Helping Kindergarteners Make Sense of Numbers to 100

The authors share what was learned about kindergarteners\u27 abilities to make sense of numbers to 100 when one of the authors, Linda Jaslow, took over a kindergarten class from February through the end of the school year. Through examples of how she engaged her students in nine weeks of problem solving and discussions focused on making sense of the number system, we provide evidence that the children grew substantially in their ability to count and show understanding when counting by 10\u27s and using 10\u27s during problem solving. Suggestions for tasks to promote continued growth are also provided. Throughout this teaching experience, Mrs. Jaslow was reminded of the complexity of making sense of our number system, and this article showcases her instructional decision making that was based on inquiry into children\u27s thinking. By valuing children\u27s existing ideas, Mrs. Jaslow could use that thinking to help guide her instruction

Dielectronic recombination rates, ionization equilibrium, and radiative emission rates for Mn ions in low-density high-temperature plasmas

The analysis of optically-thin far-ultraviolet and X-ray emission lines of multiply-charged ions is one of the basic methods for determining the temperatures and densities of laboratory and astrophysical plasmas. In addition, the energy balance in these plasmas can be significantly influenced by the emission of radiation from relatively low concentrations of multiple-charged atomic ions. Because the populations of the excited levels are expected to depart substantially from their local thermodynamic equilibrium values a detailed treatment of the elementary collisional and radiative processes must be employed in order to predict the emission line intensities. In this investigation the authors present the results of calculations based on a corona equilibrium model in which a detailed evaluation is made of the dielectronic recombination rate coefficients. The ionization and autoionization following inner-shell electron excitation from each ground state are balanced by direct radiative and dielectronic recombination. The spectral line intensities emitted by the low-lying excited states, which are assumed to undergo spontaneous radiative decay in times that are short compared with the collision time, are evaluated in terms of the corona ionization equilibrium distributions of the ground states and their electron-impact excitation states

Radiative transitions involving the (2p2)(3 Pe) metastable autodetaching of H(-)

The absorption coefficient for the free-bound transition H (ls) + e(-)+ h omega yields H(-)(2 sq p,(3)P(e)) is calculated (together with the differential emission rate for the inverse process) using ls - 2s - 2p close coupling continuum wave functions and a Hylleraas bound state wave function. A maximum in the absorption and emission spectra is found to occur at a photon wavelength of 1219.5 A, which is 2 A closer to the Lyman alpha line than predicted by the calculations of Drake, and is in closer agreement with the stellar absorption feature identified by Heap and Stecher. The free-bound absorption process appears to be a significant source of continuous ultraviolet opacity

Passive propellant system

The system utilizes a spherical tank structure A separated into two equal volume compartments by a flat bulkhead B. Each compartment has four similar gallery channel legs located in the principal vehicle axes, ensuring that bulk propellant will contact at least one gallery leg during vehicle maneuvers. The forward compartment gallery channel legs collect propellant and feed it into the aft compartment through communication screens which protrude into the aft compartment. The propellant is then collected by the screened gallery channels in the aft compartment and supplied to the propellant outlet. The invention resides in the independent gallery assembly and screen structure by means of which propellant flow from forward to aft compartments is maintained. Liquid surface tension of the liquid on the screens is used to control liquid flow. The system provides gas-free propellants in low or zero-g environments regardless of axial accelerations and propellant orientation in bulk regions of the vessel

Photoionization from excited states of helium

The cross sections for photoionization from the 2 1S, 2 3S, 2 1P and 2 3P excited states of helium are calculated for photoelectron energies below the n = 2 threshold of He(+) using Hylleraas bound state wave functions and 1s-2s-2p close coupling final state wave functions. The resonant structures associated with the lowest-lying 1S, 1P, 3P, and 1D autoionizing states of helium are found to be characterized by large values of the line profile parameter q. The cross sections and the photoelectron angular distribution asymmetry parameters for the P-states are calculated for various polarization states of the target atom and the incident photon. Experiments which would lead to the separate determinations of the S- and D- wave partial photoionization cross sections are discussed

Extended symmetrical classical electrodynamics

In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the induced charges and currents depend on the vector k and the vectors of the electromagnetic field E and B. It is shown that the vectors E and B can be defined in terms of two 4-potentials and the components of k are the components of the 4-tensor of the third rank. The Lagrangian of modified electrodynamics is defined. The conditions are derived at which only one 4-potential determines the behavior of the electromagnetic field. It is also shown that static modified electrodynamics can describe the electromagnetic field in the inner region of the electric monopole. In the outer region of the electric monopole the electric field is governed by the Maxwell equations. It follows from boundary conditions at the interface between the inner and outer regions of the monopole that the vector k has a discrete spectrum. The electric and magnetic fields, energy and angular momentum of the monopole are found for different eigenvalues of k

Exact N-vortex solutions to the Ginzburg-Landau equations for kappa=1/sqrt(2)

The N-vortex solutions to the two-dimensional Ginzburg - Landau equations for the kappa=1/\sqrt(2) parameter are built. The exact solutions are derived for the vortices with large numbers of the magnetic flux quanta. The size of vortex core is supposed to be much greater than the magnetic field penetration depth. In this limiting case the problem is reduced to the determination of vortex core shape. The corresponding nonlinear boundary problem is solved by means of the methods of the theory of analytic functions.Comment: 12 pages in RevTex, 1 Postscript figur

Local structure of In_(0.5)Ga_(0.5)As from joint high-resolution and differential pair distribution function analysis

High resolution total and indium differential atomic pair distribution functions (PDFs) for In_(0.5)Ga_(0.5)As alloys have been obtained by high energy and anomalous x-ray diffraction experiments, respectively. The first peak in the total PDF is resolved as a doublet due to the presence of two distinct bond lengths, In-As and Ga-As. The In differential PDF, which involves only atomic pairs containing In, yields chemical specific information and helps ease the structure data interpretation. Both PDFs have been fit with structure models and the way in that the underlying cubic zinc-blende lattice of In_(0.5)Ga_(0.5)As semiconductor alloy distorts locally to accommodate the distinct In-As and Ga-As bond lengths present has been quantified.Comment: 9 pages, 7 figur

In vivo Detection of Hyperoxia-induced Pulmonary Endothelial Cell Death Using \u3csup\u3e99m\u3c/sup\u3eTc-Duramycin

Introduction 99mTc-duramycin, DU, is a SPECT biomarker of tissue injury identifying cell death. The objective of this study is to investigate the potential of DU imaging to quantify capillary endothelial cell death in rat lung injury resulting from hyperoxia exposure as a model of acute lung injury. Methods Rats were exposed to room air (normoxic) or \u3e 98% O2 for 48 or 60 hours. DU was injected i.v. in anesthetized rats, scintigraphy images were acquired at steady-state, and lung DU uptake was quantified from the images. Post-mortem, the lungs were removed for histological studies. Sequential lung sections were immunostained for caspase activation and endothelial and epithelial cells. Results Lung DU uptake increased significantly (p \u3c 0.001) by 39% and 146% in 48-hr and 60-hr exposed rats, respectively, compared to normoxic rats. There was strong correlation (r2 = 0.82, p = 0.005) between lung DU uptake and the number of cleaved caspase 3 (CC3) positive cells, and endothelial cells accounted for more than 50% of CC3 positive cells in the hyperoxic lungs. Histology revealed preserved lung morphology through 48 hours. By 60 hours there was evidence of edema, and modest neutrophilic infiltrate. Conclusions Rat lung DU uptake in vivo increased after just 48 hours of \u3e 98% O2 exposure, prior to the onset of any substantial evidence of lung injury. These results suggest that apoptotic endothelial cells are the primary contributors to the enhanced DU lung uptake, and support the utility of DU imaging for detecting early endothelial cell death in vivo

Gravitational Waves in Bianchi Type-I Universes I: The Classical Theory

The propagation of classical gravitational waves in Bianchi Type-I universes is studied. We find that gravitational waves in Bianchi Type-I universes are not equivalent to two minimally coupled massless scalar fields as it is for the Robertson-Walker universe. Due to its tensorial nature, the gravitational wave is much more sensitive to the anisotropy of the spacetime than the scalar field is and it gains an effective mass term. Moreover, we find a coupling between the two polarization states of the gravitational wave which is also not present in the Robertson-Walker universe.Comment: 34 papers, written in ReVTeX, submitted to Physical Review