Locally conformal symplectic nilmanifolds with no locally conformal K\"ahler metrics

We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal K\"ahler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.Comment: 7 pages, no figures. Comments are welcome

Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations

Given a Lie-Poisson completely integrable bi-Hamiltonian system on $\mathbb{R}^n$, we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial Lie-Poisson system on a non-abelian Poisson-Lie group $G_\eta$ of dimension $n$, where $\eta \in \mathbb{R}$ is the deformation parameter. Moreover, we show that from the two multiplicative (Poisson-Lie) Hamiltonian structures on $G_\eta$ that underly the dynamics of the deformed system and by making use of the group law on $G_\eta$, one may obtain two completely integrable Hamiltonian systems on $G_\eta \times G_\eta$. By construction, both systems admit reduction, via the multiplication in $G_\eta$, to the deformed bi-Hamiltonian system in $G_\eta$. The previous approach is applied to two relevant Lie-Poisson completely integrable bi-Hamiltonian systems: the Lorenz and Euler top systems.Comment: 23 pages, 2 figures. Revised versio

Implementing Technology Enhanced Mathematical Instruction in an Algebra I Course to Increase Students’ Academic Achievement in Mathematics

In July 2015, the National Council of Teachers of Mathematics established its position about the use of technology in teaching and learning mathematics. This important step forward opened a promise for many students and teachers that deserve the excellence of high-quality education in one of the most difficult educational subjects. In the 21st century, mathematics education can be one of the greatest recipients of all technological benefits reached by the most advanced societies of the earth. The purpose of this applied dissertation was to measure the effects in mathematics academic achievement of implementing technology-enhanced mathematical instruction to a group of seventh graders taking an accelerated course of algebra I. The problem of the study was that a large number of students were not achieving proficiency levels in fundamental algebra benchmarks such as algebra modeling, function modeling and statistics, and number system. The study included one experimental group, who received mathematics instruction using technology-enhanced mathematical instruction (TEMI), and a control group, who did not receive TEMI instruction. Both groups were assessed at the beginning of the experiment with a pre-test and the end of the study with a post-test. Additionally, a motivation survey about the use of technology during mathematics instruction was given to the experimental group at the end of the study

Reduction of Poisson-Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with nondegenerate Nijenhuis tensor

We show how to reduce, under certain regularities conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with nondegenerate Nijenhuis tensor. We generalize the work done by Magri and Morosi for the reduction of Poisson-Nijenhuis manifolds. The choice of the more general framework of Lie algebroids is motivated by the geometrical study of some reduced bi-Hamiltonian systems. An explicit example of reduction of a Poisson-Nijenhuis Lie algebroid is also provided.Comment: 35 pages, final version to appear in J. Phys. A: Math. Theo