Northern Illinois University

About: Northern Illinois University is a education organization based out in DeKalb, Illinois, United States. It is known for research contribution in the topics: Large Hadron Collider & Population. The organization has 8818 authors who have published 20008 publications receiving 632341 citations. The organization is also known as: NIU.

A family of higher order mixed finite element methods for plane elasticity

Abstract: The Dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the Raviart-Thomas mixed finite elements for a scalar, second-order elliptic equation. Estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inL 2(Ω), and optimal order negative norm estimates are obtained inH s (Ω)? for a range ofs depending on the index of the finite element space. An optimal order estimate inL ?(Ω) for the displacement error is given. Also, a quasioptimal estimate is derived in an appropriate space. All estimates are valid uniformly with respect to the compressibility and apply in the incompressible case. The formulation of the elements is presented in detail.

Quantum oscillations in the underdoped cuprate YBa2Cu4O8.

Abstract: We report the observation of quantum oscillations in the underdoped cuprate superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ using a tunnel-diode oscillator technique in pulsed magnetic fields up to 85 T. There is a clear signal, periodic in inverse field, with frequency $660\ifmmode\pm\else\textpm\fi{}15\text{ }\text{ }\mathrm{T}$ and possible evidence for the presence of two components of slightly different frequency. The quasiparticle mass is ${m}^{*}=3.0\ifmmode\pm\else\textpm\fi{}0.3{m}_{e}$. In conjunction with the results of Doiron-Leyraud et al. for ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}$, the present measurements suggest that Fermi surface pockets are a general feature of underdoped copper oxide planes and provide information about the doping dependence of the Fermi surface.

Learning Fractions with Understanding: Building on Informal Knowledge

Abstract: Eight sixth-grade students received individualized instruction on addition and subtraction of fractions in a one-to-one setting for six weeks. Instruction was designed to build on the student's informal knowledge of fractions. All students possessed a rich store of informal knowledge of fractions that was based on partitioning units and treating the parts as whole numbers. Students' informal knowledge was initially disconnected from their knowledge of fraction symbols and procedures. Students related fraction symbols and procedures to their informal knowledge in ways that were meaningful to them; however, knowledge of rote procedures frequently interfered with students' attempts to build on their informal knowledge.