Effects of contemporary orthodontic composites on tooth color following short-term fixed orthodontic treatment: A controlled clinical study

Background/aim: To determine the color alterations of natural teeth associated with different orthodontic composites used in comprehensive short-term treatment. Materials and methods: Twenty-two patients were treated with fixed appliances and 22 untreated subjects were also evaluated. Lower incisors were bonded with different orthodontic composites: 42 with Grengloo, 41 with Light Bond, 31 with Kurasper F, and 32 with Transbond XT. The color parameters of the Commission Internationale de l’Eclairage (CIE) were measured for each tooth with a spectrophotometer. Color assessment in relation to time, adhesive material, and their interaction was made with 2-way mixed analysis of variance (ANOVA) and 1-way ANOVA for the color differences (ΔE*). Further analyses were done using Tukey’s honestly significant difference tests and paired-samples t-tests. Results: The color of teeth was affected by treatment. The mean L* and a* values increased, whereas the mean b* values decreased. Total color differences of teeth demonstrated visible color changes clinically after treatment, ranging from 1.12 to 3.34 ΔE units. However, there were no significant differences for color of enamel. Conclusion: Teeth may be discolored with fixed appliances during treatment. Moreover, contemporary orthodontic composites have similar effects of enamel discoloration. © TÜBİTAK

On a Perceived Expressive Inadequacy of Principia Mathematica

This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and Principia Mathematica

An axiomatic approach to the measurement of envy

We characterize a class of envy-as-inequity measures. There are three key axioms. Decomposability requires that overall envy is the sum of the envy within and between subgroups. The other two axioms deal with the two-individual setting and specify how the envy measure should react to simple changes in the individuals’ commodity bundles. The characterized class measures how much one individual envies another individual by the relative utility difference (using the envious’ utility function) between the bundle of the envied and the bundle of the envious, where the utility function that must be used to represent the ordinal preferences is the ‘ray’ utility function. The class measures overall envy by the sum of these (transformed) relative utility differences. We discuss our results in the light of previous contributions to envy measurement and multidimensional inequality measurement

On the computation of finite bottom-quark mass effects in Higgs boson production

We present analytic results for the partonic cross-sections contributing to the top-bottom interference in Higgs production via gluon fusion at hadron colliders at NLO accuracy in QCD. We develop a method of expansion in small bottom-mass for master integrals and combine it with the usual infinite top-mass effective theory. Our method of expansion admits a simple algorithmic description and can be easily generalized to any small parameter. These results for the integrated cross-sections will be needed in the computation of the renormalization counter-terms entering the computation of finite bottom-quark mass effects at NNLO.Comment: Updated affiliations and abstract, added reference, and corrected minor typo