Tensor products of subspace lattices and rank one density

We show that, if M is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, L is a commutative subspace lattice and P is the lattice of all projections on a separable Hilbert space, then L⊗M⊗P is reflexive. If M is moreover an atomic Boolean subspace lattice while L is any subspace lattice, we provide a concrete lattice theoretic description of L⊗M in terms of projection valued functions defined on the set of atoms of M . As a consequence, we show that the Lattice Tensor Product Formula holds for AlgM and any other reflexive operator algebra and give several further corollaries of these results.

Entanglement properties of spin models in triangular lattices

The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement spectrum is linked to the symmetries that protect the different quantum phases. This relation extends even further at the phase transitions where a direct link associates the entanglement spectrum to the conformal field theory describing the former. For 2D systems much less is known. The lattice geometry becomes a crucial aspect to consider when studying entanglement and phase transitions. Here, we analyze the entanglement properties of triangular spin lattice models by also considering concepts borrowed from quantum information theory such as geometric entanglement.

From ideal reactor concepts to reality:The novel drum reactor for photocatalytic wastewater treatment

This article reports the development of a novel drum photocatalytic reactor for treating dye effluent streams. The parameters for operation including drum rotation speed, light source distance, catalyst loading and H2O2 doping have been investigated using methylene blue as a model pollutant. Effluent can be generated by a number of domestic and industrial sources, including pharmaceutical, oil and gas, agricultural, food and chemical sectors. The work reported here proposes the application of semiconductor photocatalysis as a final polishing step for the removal of hydrocarbons from effluents sources, initial studies have proved effective in removing residual hydrocarbons from the effluent.

2D Monolayer MoS2–Carbon Interoverlapped Superstructure: Engineering Ideal Atomic Interface for Lithium Ion Storage: Engineering Ideal Atomic Interface for Lithium Ion Storage

A novel strategy for the controlled synthesis of 2D MoS<inf>2</inf>/C hybrid nanosheets consisting of the alternative layer-by-layer interoverlapped single-layer MoS<inf>2</inf> and mesoporous carbon (m-C) is demonstrated. Such special hybrid nanosheets with a maximized MoS<inf>2</inf>/m-C interface contact show very good performance for lithium-ion batteries in terms of high reversible capacity, excellent rate capability, and outstanding cycling stability.

Irish language education and the national ideal: The dynamics of nationalism in Northern Ireland

Since the beginning of the Northern Ireland conflict in the late 1960s, Irish nationalism has been identified as a prominent force in the political culture of the state. Recent studies have suggested, however, that the ‘Nationalist’ population has become increasingly content within the new political framework created by the peace process and the aspiration for Irish unity diminished. In placing the Northern Ireland situation within the theoretical framework of nationalism, this paper will analyse how these changing priorities have been possible. Through an analysis of Irish language study in Northern Ireland's schools, the paper will examine how the political ideals espoused by the nationalist Sinn Féin Party reflected the priorities of the ‘nationalist community’. It will be contended that the relationship between the ideology and ‘the people’ is much more complex than is often allowed for and that educational inequalities are a significant contributing factor to this.

On lattices from combinatorial game theory modularity and a representation theorem: Finite case

We show that a self-generated set of combinatorial games, S, may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question “Is there a set which will give an on-distributive but modular lattice?” appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented.

The Structure of Design Processes: ideal and reality in Bruce Archer’s 1968 doctoral thesis

The paper centres on a single document, the 1968 doctoral thesis of L Bruce Archer. It traces the author’s earlier publications and the sources that informed and inspired his thinking, as a way of understanding the trajectory of his ideas and the motivations for his work at the Royal College of Art from 1962. Analysis of the thesis suggests that Archer’s ambition for a rigorous ‘science of design’ inspired by algorithmic approaches was increasingly threatened with disruption by his experience of large, complex design projects. His attempts to deal with this problem are shown to involve a particular interpretation of cybernetics. The paper ends with Archer’s own retrospective view and a brief account of his dramatically changed opinions. Archer is located as both a theorist and someone intensely interested in the commercial world of industrial design.

Perceived Social Pressures and the Internalization of the Mesomorphic Ideal: the Role of Drive for Muscularity and Autonomy in Physically Active Men

BACKGROUND: Researchers have tested the beliefs of sportspeople and sports medicine specialists that cognitive strategies influence strength performance. Few investigators have synthesised the literature. OBJECTIVES: The specific objectives were to review evidence regarding (a) the cognitive strategy-strength performance relationship; (b) participant skill level as a moderator; and (c) cognitive, motivational, biomechanical/physiological, and emotional mediators. METHOD: Studies were sourced via electronic databases, reference lists of retrieved articles, and manual searches of relevant journals. Studies had to be randomised or counterbalanced experiments with a control group or condition, repeated measures, and a quality control score above 0.5 (out of 1). Cognitive strategies included goal setting, imagery, self-talk, preparatory arousal, and free choice. Dependent variables included maximal strength, local muscular endurance, or muscular power. RESULTS: Globally, cognitive strategies were reliability associated with increased strength performance (results ranged from 61 to 65 %). Results were mixed when examining the effects of specific strategies on particular dependent variables, although no intervention had an overall negative influence. Indeterminate relationships emerged regarding hypothesised mediators (except cognitive variables) and participant skill level as a moderator. CONCLUSIONS: Although cognitive strategies influence strength performance, there are knowledge gaps regarding specific types of strength, especially muscular power. Cognitive variables, such as concentration, show promise as possible mediators.

On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

Ideal Body Size as a Mediator for the Gender-Specific Association Between Socioeconomic Status and Body Mass Index: Evidence From an Upper-Middle-Income Country in the African Region.

While obesity continues to rise globally, the associations between body size, gender, and socioeconomic status (SES) seem to vary in different populations, and little is known on the contribution of perceived ideal body size in the social disparity of obesity in African countries. We examined the gender and socioeconomic patterns of body mass index (BMI) and perceived ideal body size in the Seychelles, a middle-income small island state in the African region. We also assessed the potential role of perceived ideal body size as a mediator for the gender-specific association between SES and BMI. A population-based survey of 1,240 adults aged 25 to 64 years conducted in December 2013. Participants' BMI was calculated based on measured weight and height; ideal body size was assessed using a nine-silhouette instrument. Three SES indicators were considered: income, education, and occupation. BMI and perceived ideal body size were both higher among men of higher versus lower SES (p< .001) but lower among women of higher versus lower SES (p< .001), irrespective of the SES indicator used. Multivariate analysis showed a strong and direct association between perceived ideal body size and BMI in both men and women (p< .001) and was consistent with a potential mediating role of perceived ideal body size in the gender-specific associations between SES and BMI. Our study emphasizes the importance of gender and socioeconomic differences in BMI and ideal body size and suggests that public health interventions that promote perception of healthy weight could help mitigate SES-related disparities in BMI.

Explorations and comparisons of actual, ideal, and ought forgiveness definitions : a Q-methodological study /

Numerous definitions of forgiveness have been proposed in the literature (e.g.. North, 1987; Enright, Freedman & Rique, 1998), most ofwhich are based on religious or philosophical notions, rather than on empirical evidence. Definitions employed by researchers have typically set very high standards for forgiveness. This research was designed to investigate the possibility that these definitions describe an ideal of forgiveness and may not reflect laypersons' beliefe and experiences. Using Higgins' Self-Discrepancy Theory as a fiamework, three types of forgiveness beliefs were investigated: actual, ideal, and ought Q-methodology (which permits intensive study ofphenomena in small samples) was employed to examine and compare participants' beliefs about forgiveness across these domains. Thirty participants (20 women), 25 to 78 years of age, were recruited firom the community. They were asked to sort a set of66 statements about forgiveness according to their level of agreement with each statement This process was repeated three times, with the goal of modelling participants' actual experiences, their ideals, and how they believed forgiveness ought to be. Three perspectives on forgiveness emerged across the domains: forgiveness as motivated by religious beliefs, reconciliation-focussed forgiveness, and conflicted forgiveness. These perspectives indicated that, for many participants, the definitions presented in the literature may coincide with their beliefs about how forgiveness would ideally be and should be, as well as with their experiences of forgiveness; however, a large number of participants' experiences of, and beliefs about, forgiveness do not conform to the standards set out in the literature, and to exclude these participants' experiences and beliefs would mean overlooking what forgiveness means to a large portion of people. Results of this study indicate that researchers need to keep an open mind about what forgiveness may mean to their participants.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.