Remarks on countable tightness

Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize indestructibility of the Lindelof property under countably closed forcing. We consider the behavior of countable tightness in generic extensions obtained by adding Cohen reals. We show that certain classes of well-studied topological spaces are indestructibly countably tight. Stronger versions of countable tightness, including selective versions of separability, are further explored.Comment: Extended from 12 pages to 23 pages. Newly extended to 27 page

Ion beam effect on Ge-Se chalcogenide glass films: Non-volatile memory array formation, structural changes and device performance

The conductive bridge non-volatile memory technology is an emerging way to replace traditional charge based memory devices for future neural networks and configurable logic applications. An array of the memory devices that fulfills logic operations must be developed for implementing such architectures. A scheme to fabricate these arrays, using ion bombardment through a mask, has been suggested and advanced by us. Performance of the memory devices is studied, based on the formation of vias and damage accumulation due to the interactions of Ar+ ions with GexSe1-x (x=0.2, 0.3 and 0.4) chalcogenide glasses as a function of the ion energy and dose dependence. Blanket films and devices were created to study the structural changes, surface roughness, and device performance. Raman Spectroscopy, Atomic Force Microscopy (AFM), Energy Dispersive X-Ray Spectroscopy (EDS) and electrical measurements expound the Ar+ ions behavior on thin films of GexSe1-x system. Raman studies show that there is a decrease in area ratio between edge-shared to corner-shared structural units, revealing occurrence of structural reorganization within the system as a result of ion/film interaction. AFM results demonstrate a tendency in surface roughness improvement with increased Ge concentration, after ion bombardment. EDS results reveal a compositional change in the vias, with a clear tendency of greater interaction between ions and the Ge atoms, as evidenced by greater compositional changes in the Ge rich films

Broken-Symmetry States in Quantum Hall Superlattices

We argue that broken-symmetry states with either spatially diagonal or spatially off-diagonal order are likely in the quantum Hall regime, for clean multiple quantum well (MQW) systems with small layer separations. We find that for MQW systems, unlike bilayers, charge order tends to be favored over spontaneous interlayer coherence. We estimate the size of the interlayer tunneling amplitude needed to stabilize superlattice Bloch minibands by comparing the variational energies of interlayer-coherent superlattice miniband states with those of states with charge order and states with no broken symmetries. We predict that when coherent miniband ground states are stable, strong interlayer electronic correlations will strongly enhance the growth-direction tunneling conductance and promote the possibility of Bloch oscillations.Comment: 9 pages LaTeX, 4 figures EPS, to be published in PR

On the visible size and geometry of aggressively expanding civilizations at cosmological distances

If a subset of advanced civilizations in the universe choose to rapidly expand into unoccupied space, these civilizations would have the opportunity to grow to a cosmological scale over the course of billions of years. If such life also makes observable changes to the galaxies they inhabit, then it is possible that vast domains of life-saturated galaxies could be visible from the Earth. Here, we describe the shape and angular size of these domains as viewed from the Earth, and calculate median visible sizes for a variety of scenarios. We also calculate the total fraction of the sky that should be covered by at least one domain. In each of the 27 scenarios we examine, the median angular size of the nearest domain is within an order of magnitude of a percent of the whole celestial sphere. Observing such a domain would likely require an analysis of galaxies on the order of a Gly from the Earth.Comment: 12 pages, 4 figures, 1 table. References added and updated. New figure added (fig. 4). Additional discussion added. Minor numerical corrections to table 1 (bug fixed

Weak covering properties and selection principles

No convenient internal characterization of spaces that are productively Lindelof is known. Perhaps the best general result known is Alster's internal characterization, under the Continuum Hypothesis, of productively Lindelof spaces which have a basis of cardinality at most $\aleph_1$. It turns out that topological spaces having Alster's property are also productively weakly Lindelof. The weakly Lindelof spaces form a much larger class of spaces than the Lindelof spaces. In many instances spaces having Alster's property satisfy a seemingly stronger version of Alster's property and consequently are productively X, where X is a covering property stronger than the Lindelof property. This paper examines the question: When is it the case that a space that is productively X is also productively Y, where X and Y are covering properties related to the Lindelof property.Comment: 16 page

A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs so that the method only requires samples of the field at (possibly scattered) nodes over the domain. Numerical results are presented demonstrating high-order convergence in both space (between 5th and 6th order) and time (up to 4th order) for some model problems in two dimensional irregular geometries.Comment: 34 pages, 8 figure

Properties of the Soliton-Lattice State in Double-Layer Quantum Hall Systems

Application of a sufficiently strong parallel magnetic field $B_\parallel > B_{c}$ produces a soliton-lattice (SL) ground state in a double-layer quantum Hall system. We calculate the ground-state properties of the SL state as a function of $B_\parallel$ for total filling factor $\nu_{T}=1$, and obtain the total energy, anisotropic SL stiffness, Kosterlitz-Thouless melting temperature, and SL magnetization. The SL magnetization might be experimentally measurable, and the magnetic susceptibility diverges as $|B_\parallel - B_{c}|^{-1}$.Comment: 4 pages LaTeX, 1 EPS figure. Proceedings of the 12th International Conference on the Electronic Properties of Two-Dimensional Electron Systems (EP2DS-12), to be published in Physica B (1998

How Educators Use Policy Documents: A Misunderstood Relationship

As an English educator and co-director of a National Writing Project site, I have had many conversations with colleagues and educators who are anxious about the Common Core State Standards (CCSS) being adopted in so many states throughout the nation. The anxiety comes in many forms, ranging from What do the CCSS mean for what and how I have to teach? to What does the drafting and implementation processes of the CCSS suggest for how people view me as a professional? to Are the CCSS really any good? and so on. As I listen to all the people I work with - preservice teachers, experienced teachers, teacher educators, curriculum coordinators, writing project directors and fellows - I keep returning to one major issue that I think is behind a lot of the concern. More specifically, I continue to wonder how educators actually use and develop policy documents (e.g., standards) in their day-to-day work. The assumption seems to be that teachers read the policies and then implement them; however, any teacher who has worked with standards documents knows that this process isn\u27t quite as clear-cut as the above assumption. It is this gap between how assumptions about educators use policy documents and how teachers actually use those policy documents. I sense this is the source for a lot of the anxiety I hear in the voices of the many educators I respect and work with

Identifying the Location in the Host Galaxy of the Short GRB 111117A with the Chandra Sub-arcsecond Position

We present our successful Chandra program designed to identify, with sub-arcsecond accuracy, the X-ray afterglow of the short GRB 111117A, which was discovered by Swift and Fermi. Thanks to our rapid target of opportunity request, Chandra clearly detected the X-ray afterglow, though no optical afterglow was found in deep optical observations. The host galaxy was clearly detected in the optical and near-infrared band, with the best photometric redshift of z=1.31_{-0.23}^{+0.46} (90% confidence), making it one of the highest known short GRB redshifts. Furthermore, we see an offset of 1.0 +- 0.2 arcseconds, which corresponds to 8.4 +- 1.7 kpc, between the host and the afterglow position. We discuss the importance of using Chandra for obtaining sub-arcsecond X-ray localizations of short GRB afterglows to study GRB environments.Comment: 17 pages, 11 figures, accepted for publication in Ap

The Fundamental Theorem on Symmetric Polynomials: History's First Whiff of Galois Theory

We describe the Fundamental Theorem on Symmetric Polynomials (FTSP), exposit a classical proof, and offer a novel proof that arose out of an informal course on group theory. The paper develops this proof in tandem with the pedagogical context that led to it. We also discuss the role of the FTSP both as a lemma in the original historical development of Galois theory and as an early example of the connection between symmetry and expressibility that is described by the theory.Comment: 15 pages, 1 figure. Corrected a misattributio