BMO\mathrm{BMO} ε\varepsilon-regularity results for solutions to Legendre-Hadamard elliptic systems

We will establish an $\varepsilon$-regularity result for weak solutions to Legendre-Hadamard elliptic systems, under the a-priori assumption that the gradient $\nabla u$ is small in $\mathrm{BMO}.$ Focusing on the case of Euler-Lagrange systems to simplify the exposition, regularity results will be obtained up to the boundary, and global consequences will be explored. Extensions to general quasilinear elliptic systems and higher-order integrands is also discussed.Comment: 37 pages, 1 figure. Accepted versio

New Jersey Anti-Bullying Bill of Rights Act: Perceptions of High School Administrators on Implementing the Law

The purpose of this study was to examine the 2011 New Jersey Anti-Bullying Bill of Rights Act (NJAB) and its perceived impact on urban school districts. Through a series of interviews with 16 participants from three urban school districts in New Jersey, the researcher sought to examine if those charged with implementing the NJAB have deemed the law and its requirements effective. The interviews were conducted with NJAB- mandated Anti-Bullying Specialists for each of the schools that participated in the study. The Anti-Bullying Specialists are the staff members in each school who are responsible for the implementation of the NJAB, district policies on bullying, and conducting bullying investigations. Data collected from this qualitative study add to the growing body of literature on the topic of bullying prevention strategies and specifically on the role that state and local policies play in helping to curtail bullying in schools. A review of the responses and data indicated that the Anti-Bullying Specialists interviewed for this study collectively have a firm grasp on the process by which bullying incidents should be investigated. Additionally, the data identified that while the law indicates that bullying prevention initiatives should take place throughout the curriculum in addition to the mandated Week of Respect, there seems to be relatively little infusion of the bullying prevention pedagogy within the schools and districts that were participants in this study. Last, the participants, all of whom work at traditional (Grades 9-12) high schools, indicated that the bulk of bullying incidents occur in their freshman population first and sophomores population second. They also indicated that there is a steep decline in incidents and reporting at the junior and senior grade levels

New Jersey Anti-Bullying Bill of Rights Act: Perceptions of High School Administrators on Implementing the Law

The purpose of this study was to examine the 2011 New Jersey Anti-Bullying Bill of Rights Act (NJAB) and its perceived impact on urban school districts. Through a series of interviews with 16 participants from three urban school districts in New Jersey, the researcher sought to examine if those charged with implementing the NJAB have deemed the law and its requirements effective. The interviews were conducted with NJAB- mandated Anti-Bullying Specialists for each of the schools that participated in the study. The Anti-Bullying Specialists are the staff members in each school who are responsible for the implementation of the NJAB, district policies on bullying, and conducting bullying investigations. Data collected from this qualitative study add to the growing body of literature on the topic of bullying prevention strategies and specifically on the role that state and local policies play in helping to curtail bullying in schools. A review of the responses and data indicated that the Anti-Bullying Specialists interviewed for this study collectively have a firm grasp on the process by which bullying incidents should be investigated. Additionally, the data identified that while the law indicates that bullying prevention initiatives should take place throughout the curriculum in addition to the mandated Week of Respect, there seems to be relatively little infusion of the bullying prevention pedagogy within the schools and districts that were participants in this study. Last, the participants, all of whom work at traditional (Grades 9-12) high schools, indicated that the bulk of bullying incidents occur in their freshman population first and sophomores population second. They also indicated that there is a steep decline in incidents and reporting at the junior and senior grade levels

Numerical Stability of Lanczos Methods

The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature. A recent application of the Lanczos algorithm proposed by Bai, Fahey and Golub allows quadrature evaluation of inner products of the form $\psi^\dagger g(A) \psi$. We show that this quadrature evaluation is numerically stable and explain how the numerical errors which are such a fundamental element of the finite precision Lanczos tridiagonalisation procedure are automatically and exactly compensated in the Bai, Fahey and Golub algorithm. In the process, we shed new light on the mechanism by which roundoff error corrupts the Lanczos procedureComment: 3 pages, Lattice 99 contributio

Glueball mass measurements from improved staggered fermion simulations

We present the first 2+1 flavour spectrum measurements of glueball states using high statistics simulations with improved staggered fermions. We find a spectrum consistent with quenched measurements of scalar, pseudoscalar andtensor glueball states. The measurements were made using 5000 configurations at a lattice spacing of 0.123 fm and pion mass of 280 MeV and 3000 configurations at 0.092 fm with a pion mass of 360 MeV. We see some evidence of coupling to 2 pion states. We compare our results with the experimental glueball candidate spectrum as well as quenched glueball estimates.Comment: 22 pages, 19 figures and 8 tables, minor additions on mixing post-refere

A\mathcal{A}-harmonic approximation and partial regularity, revisited

We give a direct harmonic approximation lemma for local minima of quasiconvex multiple integrals that entails their $\mathrm{C}^{1,\alpha}$ or $\mathrm{C}^{\infty}$-partial regularity. Different from previous contributions, the method is fully direct and elementary, only hinging on the $\mathrm{L}^{p}$-theory for strongly elliptic linear systems and Sobolev's embedding theorem. Especially, no heavier tools such as Lipschitz truncations are required.Comment: 18 page