboxylation in a Cerium (IV)-Mediated Oxidative Decarboxylation. Preliminary communication

Evidence is provided for the occurrence of a non-oxidative decarboxylation in an iminium cation intermediate which is produced in an oxidative decarboxylation induced by cerium (IV).     

Thermally stable silarylene-1,3,4-oxadiazole polymers

The effects of incorporating a p-phenylene- (or m-phenylene)-1,3,4-oxadiazole fragment into the backbone of poly[1,4-phenylene(diphenylsilyl)-1,4-phenylene-2,5-(1,3,4-oxadiazole)], which was developed by the authors, was investigated. Bis[(p-carbohydrazidophenyl)]diphenylsilane was copolymerized with dipentachlorophenyl terephthalate or isophthalate to produce the prepolymers poly[N-(p-diphenylsilylbenzoyl)-N′N″-(terephthaloyl)-N″′-(p-benzoyl)dihydrazide] and poly[N-(p-diphenylsilylbenzoyl)-N′,-N″-(isophthaloyl)-N″′-p-(benzoyl) dihydrazide], respectively. The polyhydrazides were converted by thermal dehydration into poly[1,4-phenylene(diphenylsilyl)-1,4-phenylene-(1,3,4-oxadiazole-2,5-diyl)-1,4-phenylene-2,5-(1,3,4-oxadiazole)] and poly[1,4-phenyl-ene(diphenylsilyl)-1,4-phenylene-(1,3,4-oxadiazole-2,5-diyl)-1,3,4-(oxadiazole)]. The new polymers were soluble in organic solvents. Films cast from these solutions exhibited good adhesion to glass and metal surfaces. Thermal analysis showed that the heat stability of all these polymers was about the same and that they were resistant to decomposition when heated in air to about 400°C. The results also indicated that these polymers were somewhat less heat-resistant than samples of poly-[1,4-phenylene(diphenylsilyl)-1,4-phenylene-2,5-]1,3,4-(oxadiazole) synthesized from bis(p-carbohydrazidophenyl)diphenylsilane and bis-(p-carbopentachlorophenoxy-phenyl)diphenylsilane.     

MiniMax: What has been learned thus far

Summary A small experiment, ?MiniMax?, has been set up in the C0 intersection region of the Fermilab Tevatron to seek evidence for disoriented chiral condensates and to study other forward physics phenomena. The experiment consists of a proportional wire chamber telescope accompanied by scintillation (trigger) counters, a lead converter, and followed by an electromagnetic calorimeter. The solid angle accepted is a cone centered at pseudorapidity (η) of 4.1 and of radius (in η-ϕ space) of about 0.6. Over 2.5 million events thus far have demonstrated the successful operation of the apparatus, however to date the analysis has not progressed sufficiently to permit any conclusions concerning disoriented chiral condensates. presented byL. W. Jones Paper presented at the Special Session on very high-energy cosmic-ray interactions (superfamilies) of the XXIV International Cosmic-Ray Conference, Rome, August 28–September 8, 1995.     

13C NMR study of alcohols complexed with nitroxide radical

The contact shifts of carbon nuclei in 8 alcohols complexed with 2,2,6,6-tetramethylpiperidine nitroxide radical were determined from the ¹³C NMR spectra and explained by hydrogen bonding and collision interactions.     

A prism reflector of anti-resonant ring configuration

Two identical prisms are combined to form an anti-resonant ring reflector, giving total reflection without the use of coatings or roof edges. When used as the total reflector in a Q-switched NdYAG laser this device has shown a damage threshold twice that of a multilayer reflector.