Active Facilitation: What Do Specialists Need to Know and How Might They Learn It?

Sustained, innovative professional development is now widely acknowledged as essential to the improvement of mathematics instruction in the nation’s schools. In recent years, this recognition has prompted the production of a variety of materials designed to support new teacher development programs. However, with the availability of such materials, serious concerns arise as to the kinds of knowledge required of professional development providers, often teachers who have been assigned Mathematics Specialist roles, and the means by which this knowledge is to be acquired. The authors of this paper address such questions in the context of one professional development seminar, Developing Mathematical Ideas [1]. Our paper builds on the research of Remillard and Geist who identify the potential for learning in those moments of discontinuity—“openings in the curriculum —in which the beliefs, knowledge, and commitments of seminar participants diverge from those of facilitators or materials developers [2]. By looking closely at several such moments. we establish how successful facilitation entails deep content knowledge, awareness of seminar goals, and appreciation of the beliefs and understandings of seminar participants. We then describe the kinds of supports available to DMI facilitators to help them cultivate the skills and knowledge needed to exploit these openings productively. While the paper focuses particularly on professional development seminars. we suggest that our conclusions apply to Mathematics Specialists‘ tasks more generally

On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function.Comment: 11 page

High spatial resolution 100 micron observations of the M83 bar

A program of high spatial resolution far-infrared observations of galaxies using the Kuiper Airborne Observatory (KAO), was conducted to better understand the role of star formation, the general interstellar radiation field, and non-thermal activity in powering the prodigious far-infrared luminosities seen in spiral and interacting galaxies. Here, researchers present observations of the central region of the well-known barred spiral M83 (NGC 5236). The resultant channel 3 scans for M83 and IRC + 10216, after co-addition and smoothing, are shown. These data show that M83 is extended at 100 microns compared to a point source. A simple Gaussian deconvolution of the M83 data with the point source profile from IRC+10216 gives a full width half maximum (FWHM) of about 19 seconds for M83. By comparison with IRC+10216, researchers obtain a flux for the unresolved component in M83 of about 110 Jy. This is about 1/6 the total flux for M83 (Rice et al. 1988) and about 1/2 the PSC flux. The M83 and IRC+10216 profiles in the cross-scan direction (SE-NW) were also compared, and show that M83 is extended in this direction as well, with a width of about 18 seconds. A comparison of the different channel profiles for M83 and IRC+10216 shows that there is an asymmetry in the M83 data, in that the maximum in the profiles shifts from southeast to northwest as channel number increases. This corresponds to the extension in the bar seen in the CO data. Thus the far-infrared emission in the central region of M83 tends to trace the CO bar. The new 100 micron data is also compared with previous H alpha observations from the literature, to determine how well the far-infrared traces the stellar structure, the star formation as measured by H alpha, and the optical colors

An evaluation of active noise control in a cylindrical shell

The physical mechanisms governing the use of active noise control in an extended volume of a cylindrical shell are discussed. Measured data was compared with computer results from a previously derived analytical model based on an infinite shell theory. For both the analytical model and experiment, the radiation of the external monopoles is coupled to the internal acoustic field through the radial displacement of the thin, elastic cylindrical shell. An active noise control system was implemented in the cylinder using a fixed array of discrete monopole sources, all of which lie in the plane of the exterior noise sources. Good agreement between measurement and prediction was obtained for both internal pressure response and overall noise reduction. Attenuations in the source plane greater than 15 dB were recorded along with a uniformly quieted noise environment over the entire length of the experimental model. Results indicate that for extended axial forcing distributions or very low shell damping, axial arrays of control sources may be required. Finally, the Nyquist criteria for the number of azimuthal control sources is shown to provide for effective control over the full cylinder cross section

Limb darkening in spherical stellar atmospheres

(Abridged) Context. Stellar limb darkening, I({\mu} = cos{\theta}), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume limb-darkening coefficients computed from model stellar atmospheres. However, previous studies, using I({\mu}) from plane- parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common {\mu} location on the stellar disk, for all values of T eff, log g and wavelength. Aims. We study this fixed {\mu}-point to determine if it is a property of the model stellar atmospheres or a property of the limb-darkening laws. Furthermore, we use this limb-darkening law as a tool to probe properties of stellar atmospheres for comparison to limb- darkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental parameters L\star, M\star and R\star) are used to reexamine the existence of the fixed {\mu}-point for the parametrized curves. Results. We find that the intensities from our spherical models do not have a fixed point, although the curves do have a minimum spread at a {\mu}-value similar to the parametrized curves. We also find that the parametrized curves have two fixed points, {\mu}1 and {\mu}2, although {\mu}2 is so close to the edge of the disk that it is missed using plane-parallel atmospheres. We also find that the spherically- symmetric models appear to agree better with published microlensing observations relative to plane-parallel models.Comment: 8 pages, 8 figures, figures 4 and 6 have lower resolution. A&A in pres

Evaluating the Consumption Tax Proposals: Changes in the Taxation of Interspousal Transactions, Use of Trusts, and Revising the Meaning of Tax Planning

This Article focuses on two proposals to revise the federal income tax system: the Armey flat tax and the USA tax. It compares these tax reform measures with the current Internal Revenue Code for income tax in three areas: (1) corporate stock redemptions and divorce; (2) the use of alimony trusts; and (3) nonqualified deferred compensation (so-called rabbi ) trusts. In assessing the proposed changes, the Article also addresses the amount of simplification that will be achieved, the possible undertaxation of recipients of profits, tax avoidance, and the extent to which one must cast aside conventional tax planning and tax policy concepts in the new tax regime

Using limb darkening to measure fundamental parameters of stars

Context. Limb darkening is an important tool for understanding stellar atmospheres, but most observations measuring limb darkening assume various parameterizations that yield no significant information about the structure of stellar atmospheres. Aims. We use a specific limb-darkening relation to study how the best-fit coefficients relate to fundamental stellar parameters from spherically symmetric model stellar atmospheres. Methods. Using a grid of spherically symmetric Atlas model atmospheres, we compute limb-darkening coefficients, and develop a novel method to predict fundamental stellar parameters. Results. We find our proposed method predicts the mass of stellar atmosphere models given only the radius and limb-darkening coefficients, suggesting that microlensing, interferometric, transit and eclipse observations can constrain stellar masses. Conclusions. This novel method demonstrates that limb-darkening parameterizations contain important information about the structure of stellar atmospheres, with the potential to be a valuable tool for measuring stellar masses.Comment: 8 pages, 6 figures, 2 tables, A&A accepte

Joule-Thomson valves for long term service in space cryocoolers

Joule-Thomson valves for small cryocoolers have throttling passages on the order of 0.1 millimeter in diameter. Consequently, they can become plugged easily and stop the operation of the cooler. Plugging can be caused by solid particles, liquids or gases. Plugging is usually caused by the freezing of contaminant gases from the process stream. In small open loop coolers and in closed loop coolers where periodic maintenance is allowed, the problem is overcome by using careful assembly techniques, pure process gases, warm filters and cold adsorbers. A more thorough approach is required for closed loop cryocoolers which must operate unattended for long periods. This paper presents the results of an effort to solve this problem. The causes of plugging are examined, and various ways to eliminate plugging are discussed. Finally, the development of a J-T defroster is explained. It is concluded that a combination of preventive measures and a defroster will reduce the chance of cooler failure by plugging to such a degree that J-T coolers can be used for long term space missions

SUSY and Dark Matter Constraints from the LHC

The ability of the LHC to make statements about the dark matter problem is considered, with a specific focus on supersymmetry. After reviewing the current strategies for supersymmetry searches at the LHC (in both CMS and ATLAS), some key ATLAS studies are used to demonstrate how one could establish that SUSY exists before going on to measure the relic density of a neutralino WIMP candidate. Finally, the general prospects for success at the LHC are investigated by looking at different points in the MSSM parameter space.Comment: Talk given at the XLIrst Rencontres de Moriond session devoted to Electroweak Interactions And Unified Theories in March 2006, to be published in the associated proceedings. 10 pages, 8 figure

Voltage-dependent Block of the Cystic Fibrosis Transmembrane Conductance Regulator Cl- Channel by Two Closely Related Arylaminobenzoates

The gene defective in cystic fibrosis encodes a Cl- channel, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is blocked by diphenylamine-2-carboxylate (DPC) when applied extracellularly at millimolar concentrations. We studied the block of CFTR expressed in Xenopus oocytes by DPC or by a closely related molecule, flufenamic acid (FFA). Block of whole-cell CFTR currents by bath-applied DPC or by FFA, both at 200 µM, requires several minutes to reach full effect. Blockade is voltage dependent, suggesting open-channel block: currents at positive potentials are not affected but currents at negative potentials are reduced. The binding site for both drugs senses ~40% of the electric field across the membrane, measured from the inside. In single-channel recordings from excised patches without blockers, the conductance was 8.0 ± 0.4 pS in symmetric 150 mM Cl^-. A subconductance state, measuring ~60% of the main conductance, was often observed. Bursts to the full open state lasting up to tens of seconds were uninterrupted at depolarizing membrane voltages. At hyperpolarizing voltages, bursts were interrupted by brief closures. Either DPC or FFA (50 µM) applied to the cytoplasmic or extracellular face of the channel led to an increase in flicker at V_m =-100 mV and not at V_m = +100 mV, in agreement with whole-cell experiments. DPC induced a higher frequency of flickers from the cytoplasmic side than the extracellular side. FFA produced longer closures than DPC; the FFA closed time was roughly equal (~ 1.2 ms) at -100 mV with application from either side. In cell-attached patch recordings with DPC or FFA applied to the bath, there was flickery block at V_m = -100 mV, confirming that the drugs permeate through the membrane to reach the binding site. The data are consistent with the presence of a single binding site for both drugs, reached from either end of the channel. Open-channel block by DPC or FFA may offer tools for use with site-directed mutagenesis to describe the permeation pathway