This study is designed to understand embarrassment in the second/foreign language (L2) context. Following a mixed-method design, in Phase 1, a sample of 141 tertiary-level Austrian English language learners were asked to write a narrative about their experiences of embarrassment in their language learning histories. Analyzing the narratives showed that L2 embarrassment is a multidimensional construct that is frequently experienced by a range of language learners. In Phase 2, we developed and validated an L2 classroom speaking embarrassment (L2CSE) scale among a sample of 402 international English language learners drawing on the literature and analysis of the narratives. Data showed that L2 embarrassment is best represented by a bifactor exploratory structural equation model, capturing both general and specific aspects of L2 embarrassment. We found that a supportive classroom environment and fostering a growth mindset can decrease the risk of L2 embarrassment. As expected, L2 embarrassment was a negative predictor of willingness to communicate and self-perceived language proficiency. These initial findings suggest that L2 embarrassment could be an important and influential emotion in the language learning classroom context which requires further research.

The TEDI (TripleSpec - Exoplanet Discovery Instrument) is a dedicated instrument for the near-infrared radial velocity search for planetary companions to low-mass stars with the goal of achieving meters-per-second radial velocity precision. Heretofore, such planet searches have been limited almost entirely to the optical band and to stars that are bright in this band. Consequently, knowledge about planetary companions to the populous but visibly faint low-mass stars is limited. In addition to the opportunity afforded by precision radial velocity searches directly for planets around low mass stars, transits around the smallest M dwarfs offer a chance to detect the smallest possible planets in the habitable zones of the parent stars. As has been the the case with followup of planet candidates detected by the transit method requiring radial velocity confirmation, the capability to undertake efficient precision radial velocity measurements of mid-late M dwarfs will be required. TEDI has been commissioned on the Palomar 200” telescope in December 2007, and is currently in a science verification phase.

A holistic approach to care has traditionally been the central tenet of general practice in the UK. However, recent major changes in general practice may be diminishing the importance and/or deliverability of such an approach. We sought to explore the views of Scotland’s general practitioner (GP) principals. We surveyed all 3713 GP principals in Scotland during February to July 2001 by postal questionnaire. Nearly 9 in 10 GPs (87%) felt that a holistic approach was essential to providing good health care, but only 1 in 5 (21%) felt that primary care was currently delivering high-quality holistic care, and only 1 in 15 (7%) felt that the current organization of primary care was conducive to such care. Constraints on holism were thought to contribute significantly to higher rates of prescribing (73% agreed), more referrals to secondary care (63% agreed), and increased demand for complementary therapies (57% agreed). Psychological factors were considered to play an important role in organic physical disease – its causation (67% agreed), course (94% agreed) and reversal (69% agreed) – yet when either the GP or the patient wished to explore issues relating to stress or emotional difficulties the GPs felt significantly constrained, mainly by time and their own stress (mean values (95% CI); 0: not limiting, 10: extremely limiting; time 7.6 (7.49–7.67); stress 4.9 (4.84–5.04); training 4.7 (4.66–4.84); skills 4.2 (4.13–4.30); motivation 3.4 (3.33–3.50)). In this survey Scotland’s principal GPs overwhelmingly endorse the traditional holistic approach of general practice and primary care, but feel that it is failing to be delivered due to organizational and time constraints, with consequent human and financial costs. These results give voice to deep concerns among GPs who remain committed to a holism they are struggling to deliver.

We call $\alpha \left( z \right)={{a}_{0}}+{{a}_{1}}z+\cdot \cdot \cdot +{{a}_{n-1}}{{z}^{n-1}}$ a Littlewood polynomial if ${{a}_{j}}=\pm 1$ for all $j$ . We call $\alpha \left( z \right)$ self-reciprocal if $\alpha \left( z \right)={{z}^{n-1}}\alpha \left( 1/z \right)$ , and call $\alpha \left( z \right)$ skewsymmetric if $n=2m+1$ and ${{a}_{m+j}}={{\left( -1 \right)}^{j}}{{a}_{m-j}}$ for all $j$ . It has been observed that Littlewood polynomials with particularly high minimum modulus on the unit circle in $\mathbb{C}$ tend to be skewsymmetric. In this paper, we prove that a skewsymmetric Littlewood polynomial cannot have any zeros on the unit circle, as well as providing a new proof of the known result that a self-reciprocal Littlewood polynomial must have a zero on the unit circle.

We define ${\mathcal B}_n$ to be the set of $n$-tuples of the form $(a_0, {\ldots}\,, a_{n-1})$ where $a_j = \pm 1$. If $A \in {\mathcal B}_n$, then we call $A$ a binary sequence and define the autocorrelations of $A$ by $c_k := \sum_{j=0}^{n-k-1} a_j a_{j+k}$ for $0 \leq k \leq n-1$. The problem of finding binary sequences with autocorrelations ‘near zero’ has arisen in communications engineering and is also relevant to conjectures of Littlewood and Erdős on ‘flat’ polynomials with $\pm 1$ coefficients. Following Turyn, we define \[ b(n) := \min_{A \in {\mathcal B}_n} \max_{1 \leq k \leq n-1} |c_k|.\] The purpose of this article is to show that, using some known techniques from discrete probability, we can improve upon the best upper bound on $b(n)$ appearing in the previous literature, and we can obtain both asymptotic and exact expressions for the expected value of $c_k^m$ if the $a_j$ are independent $\pm 1$ random variables with mean 0. We also include some brief heuristic remarks in support of the unproved conjecture that $b(n) = O(\sqrt{n})$.

In the years leading up to the First World War the academic understanding of the earthen mounds we know as mottes underwent a series of dramatic changes. Exploration of the paradigms behind these viewpoints tells us much about the way in which knowledge comes into being and is used. In particular, archaeologists have created their own foundation myths, complete with hero and demon figures, which serve to emphasize a progressive account of research. The reality is often somewhat more reactionary. In this paper I argue that archaeological histories have impeded understanding of the discipline as the complexities of research remain hidden. As viewpoints become entrenched, creative thought is stifled because the subject is believed to be understood. In castle studies, one a-priori paradigm is that the English motte-and-bailey castle was introduced by the Normans, an idea commonly attributed to Ella Armitage. This paper explores the context behind the adoption of this idea through a case study focusing on changes in understanding. Acrimonious dismissal of alternative points of view has maintained the dominance of this paradigm. I conclude that critical historiographies such as this best serve the development of future understanding of the discipline.