Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations

Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear differential equations, we apply a technique based on finite differences and sparse SDP relaxations for polynomial optimization problems (POP) to obtain a discrete approximation of its solution. In a second step we apply maximum entropy estimation (using moments of a Borel measure associated with the discrete solution) to obtain a smooth closed-form approximation. The approach is illustrated on a variety of linear and nonlinear ordinary differential equations (ODE), partial differential equations (PDE) and optimal control problems (OCP), and preliminary numerical results are reported

How Can An Intermediate Elementary Educator Use Critical Literacy To Promote Social Justice Through Book Clubs?

The purpose of this action research is to better understand, “How can an intermediate elementary educator use critical literacy to promote social justice through book clubs?” The author researched and defined social justice, critical literacy and book clubs. After, the author administered a pre assessment, helped facilitate book clubs and a post assessment. The action research was conducted in a suburban school that is mainly comprised of white students. Two groups, having selected the same text, were chosen as a focus group. The author notes and highlights themes across all seven of the students’ experiences throughout the unit. The author discovered that one group used a social justice critical lens while reading and discussing the book and proceeded to provide a solution a problem in the text. The other group developed a critical literacy lens while reading and discussing the text