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Many students are attracted to astronomy due to its inviting nature of spectacular wonders. However, studying astronomy goes beyond these wonders, which poses a challenge to students' knowledge and understanding of basic astronomical phenomena. The University of Cape Town has developed a series of research studies that probe the nature of student difficulties at a fine-grained level, in particular looking into how students conceive of astronomical distances which are beyond immediate human comprehension. The key experimental findings from this study were that as distances increased different modes of thinking were employed to make sense of them. The experimental findings could be explained by the embodied cognition framework which posits that the way we think (all thought) is ultimately grounded in infant sensory-motor experiences. In this case, the thinking template or image schema was suggested to be the "source-path-goal". Having identified the "thinking" framework allows for a research-based construction of learning activities that lead to sense-making. Thus, the notion of the Source-Path-Goal Thinking Template / Image Schema was used to create an activity that would trigger this mode of thinking for large-scale distances. Based on the current experimental findings that can be explained by an "embodied cognition" framework, learning activities were piloted that appear to have had a measure of success.

We highlight the fundamental influence that the work of Alasdair Urquhart has had in the area of distributive lattice-ordered algebras and in particular to the development of Ockham algebras, to which we attach some new results.

Compared with STEM fields, foreign language (FL) education and second language acquisition have only slowly embraced open education and the new knowledge ecologies it produces. FL educators may have been hesitant to participate in the open education movement due to a lack of research which investigates the benefits and challenges of FL learning and teaching in open environments. This book contextualizes open education in FL learning and teaching via an historical overview of the movement, along with an in-depth exploration of how the open movement affects FL education beyond the classroom context; fills the research void by exploring aspects of open second language learning and teaching across a range of educational contexts; and illustrates new ways of creating, adapting and curating FL materials that are freely shared among FL educators and students.This book is open access under a CC BY ND licence.&nbsp

We consider, in the context of an Ockham algebra $${{\mathcal{L} = (L; f)}}$$ , the ideals I of L that are kernels of congruences on $${\mathcal{L}}$$ . We describe the smallest and the largest congruences having a given kernel ideal, and show that every congruence kernel $${I \neq L}$$ is the intersection of the prime ideals P such that $${I \subseteq P}$$ , $${P \cap f(I) = \emptyset}$$ , and $${f^{2}(I) \subseteq P}$$ . The congruence kernels form a complete lattice which in general is not modular. For every non-empty subset X of L, we also describe the smallest congruence kernel to contain X, in terms of which we obtain necessary and sufficient conditions for modularity and distributivity. The case where L is of finite length is highlighted.

This work was partially supported by the Portuguese Foundation for Science and Technology through the grant UID/MAT/00297/2013 (CMA). Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations. Postprint

This Letter reports the first extraction of individual antineutrino spectra from ^{235}U and ^{239}Pu fission and an improved measurement of the prompt energy spectrum of reactor antineutrinos at Daya Bay. The analysis uses 3.5×10^{6} inverse beta-decay candidates in four near antineutrino detectors in 1958 days. The individual antineutrino spectra of the two dominant isotopes, ^{235}U and ^{239}Pu, are extracted using the evolution of the prompt spectrum as a function of the isotope fission fractions. In the energy window of 4-6 MeV, a 7% (9%) excess of events is observed for the ^{235}U (^{239}Pu) spectrum compared with the normalized Huber-Mueller model prediction. The significance of discrepancy is 4.0σ for ^{235}U spectral shape compared with the Huber-Mueller model prediction. The shape of the measured inverse beta-decay prompt energy spectrum disagrees with the prediction of the Huber-Mueller model at 5.3σ. In the energy range of 4-6 MeV, a maximal local discrepancy of 6.3σ is observed.

In brief Football fatality and catastrophic injury data for 1976 through 1981 are compared with earlier data. The purpose is to analyze the data in regard to rule and equipment changes that have taken place in football since 1976 and to demonstrate the reduction in fatalities and catastrophic injuries. Fatality data for 1981 show five high school and two college fatalities. In 1981 there were five permanent spinal cord injuries in high schools and one in college.

Improved conditioning, rule changes, and a helmet standard helped reduce football fatalities to an all-time low in 1979.

An ordered regular semigroup S is E-special if for every x ∈ S there is a biggest x + ∈ S such that both xx + and x + x are idempotent. Every regular strong Dubreil–Jacotin semigroup is E-special, as is every ordered completely simple semigroup with biggest inverses. In an E-special ordered regular semigroup S in which the unary operation x → x + is antitone the subset P of perfect elements is a regular ideal, the biggest inverses in which form an inverse transversal of P if and only if S has a biggest idempotent. If S + is a subsemigroup and S does not have a biggest idempotent, then P contains a copy of the crown bootlace semigroup.

Muon-induced neutrons are one of the major backgrounds to various underground experiments, such as dark matter searches, low-energy neutrino oscillation experiments and neutrino-less double beta-decay experiments. Previous experiments on the underground production rate of muon-induced neutrons were mostly carried out either at shallow sites or at very deep sites. The Aberdeen Tunnel experiment aims to measure the neutron production rate at a moderate depth of 611 meters water equivalent. Our apparatus comprises of six layers of plastic-scintillator hodoscopes for tracking the incident cosmic-ray muons, and 760 L of gadolinium-doped liquid-scintillator for both neutron production and detection targets. In this paper, we describe the design and the performance of the apparatus. The preliminary result on the measurement of neutron production rate is also presented.

We consider particular compatible orders on a given completely simple semigroup Sx=M(〈x〉; I ,Λ;P) where 〈x〉 is an ordered cyclic group with x > 1 and P11=x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.

We investigate the class BA of ordered regular semigroups in which each element has a biggest associate x† = max {y | xyx = x}. This class properly contains the class PO of principally ordered regular semigroups (in which there exists x⋆ = max {y | xyx ⩽x}) and is properly contained in the class BI of ordered regular semigroups in which each element has a biggest inverse x◦. We show that several basic properties of the unary operation x ↦ x⋆ in PO extend to corresponding properties of the unary operation x ↦ x† in BA. We consider naturally ordered semigroups in BA and prove that those that are orthodox contain a biggest idempotent. We determine the structure of some such semigroups in terms of a principal left ideal and a principal right ideal. We also characterise the completely simple members of BA. Finally, we consider the naturally ordered semigroups in BA that do not have a biggest idempotent.

In this paper, we describe the design, construction and performance of an apparatus installed in the Aberdeen Tunnel laboratory in Hong Kong for studying spallation neutrons induced by cosmic-ray muons under a vertical rock overburden of 611 m water equivalent (m.w.e.). The apparatus comprises six horizontal layers of plastic-scintillator hodoscopes for determining the direction and position of the incident cosmic-ray muons. Sandwiched between the hodoscope planes is a neutron detector filled with 650 kg of liquid scintillator doped with about 0.06% of Gadolinium by weight for improving the efficiency of detecting the spallation neutrons. Performance of the apparatus is also presented.

In this article we report on an 8-year process that included three successive iterations of the following cycle: (a) development of instructional technology, (b) formative evaluation, and (c) modification of the technology. From the first formative evaluation to the last, our students told us that they found heavily contextualized language difficult to learn and frequently requested more decontextualized language for textbook presentations and for practice. With the aid of formative evaluation data (e.g., performance data based on think aloud protocols, attitudinal data, retrospective interviews, and course surveys), we tried to strike a balance between what students said they wanted (i.e., more decontextualized language input and practice) and what we as language teachers and curriculum developers believed that they needed (i.e., more contextualized language input and practice). Three theoretical constructs proved particularly relevant in helping us interpret the data: activity theory (Lantolf & Appel, 1994; Lantolf, 2000); the naïve lexical hypothesis (Bland, Noblitt, Armington, & Gay, 1990); and the lexical approach (Lewis, 1993), also known as the lexical syllabus (Willis, 1990). We argue that when formative evaluation becomes a central part of the development of instructional technology, the results are a more learner-centered curriculum with more user-friendly technology.

In brief: Catastrophic spine injuries among football players are decreasing, according to data furnished by the National Collegiate Athletic Association. A total of 105 players incurred permanent cervical cord injuries from 1977 through 1987, with 13 such injuries in 1980 and only seven in 1987. Defensive players are at greater risk for quadriplegia than offensive players, and most are injured while tackling. To further reduce catastrophic spine injuries, players must stop using the head as a battering ram and use the shoulder for blocking and tackling instead.

In brief: The latest data on football deaths and injuries at the college, high school, and youth league levels show that seven direct fatalities and seven permanent cervical cord injuries occurred in 1985, for an incidence in each category of 0.44 per 100,000 players. Direct fatalities have been in single digits for eight years, and the total for the 1975 to 1984 period was significantly lower than for the preceding decade (83 vs 204). Overall, the latest figures indicate a continued decline in football deaths and catastrophic injuries, which is credited to a ban on spearing and to a helmet standard, Guidelines for prevention of fatalities and catastrophic injuries are listed.