We consider an important class of nonsymmetric networks that lies between the class of general networks and the class of symmetric networks, where group theoretic methods still apply—namely, networks admitting “interior symmetries.” The main result of this paper is the full analogue of the equivariant Hopf theorem for networks with symmetries. We extend the result of Golubitsky, Pivato, and Stewart [Dyn. Syst., 19 (2004), pp. 389–407] to obtain states whose linearizations on certain subsets of cells, near bifurcation, are superpositions of synchronous states with states having spatio-temporal symmetries.

A proper bond between root canal filling materials and dentin surface is essential to resist dislodgement and guarantee long-term success. Blood exposure is likely to occur in various clinical situations in which calcium silicate-based materials are used; therefore, it is fundamental to render data concerning the influence of blood on bond strength. The present study aims to evaluate the effect of blood contamination on the push-out bond strength obtained with three different biomaterials to root canal dentin; Ninety extracted human mono-radicular permanent teeth were selected. The root canals were prepared with Gates Glidden burs until a diameter of 1.10 mm was achieved. Teeth were then randomly divided into six experimental groups (n = 15) according to the presence/absence of blood contamination and biomaterial used for root canal filling (ProRoot^® MTA, Biodentine^TM, and TotalFill^® BC Putty). After one week, each root was sectioned in three segments (coronal, middle, and apical regions). Specimens were then submitted to push-out bond strength tests. Fracture pattern evaluation was performed. The significance level was set at 5%.; Blood contamination did not affect the push-out bond strength of any of the three tested calcium silicate-based cements (p > 0.05). Regardless of blood contamination, TotalFill showed statistically higher push-out bond strength when compared with Biodentine (p = 0.040) and MTA (p = 0.004). Biodentine exhibited higher bond strength than MTA (p = 0.043). Biomaterials’ comparison within each radicular segment revealed statistically superior bond strength of both Biodentine and TotalFill over MTA (p < 0.05) in the coronal segment. TotalFill presented higher push-out bond strength regarding the apical segment compared to Biodentine (p = 0.003). Fractures were mostly adhesive.; Overall results indicate TotalFill presents the highest push-out bond strength values, followed by Biodentine and, lastly, MTA. Blood contamination did not affect the dislodgement resistance. Biomaterials’ comparison within each radicular segment revealed both TotalFill and Biodentine as the preferable alternatives for application in the coronal region. TotalFill might be the biomaterial of choice for placement in the apical region.

This article presents a research study addressing the development, implementation, evaluation, and use of Interactive Modules for Online Training (MITO) of mathematics in higher education. This work was carried out in the context of the MITO project, which combined several features of the learning and management system Moodle, the computer-aided assessment for mathematics STACK, the mathematical software GeoGebra, several packages from the type-setting program LaTeX, and tutorial videos. A total of 1,962 students participated in this study. Two groups of students taking a calculus course were selected for a deeper analysis. With regard to usability and functionality, the results indicate that MITO scored well in almost all aspects, which is fundamental for their introduction into formal university courses. The analysis of the data reveals that the use of MITO educational contents by students mainly occurs about 1 week and a half prior to the evaluations. Moreover, there is a strong correlation between the results of online assessments on MITO in a continuous assessment model and the final grade on the course.

We consider the standard action of the dihedral group Dn of order 2n on C. This representation is absolutely irreducible and so the corresponding Hopf bifurcation oc- curs on C C. Golubitsky and Stewart (Hopf bifurcation with dihedral group sym- metry: Coupled nonlinear oscillators. In: Multiparameter Bifurcation Series, M. Gol- ubitsky and J. Guckenheimer, eds., Contemporary Mathematics 46, Am. Math. Soc., Providence, R.I.1986, 131{173) and van Gils and Valkering (Hopf bifurcation and sym- metry: standing and travelling waves in a circular chain. Japan J. Appl. Math. 3, 207-222, 1986) prove the generic existence of three branches of periodic solutions, up to conjugacy, in systems of ordinary dieren tial equations with Dn-symmetry, depend- ing on one real parameter, that present Hopf bifurcation. These solutions are found by using the Equivariant Hopf Theorem. We prove that generically, when n 6= 4 and assuming Birkho normal form, these are the only branches of periodic solutions that bifurcate from the trivial solution. AMS classication scheme numbers: 37G40 34C23 34C25