Several authors (e.g. Dehaene, 1997) have proposed that mathematical concepts build upon an evolved innate number sense, which we share with many other species. However, they have left unspecified how these mathematical concepts can come into existence and how they are transmitted. Models of content biased cultural transmission (e.g. Boyer, 2001) predict that cultural traits that bear a close f...

A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. For hypersingular integral equations in 2D with positive-order Sobolev space, we analyze the mathematical relation between the h − h/2error estimator from [18], the two-level error estimator from [22], and the averaging error estimator from [7]. All of these a posteriori error e...

A detailed mathematical model for the fission yeast mitotic cycle is developed based on positive and negative feedback loops by which Cdc13/Cdc2 kinase activates and inactivates itself. Positive feedbacks are created by Cdc13/Cdc2-dependent phosphorylation of specific substrates: inactivating its negative regulators (Rum1, Ste9 and Wee1/Mik1) and activating its positive regulator (Cdc25). A slo...

Children’s understanding of mathematical language has been put forward as an important correlate their abilities. To date, no study disentangled the precise roles different types language, such quantitative (e.g., more) or spatial above) in preschool children. The existing studies have limited assessment mathematics to children’s numerical competencies, but they did not consider broader aspects...

A mathematical problem arising in the modelling of travelling waves in self-focusing waveguides is studied. It involves a nonlinear Schrödinger equation in R. In the paraxial approximation, the travelling waves are interpreted as standing waves of the NLS. Local and global bifurcation results are established for the corresponding “stationary” equation. The combination of variational arguments w...

Co-teachers in a ninth-grade algebra 1 class offered instruction that integrates mathematical learning with social and emotional during hybrid (online face-to-face) meetings, promoting healing positive identity development among students.

We outline a new approach to the characterization as well as to the classification of positive maps. This approach is based on the facial structures of the set of states and of the cone of positive maps. In particular, the equivalence between Schroedinger’s and Heisenberg’s pictures is reviewed in this more general setting. Furthermore, we discuss in detail the structure of positive maps for tw...

This study aims to determine the mathematical critical thinking skills of class XII IPA 1 students at SMAN 5 Sidrap in solving problems arithmetic sequences and series. The type research used is descriptive with a qualitative approach. In this study, there were 3 subjects, namely high, medium low abilities. instruments data collection observation sheets, written tests interview guidelines. resu...