Indexing Distributions of Data: Preservice Teachers' Notions of Representativeness

The purpose of the study was to identify strategies used by preservice elementary teachers to index distributions of data. A secondary purpose of the study was to investigate whether representational form influenced the type of representative values constructed. Two hundred eighty‐three preservice teachers were administered a selection of tasks requiring them to construct representative values for a variety of distributional shapes. Participants were asked to provide justifications for their chosen representative measures. Data were analyzed from two perspectives: nature and adequacy of representative measure. Results indicated that when presented with skewed data sets, over half of the participants constructed poorly representative values. Symmetric data sets were best indexed with 67% of participants constructing highly representative values. Representational form played a significant role in determining representative values. Data presented graphically were more likely to be represented using measures of variability than were those presented nongraphically. Conversely, measures of central tendency were more frequently used to represent nongraphical data. The information arising from this study indicates that many preservice teachers construct poorly representative values to index data sets and utilize identical measures of representativeness regardless of distributional shape. The findings of the study highlight the need for exploratory data activities at the preservice level, call for provision of experiences affording insights into construction of representative values, and thus, have implications for the design of preservice mathematics education curricula.     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.     

Determination of flutter derivatives via a neural network approach

A neural-network-based method is offered to determine the flutter derivatives of section models under smooth and turbulent flows. The approach uses the observed dynamic responses to train an appropriate neural network. Subsequently, the modal parameters of the model for different mean velocities of wind flow are directly estimated using weight matrices in the neural network. The flutter derivatives can then be determined accurately. The validity of the present method is verified through numerical studies. Finally, the procedure is employed to process experimental data from an inverted-U-type section model, obtained from wind tunnel tests.     

Transition flow of rarefied gases: Current models and methods of simulation

Transition (molecular-viscous) isothermal channel flow of rarefied gases is considered. Present-day engineering physical models of transition gas flow and methods of simulation are analyzed and verified in terms of the kinetic theory on the micro-and macrolevels.     

On theL p-bounds for maximal functions associated to convex bodies inR n

The dimension-freeL ²-maximal inequality for convex symmetric bodies obtained in [2] is extended forp>3/2.     

Optical detection of NO3 and NO2 in “pure” HNO3 vapor,the liquid-phase decomposition of HNO3

Flowing and static gas-phase samples of HNO₃ in O₂ and N₂ were analyzed by long-path ultraviolet/visible (UV/VIS) spectroscopy to reveal the presence of both NO₂ and NO₃, the concentrations of which were calculated using differential absorption cross sections. NO₂ is produced predominantly by the heterogeneous decomposition of HNO₃, whereas NO₃ is generated in the gas phase by the thermal decomposition of N₂O₅, a product of the self-disproportionation of liquid HNO₃. © 1993 John Wiley & Sons, Inc.     

Double-diffusive convection for a heated cylinder submerged in a salt-stratified fluid layer

Double-diffusive convection due to a cylindrical source submerged in a salt-stratified solution is numerically investigated in this study. For proper simulation of the vortex generated around the cylinder, a computational domain with irregular shape is employed. Flow conditions depend strongly on the thermal Rayleigh number, Ra _T , and the buoyancy ratio, R _ρ. There are two types of onset of instability existing in the flow field. Both types are due to either the interaction of the upward temperature gradient and downward salinity gradient or the interaction of the lateral temperature gradient and downward salinity gradient. The onset of layer instability due to plume convection is due to the former, whereas, the onset of layer instability of layers around the cylinder is due to the latter. Both types can be found in the flow field. The transport mechanism of layers at the top of the basic plume belongs to former while that due to basic plume and layer around the cylinder are the latter. The increase in Ra _T reinforces the plume convection and reduces the layer numbers generated around the cylinder for the same buoyancy ratio. For the same Ra _T , the increase of R _ρ suppresses the plume convection but reinforces the layers generated around the cylinder. The profiles of local Nusselt number reflects the heat transfer characteristics of plume convection and layered structure. The profiles of averaged Nusselt number are between the pure conduction and natural convection modes and the variation is due to the evolution of layers. Received on 13 September 1996     

Thickness and temperature dependence of subsidiary absorption thresholds in yttrium-iron-garnet thin films

The microwave subsidiary absorption threshold in tangentially magnetized yttrium-iron-garnet (YIG) films was measured as a function of the static magnetic field, film thickness and decrease in the 0.3–3 μm range is observed. The effect is explained quantitatively by using modified Damon-Eshbach dispersion relations which take into account exchange interactions.

The effect of temperature on h_crit, the smallest threshold field amplitude, in the 250<T< 450 K temperature range can be expressed by an empirical relationship h_crit M_s(T)^-1.6 where M_s is the saturation magnetization. This h_crit vs M_s relationship is similar to that obtained for the magnetization dependence of parallel pump thresholds in Li-Ti ferrite compounds.