The construction of self-dual normal polynomials over GF(2) and their applications to the Massey-Omura algorithm

Gaussian periods are used to locate a normal element of the finite field GF(2e) of odd degree e and an algorithm is presented for the construction of self-dual normal polynomials over GF(2) for any odd degree. This gives a new constructive proof of the existence of a self-dual basis for odd degree. The use of such polynomials in the Massey-Omura multiplier improves the efficiency and decreases the complexity of the multiplie

An exploration of teachers’ culturally responsive teaching practices and students’ acculturation experiences in the elementary school classroom

Supporting students from culturally diverse backgrounds requires a restructuring of current pedagogical practices. However, many teachers feel unprepared and lack the knowledge and practices necessary to work with students from diverse cultural backgrounds (Ballantyne, Sanderman, & Levy, 2008; Bankeree &Luckner, 2013). Considering this, a new theoretical model is presented which combines Third Space Theory and Culturally Responsive Teaching (CRT) so educators are equipped with a model that supports students’ cultural, academic, and psychological well-being collectively. Next, a qualitative phenomenological case study is shared that explores three teacher’s CRT practices, their students’ perceptions of these practices, and students’ strategy use within the same elementary school. The study, which was conducted in a large, diverse school in the Midwest utilized the Culturally Responsive Teacher Self-Efficacy Scale (Siwatuet al., 2015) and teacher and student interviews in order to explore the phenomenon at study. Results from the study revealed that CRT is a multifaceted phenomenon and even within classrooms where CRT practices are prevalent, how these practices are perceived often differ from student to student due to various factors (i.e., students’ purpose or goal, immigration experience, time in host country, or English language proficiency) and this has a reciprocal impact on their strategy use. Last, based on the theoretical model presented, educators are provided with a ready-to-use display that includes practices to support students’ cultural, academic, and psychological well-being

Tribes, state, and technology adoption in arid land management, Syria:

Arid shrub-lands in Syria and elsewhere in West Asia and North Africa are widely thought degraded. Characteristic of these areas is a preponderance of unpalatable shrubs or a lack of overall ground cover with a rise in the associated risks of soil erosion. Migrating pastoralists have been the scapegoats for this condition of the range. State steppe interventions of the last forty years have reflected this with programs to supplant customary systems with structures and institutions promoting western grazing systems and technologies. Principal amongst the latter has been shrub technology, particularly Atriplex species, for use in land rehabilitation and as a fodder reserve. This paper deconstructs state steppe policy in Syria by examining the overlap and interface of government and customary legal systems as a factor in the history of shrub technology transfer in the Syrian steppe. It is argued that the link made between signs of degradation and perceived moribund customary systems is not at all causal. Indeed, customary systems are found to be adaptive and resilient, and a strong influence on steppe management and the fate of technology transfer initiatives. Furthermore, developments in rangeland ecology raise questions about claims for grazing-induced degradation and call for a reinterpretation of recent shifts in vegetation on the Syrian steppe. Given the ineffectiveness of past state interventions, and in view of renewed understanding of customary systems and rangeland ecology, decentralization and some devolution of formal management responsibility is likely to be a viable and an attractive option for policymakers.

On the magnetospheric ULF wave counterpart of substorm onset

One near‐ubiquitous signature of substorms observed on the ground is the azimuthal structuring of the onset auroral arc in the minutes prior to onset. Termed auroral beads, these optical signatures correspond to concurrent exponential increases in ground ultralow frequency (ULF) wave power and are likely the result of a plasma instability in the magnetosphere. Here, we present a case study showing the development of auroral beads from a Time History of Events and Macroscale Interactions during Substorms (THEMIS) all‐sky camera with near simultaneous exponential increases in auroral brightness, ionospheric and conjugate magnetotail ULF wave power, evidencing their intrinsic link. We further present a survey of magnetic field fluctuations in the magnetotail around substorm onset. We find remarkably similar superposed epoch analyses of ULF power around substorm onset from space and conjugate ionospheric observations. Examining periods of exponential wave growth, we find the ground‐ and space‐based observations to be consistent, with average growth rates of ∼0.01 s−1, lasting for ∼4 min. Cross‐correlation suggests that the space‐based observations lead those on the ground by approximately 1–1.5 min. Meanwhile, spacecraft located premidnight and ∼10 RE downtail are more likely to observe enhanced wave power. These combined observations lead us to conclude that there is a magnetospheric counterpart of auroral beads and exponentially increasing ground ULF wave power. This is likely the result of the linear phase of a magnetospheric instability, active in the magnetotail for several minutes prior to auroral breakup

Effective grain surface area in the formation of molecular hydrogen in interstellar clouds

In the interstellar clouds, molecular hydrogens are formed from atomic hydrogen on grain surfaces. An atomic hydrogen hops around till it finds another one with which it combines. This necessarily implies that the average recombination time, or equivalently, the effective grain surface area depends on the relative numbers of atomic hydrogen influx rate and the number of sites on the grain. Our aim is to discover this dependency. We perform a numerical simulation to study the recombination of hydrogen on grain surfaces in a variety of cloud conditions. We use a square lattice (with a periodic boundary condition) of various sizes on two types of grains, namely, amorphous carbon and olivine. We find that the steady state results of our simulation match very well with those obtained from a simpler analytical consideration provided the `effective' grain surface area is written as $\sim S^{\alpha}$, where, $S$ is the actual physical grain area and $\alpha$ is a function of the flux of atomic hydrogen which is determined from our simulation. We carry out the simulation for various astrophysically relevant accretion rates. For high accretion rates, small grains tend to become partly saturated with $H$ and $H_2$ and the subsequent accretion will be partly inhibited. For very low accretion rates, the number of sites to be swept before a molecular hydrogen can form is too large compared to the actual number of sites on the grain, implying that $\alpha$ is greater than unity.Comment: 8 pages, 5 figures in eps forma

Listening to students

Written assessment feedback has not been widely researched despite higher education students continually expressing the need for meaningful and constructive feedback. This qualitative study employing focus groups captures and interprets the student perspective of written assessment feedback. Participants were Registered Nurses and non-traditional entrants to higher education. The findings generated a framework of themes and categories representing the feedback process experienced by the students. The themes were `learning from', `the process of receiving' and `making sense of' feedback. When this framework incorporates strategies such as `feed-forward', self-managed learning and personalized guidance it then represents a heuristic model of effective written assessment feedback. The model, created as a result of the research, should enhance the student experience and aid understanding of the complex processes associated with providing written assessment feedback

Variations of Field Line Eigenfrequencies With Ring Current Intensity

We present results from the closed magnetosphere (5.9≤L < 9.5 over all magnetic local times) to demonstrate and assess the variations in field line eigenfrequency with geomagnetic activity. Using the time-of-flight technique with realistic magnetic field and mass density models, the spatial distributions of field line eigenfrequencies are determined for a range of different geomagnetic activity levels, as defined by the Dst index. The results indicate that during geomagnetically active conditions, the eigenfrequency of a given field line is generally decreased compared to quiet times, in addition to variations in local asymmetries. By comparing the dependence to changes in the magnetic field and mass density distribution, it is established that the inflation and weakening of the geomagnetic field outweighs decreased plasma mass density and is the sole contributor to decreased eigenfrequencies with increased geomagnetic activity. We highlight the importance of considering the magnetic field, mass density, and average ion mass contributions when using observed eigenfrequencies to probe magnetospheric conditions. Furthermore, the estimates significantly improve upon existing time-of-flight results, through a consideration of mass density changes with geomagnetic activity. We also provide estimates of eigenfrequencies for a comparatively extended spatial region than available from prior direct observations of field line resonances. The results have clear implications for furthering our understanding of how wave energy propagates throughout the magnetosphere during geomagnetic storms

Laser cooling of a nanomechanical resonator mode to its quantum ground state

We show that it is possible to cool a nanomechanical resonator mode to its ground state. The proposed technique is based on resonant laser excitation of a phonon sideband of an embedded quantum dot. The strength of the sideband coupling is determined directly by the difference between the electron-phonon couplings of the initial and final states of the quantum dot optical transition. Possible applications of the technique we describe include generation of non-classical states of mechanical motion.Comment: 5 pages, 3 figures, revtex