Trends in the selection of spelling textbooks for public schools.

More than a million teachers and administrators are engaged in the work of educating some thirty million pupils enrolled 1n the schools of the United States. Since textbooks are without doubt the most effective single instructional tool provided for the use of these millions of pupils and their teachers, the selection of textbooks is a matter or utmost importance to educators and to the youth of today

High-resolution imaging spectroscopy of two micro-pores and an arch filament system in a small emerging-flux region

Aims. The purpose of this investigation is to characterize the temporal evolution of an emerging flux region, the associated photospheric and chromospheric flow fields, and the properties of the accompanying arch filament system. Methods. This study is based on imaging spectroscopy with the G\"ottingen Fabry-P\'erot Interferometer at the Vacuum Tower Telescope, on 2008 August 7. Cloud model (CM) inversions of line scans in the strong chromospheric absorption H$\alpha$ line yielded CM parameters, which describe the cool plasma contained in the arch filament system. Results. The observations cover the decay and convergence of two micro-pores with diameters of less than one arcsecond and provide decay rates for intensity and area. The photospheric horizontal flow speed is suppressed near the two micro-pores indicating that the magnetic field is sufficiently strong to affect the convective energy transport. The micro-pores are accompanied by an arch filament system, where small-scale loops connect two regions with H$\alpha$ line-core brightenings containing an emerging flux region with opposite polarities. The chromospheric velocity of the cloud material is predominantly directed downwards near the footpoints of the loops with velocities of up to 12 km/s, whereas loop tops show upward motions of about 3 km/s. Conclusions. Micro-pores are the smallest magnetic field concentrations leaving a photometric signature in the photosphere. In the observed case, they are accompanied by a miniature arch filament system indicative of newly emerging flux in the form of $\Omega$-loops. Flux emergence and decay take place on a time-scale of about two days, whereas the photometric decay of the micro-pores is much more rapid (a few hours), which is consistent with the incipient submergence of $\Omega$-loops. The results are representative for the smallest emerging flux regions still recognizable as such.Comment: 15 pages, 16 figures, 3 tables, published in A&

Two-Dimensional Spectroscopy of Photospheric Shear Flows in a Small delta Spot

In recent high-resolution observations of complex active regions, long-lasting and well-defined regions of strong flows were identified in major flares and associated with bright kernels of visible, near-infrared, and X-ray radiation. These flows, which occurred in the proximity of the magnetic neutral line, significantly contributed to the generation of magnetic shear. Signatures of these shear flows are strongly curved penumbral filaments, which are almost tangential to sunspot umbrae rather than exhibiting the typical radial filamentary structure. Solar active region NOAA 10756 was a moderately complex, beta-delta sunspot group, which provided an opportunity to extend previous studies of such shear flows to quieter settings. We conclude that shear flows are a common phenomenon in complex active regions and delta spots. However, they are not necessarily a prerequisite condition for flaring. Indeed, in the present observations, the photospheric shear flows along the magnetic neutral line are not related to any change of the local magnetic shear. We present high-resolution observations of NOAA 10756 obtained with the 65-cm vacuum reflector at Big Bear Solar Observatory (BBSO). Time series of speckle-reconstructed white-light images and two-dimensional spectroscopic data were combined to study the temporal evolution of the three-dimensional vector flow field in the beta-delta sunspot group. An hour-long data set of consistent high quality was obtained, which had a cadence of better than 30 seconds and sub-arcsecond spatial resolution.Comment: 23 pages, 6 gray-scale figures, 4 color figures, 2 tables, submitted to Solar Physic

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure

High-resolution imaging and near-infrared spectroscopy of penumbral decay

Combining high-resolution spectropolarimetric and imaging data is key to understanding the decay process of sunspots as it allows us scrutinizing the velocity and magnetic fields of sunspots and their surroundings. Active region NOAA 12597 was observed on 24/09/2016 with the 1.5-m GREGOR solar telescope using high-spatial resolution imaging as well as imaging spectroscopy and near-infrared (NIR) spectropolarimetry. Horizontal proper motions were estimated with LCT, whereas LOS velocities were computed with spectral line fitting methods. The magnetic field properties were inferred with the SIR code for the Si I and Ca I NIR lines. At the time of the GREGOR observations, the leading sunspot had two light-bridges indicating the onset of its decay. One of the light-bridges disappeared, and an elongated, dark umbral core at its edge appeared in a decaying penumbral sector facing the newly emerging flux. The flow and magnetic field properties of this penumbral sector exhibited weak Evershed flow, moat flow, and horizontal magnetic field. The penumbral gap adjacent to the elongated umbral core and the penumbra in that penumbral sector displayed LOS velocities similar to granulation. The separating polarities of a new flux system interacted with the leading and central part of the already established active region. As a consequence, the leading spot rotated 55-degree in clockwise direction over 12 hours. In the high-resolution observations of a decaying sunspot, the penumbral filaments facing flux emergence site contained a darkened area resembling an umbral core filled with umbral dots. This umbral core had velocity and magnetic field properties similar to the sunspot umbra. This implies that the horizontal magnetic fields in the decaying penumbra became vertical as observed in flare-induced rapid penumbral decay, but on a very different time-scale.Comment: 14 pages, 11 figures, Accepted to be published in Astronomy and Astrophysic

Horizontal flow fields observed in Hinode G-band images II. Flow fields in the final stages of sunspot decay

We present a subset of multi-wavelengths observations obtained with the Japanese Hinode mission, the Solar Dynamics Observatory (SDO), and the Vacuum Tower Telescope (VTT) at Observatorio del Teide, Tenerife, Spain during the time period from 2010 November 18-23. Horizontal proper motions were derived from G-band and Ca II H images, whereas line-of-sight velocities were extracted from VTT Echelle H-alpha 656.28 nm spectra and Fe I 630.25 nm spectral data of the Hinode/Spectro-Polarimeter, which also provided three-dimensional magnetic field information. The Helioseismic and Magnetic Imager on board SDO provided continuum images and line-of-sight magnetograms as context for the high-resolution observations for the entire disk passage of the active region. We have performed a quantitative study of photospheric and chromospheric flow fields in and around decaying sunspots. In one of the trailing sunspots of active region NOAA 11126, we observed moat flow and moving magnetic features (MMFs), even after its penumbra had decayed. We also noticed a superpenumbral structure around this pore. MMFs follow well-defined, radial paths from the spot all the way to the border of a supergranular cell surrounding the spot. In contrast, flux emergence near the other sunspot prevented it from establishing such well ordered flow patterns, which could even be observed around a tiny pore of just 2 Mm diameter. After the disappearance of the sunspots/pores a coherent patch of abnormal granulation remained at their location, which was characterized by more uniform horizontal proper motions, low divergence values, and diminished photospheric Doppler velocities. This region, thus, differs significantly from granulation and other areas covered by G-band bright points. We conclude that this peculiar flow pattern is a signature of sunspot decay and the dispersal of magnetic flux.Comment: 13 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Periods implying almost all periods, trees with snowflakes, and zero entropy maps

Let $X$ be a compact tree, $f$ be a continuous map from $X$ to itself, $End(X)$ be the number of endpoints and $Edg(X)$ be the number of edges of $X$. We show that if $n>1$ has no prime divisors less than $End(X)+1$ and $f$ has a cycle of period $n$, then $f$ has cycles of all periods greater than $2End(X)(n-1)$ and topological entropy $h(f)>0$; so if $p$ is the least prime number greater than $End(X)$ and $f$ has cycles of all periods from 1 to $2End(X)(p-1)$, then $f$ has cycles of all periods (this verifies a conjecture of Misiurewicz for tree maps). Together with the spectral decomposition theorem for graph maps it implies that $h(f)>0$ iff there exists $n$ such that $f$ has a cycle of period $mn$ for any $m$. We also define {\it snowflakes} for tree maps and show that $h(f)=0$ iff every cycle of $f$ is a snowflake or iff the period of every cycle of $f$ is of form $2^lm$ where $m\le Edg(X)$ is an odd integer with prime divisors less than $End(X)+1$