Correlations between two sets of angular relation equations

It is shown here that the angular relation equations between direct and reciprocal vectors are very similar to the angular relation equations in Euler's theorem. These two sets of equations are usually treated separately as unrelated equations in different fields. In this careful study, the connection between the two sets of angular equations is revealed by considering the cosine rule for the spherical triangle. It is found that understanding of the correlation is hindered by the facts that the same variables are defined differently and different symbols are used to represent them in the two fields. Understanding the connection between different concepts is not only stimulating and beneficial, but also a fundamental tool in innovation and research, and has historical significance. The background of the work presented here contains elements of many scientific disciplines. This work illustrates the common ground of two theories usually considered separately and is therefore of benefit not only for its own sake but also to illustrate a general principle that a theory relevant to one discipline can often be used in another. The paper works with chemistry related concepts using mathematical methodologies unfamiliar to the usual audience of mainstream experimental and theoretical chemists.

W(h)ither phonological awareness? Literate trainee teachers’ lack of stable knowledge about the sound structure of words

Recent national developments in the teaching of literacy in the early years in the UK mean that teachers need to have explicit fluent knowledge of the sound structure of the language and its relationship to orthography in order to teach reading effectively. In this study, a group of 38 graduate trainee primary teachers were given a pencil and paper test of phonological awareness as part of a course on teaching literacy. Results from the pencil and paper test were used as the basis of teaching about the sound structure of words. The test was repeated six months later. The results showed that they did not use a consistent system for segmenting words into component sounds. Though there was substantial improvement on second testing, many trainees still did not show evidence that they had yet developed sufficient insights into the sound structure of words to be able to teach children about phonemes with certainty. It is argued that student teachers need substantial explicit training and practice in manipulating the sound structure of words to enable them to teach this aspect of language confidently.

Immediate auditory repetition of words and nonwords: An ERP study of lexical and sublexical processing

ERPs were elicited to (1) words, (2) pseudowords derived from these words, and (3) nonwords with no lexical neighbors, in a task involving listening to immediately repeated auditory stimuli. There was a significant early (P200) effect of phonotactic probability in the first auditory presentation, which discriminated words and pseudowords from nonwords; and a significant somewhat later (N400) effect of lexicality, which discriminated words from pseudowords and nonwords. There was no reliable effect of lexicality in the ERPs to the second auditory presentation. We conclude that early sublexical phonological processing differed according to phonotactic probability of the stimuli, and that lexically-based redintegration occurred for words but did not occur for pseudowords or nonwords. Thus, in online word recognition and immediate retrieval, phonological and/or sublexical processing plays a more important role than lexical level redintegration.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Ratings of age of acquisition of 299 words across 25 languages: is there a cross-linguistic order of words?

We present a new set of subjective age-of-acquisition (AoA) ratings for 299 words (158 nouns, 141 verbs) in 25 languages from five language families (Afro-Asiatic: Semitic languages; Altaic: one Turkic language: Indo-European: Baltic, Celtic, Germanic, Hellenic, Slavic, and Romance languages; Niger-Congo: one Bantu language; Uralic: Finnic and Ugric languages). Adult native speakers reported the age at which they had learned each word. We present a comparison of the AoA ratings across all languages by contrasting them in pairs. This comparison shows a consistency in the orders of ratings across the 25 languages. The data were then analyzed (1) to ascertain how the demographic characteristics of the participants influenced AoA estimations and (2) to assess differences caused by the exact form of the target question (when did you learn vs. when do children learn this word); (3) to compare the ratings obtained in our study to those of previous studies; and (4) to assess the validity of our study by comparison with quasi-objective AoA norms derived from the MacArthur–Bates Communicative Development Inventories (MB-CDI). All 299 words were judged as being acquired early (mostly before the age of 6 years). AoA ratings were associated with the raters’ social or language status, but not with the raters’ age or education. Parents reported words as being learned earlier, and bilinguals reported learning them later. Estimations of the age at which children learn the words revealed significantly lower ratings of AoA. Finally, comparisons with previous AoA and MB-CDI norms support the validity of the present estimations. Our AoA ratings are available for research or other purposes.

Arnold v. Britton: a ratio and two sets of obiter dicta

Arnold v Britton marks the final stage of the longstanding dispute as to the correct interpretation of a number of 99-year leases of chalets on a leisure park at Oxwich, in the Gower peninsula, near Swansea. The aspect of the case which has attracted most discussion has, understandably, been its main ratio: the proper way to construe a provision of a lease which arguably has an absurd result. This will be considered in this case-note. The judgment of the Supreme Court – particularly the judgment of Lord Neuberger PSC – does, however contain some observations on the possible reform of the law on service charges which are of interest to those engaged in this field. It also contains some obiter comments on ‘letting schemes’ which are – in the view of the present author – highly unorthodox. These three rather disparate issues which are raised by this case will be considered in turn. As they have little in common with each other, they will be considered as separate sections.

Phonological therapy in jargon aphasia: effects on naming and neologisms

Background: Jargon aphasia is one of the most intractable forms of aphasia with limited recommendation on amelioration of associated naming difficulties and neologisms. The few naming therapy studies that exist in jargon aphasia have utilized either semantic or phonological approaches but the results have been equivocal. Moreover, the effect of therapy on characteristics of neologisms is less explored. Aims: This study investigates the effectiveness of a phonological naming therapy (i.e., phonological component analysis, PCA) on picture naming abilities and on quantitative and qualitative changes in neologisms for an individual with jargon aphasia (FF). Methods: FF showed evidence of jargon aphasia with severe naming difficulties and produced a very high proportion of neologisms. A single-subject multiple probe design across behaviors was employed to evaluate the effects of PCA therapy on the accuracy for three sets of words. In therapy, a phonological components analysis chart was used to identify five phonological components (i.e., rhymes, first sound, first sound associate, final sound, number of syllables) for each target word. Generalization effects—change in percent accuracy and error pattern—were examined comparing pre-and post-therapy responses on the Philadelphia Naming Test and these responses were analyzed to explore the characteristics of the neologisms. The quantitative change in neologisms was measured by change in the proportion of neologisms from pre- to post-therapy and the qualitative change was indexed by the phonological overlap between target and neologism. Results: As a consequence of PCA therapy, FF showed a significant improvement in his ability to name the treated items. His performance in maintenance and follow-up phases remained comparable to his performance during the therapy phases. Generalization to other naming tasks did not show a change in accuracy but distinct differences in error pattern (an increase in proportion of real word responses and a decrease in proportion of neologisms) were observed. Notably, the decrease in neologisms occurred with a corresponding trend for increase in the phonological similarity between the neologisms and the targets. Conclusions: This study demonstrated the effectiveness of a phonological therapy for improving naming abilities and reducing the amount of neologisms in an individual with severe jargon aphasia. The positive outcome of this research is encouraging, as it provides evidence for effective therapies for jargon aphasia and also emphasizes that use of the quality and quantity of errors may provide a sensitive outcome measure to determine therapy effectiveness, in particular for client groups who are difficult to treat.

Preparation of consistent soil data sets for modelling purposes: Secondary SOTER data for four case study areas

The common GIS-based approach to regional analyses of soil organic carbon (SOC) stocks and changes is to define geographic layers for which unique sets of driving variables are derived, which include land use, climate, and soils. These GIS layers, with their associated attribute data, can then be fed into a range of empirical and dynamic models. Common methodologies for collating and formatting regional data sets on land use, climate, and soils were adopted for the project Assessment of Soil Organic Carbon Stocks and Changes at National Scale (GEFSOC). This permitted the development of a uniform protocol for handling the various input for the dynamic GEFSOC Modelling System. Consistent soil data sets for Amazon-Brazil, the Indo-Gangetic Plains (IGP) of India, Jordan and Kenya, the case study areas considered in the GEFSOC project, were prepared using methodologies developed for the World Soils and Terrain Database (SOTER). The approach involved three main stages: (1) compiling new soil geographic and attribute data in SOTER format; (2) using expert estimates and common sense to fill selected gaps in the measured or primary data; (3) using a scheme of taxonomy-based pedotransfer rules and expert-rules to derive soil parameter estimates for similar soil units with missing soil analytical data. The most appropriate approach varied from country to country, depending largely on the overall accessibility and quality of the primary soil data available in the case study areas. The secondary SOTER data sets discussed here are appropriate for a wide range of environmental applications at national scale. These include agro-ecological zoning, land evaluation, modelling of soil C stocks and changes, and studies of soil vulnerability to pollution. Estimates of national-scale stocks of SOC, calculated using SOTER methods, are presented as a first example of database application. Independent estimates of SOC stocks are needed to evaluate the outcome of the GEFSOC Modelling System for current conditions of land use and climate. (C) 2007 Elsevier B.V. All rights reserved.

Processing of zero-derived words in English: an fMRI investigation

Derivational morphological processes allow us to create new words (e.g. punish (V) to noun (N) punishment) from base forms. The number of steps from the basic units to derived words often varies (e.g., nationalityof multiple surface morphemes. Here we report the first study to investigate morphological processing where derivational steps are not overtly marked (e.g., bridge-N>bridge-V) i.e., zero-derivation ( Aronoff, 1980). We compared the processing of one-step (soakingwords (grumble) in an fMRI experiment. Participants were presented with derived forms of words (soaking, bridging) in a lexical decision task. Although the surface derived -ing forms can be contextually participles, gerunds, or even nouns, they are all derived from verbs since the suffix -ing can only be attached to verb roots. Crucially, the verb root is the basic form for the one-step words, whereas for the two-step words the verb root is zero derived from a basic noun. Significantly increased brain activity was observed for complex (one-step and two-step) versus simple (zero-step) forms in regions involved in morphological processing, such as the left inferior frontal gyrus (LIFG). Critically, activation was also more pronounced for two-step compared to one-step forms. Since both types of derived words have the same surface structure, our findings suggest that morphological processing is based on underlying morphological complexity, independent of overt affixation. This study is the first to provide evidence for the processing of zero derivation, and demonstrates that morphological processing cannot be reduced to surface form-based segmentation.

On the impact of humidity observations in numerical weather prediction

The impact of humidity observations on forecast skill is explored by producing a series of global forecasts using initial data derived from the ERA-40 reanalyses system, in which all humidity data have been removed during the data assimilation. The new forecasts have been compared with the original ERA-40 analyses and forecasts made from them. Both sets of forecasts show virtually identical prediction skill in the extratropics and the tropics. Differences between the forecasts are small and undergo characteristic amplification rate. There are larger differences in temperature and geopotential in the tropics but the differences are small-scale and unstructured and have no noticeable effect on the skill of the wind forecasts. The results highlight the current very limited impact of the humidity observations, used to produce the initial state, on the forecasts.

The frequency and dynamics of stratospheric sudden warmings in the 21st century

Changes to stratospheric sudden warmings (SSWs) over the coming century, as predicted by the Geophysical Fluid Dynamics Laboratory (GFDL) chemistry climate model [Atmospheric Model With Transport and Chemistry (AMTRAC)], are investigated in detail. Two sets of integrations, each a three-member ensemble, are analyzed. The first set is driven with observed climate forcings between 1960 and 2004; the second is driven with climate forcings from a coupled model run, including trace gas concentrations representing a midrange estimate of future anthropogenic emissions between 1990 and 2099. A small positive trend in the frequency of SSWs is found. This trend, amounting to 1 event/decade over a century, is statistically significant at the 90% confidence level and is consistent over the two sets of model integrations. Comparison of the model SSW climatology between the late 20th and 21st centuries shows that the increase is largest toward the end of the winter season. In contrast, the dynamical properties are not significantly altered in the coming century, despite the increase in SSW frequency. Owing to the intrinsic complexity of our model, the direct cause of the predicted trend in SSW frequency remains an open question.

A comparison of diatom phosphorus transfer functions and export coefficient models as tools for reconstructing lake nutrient histories

1. We compared the baseline phosphorus (P) concentrations inferred by diatom-P transfer functions and export coefficient models at 62 lakes in Great Britain to assess whether the techniques produce similar estimates of historical nutrient status. 2. There was a strong linear relationship between the two sets of values over the whole total P (TP) gradient (2-200 mu g TP L-1). However, a systematic bias was observed with the diatom model producing the higher values in 46 lakes (of which values differed by more than 10 mu g TP L-1 in 21). The export coefficient model gave the higher values in 10 lakes (of which the values differed by more than 10 mu g TP L-1 in only 4). 3. The difference between baseline and present-day TP concentrations was calculated to compare the extent of eutrophication inferred by the two sets of model output. There was generally poor agreement between the amounts of change estimated by the two approaches. The discrepancy in both the baseline values and the degree of change inferred by the models was greatest in the shallow and more productive sites. 4. Both approaches were applied to two lakes in the English Lake District where long-term P data exist, to assess how well the models track measured P concentrations since approximately 1850. There was good agreement between the pre-enrichment TP concentrations generated by the models. The diatom model paralleled the steeper rise in maximum soluble reactive P (SRP) more closely than the gradual increase in annual mean TP in both lakes. The export coefficient model produced a closer fit to observed annual mean TP concentrations for both sites, tracking the changes in total external nutrient loading. 5. A combined approach is recommended, with the diatom model employed to reflect the nature and timing of the in-lake response to changes in nutrient loading, and the export coefficient model used to establish the origins and extent of changes in the external load and to assess potential reduction in loading under different management scenarios. 6. However, caution must be exercised when applying these models to shallow lakes where the export coefficient model TP estimate will not include internal P loading from lake sediments and where the diatom TP inferences may over-estimate TP concentrations because of the high abundance of benthic taxa, many of which are poor indicators of trophic state.