Free and projective Banach lattices

We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms, and establish some of their fundamental properties. We give much more detailed results about their structure in the case when there are only a finite number of generators, and give several Banach lattice characterizations of the number of generators being, respectively, one, finite or countable. We define a Banach lattice P to be projective if, whenever X is a Banach lattice, J is a closed ideal in X, Q : X → X/J is the quotient map, T: P → X/J is a linear lattice homomorphism and ε > 0, there exists a linear lattice homomorphism : P → X such thatT = Q º and ∥∥ ≤ (1 + ε)∥T∥. We establish the connection between projective Banach lattices and free Banach lattices, describe several families of Banach lattices that are projective and prove that some are not.

Performance enhancement of a wideband spiral antenna using a stepped ground plane

This study presents the use of a stepped ground plane as a means to increase the gain and front-to-back ratio of an Archimedean spiral which operates in the frequency range 3–10 GHz. The backing structure is designed to optimize the antenna performance in discrete 1 GHz bands by placing each of the eight metal steps one quarter wavelength below the corresponding active regions of the spiral. Simulated and experimental results show that this type of ground plane can be designed to enhance the antenna performance over the entire 105% operating bandwidth of the spiral.

Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements

We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.

Vector bundles on the projective line and finite domination of chain complexes

We present an algebro-geometric approach to a theorem on finite domination of chain complexes over a Laurent polynomial ring. The approach uses extension of chain complexes to sheaves on the projective line, which is governed by a K-theoretical obstruction.

Temperature dependence of the mid-infrared dielectric function of YBCO in the ab plane

We have excited mid-infrared surface plasmons in two YBCO thin films of contrasting properties using attenuated total reflection of light and found that the imaginary part of the dielectric function decreases linearly with reduction in temperature. This result is in contrast with the commonly reported conclusion of infrared normal reflectance studies. If sustained it may clarify the problem of understanding the normal state properties of YBCO and the other cuprates. The dielectric function of the films, epsilon = epsilon(1) + i epsilon(2), was determined between room temperature and 80K: epsilon(1) was found to be only slightly temperature dependent but somewhat sample dependent, probably as a result of surface and grain boundary contamination. The imaginary part, epsilon(2), (and the real part of the conductivity, sigma(1),) decreased linearly with reduction in temperature in both films. Results obtained were: for film 1: epsilon(1) = - 14.05 - 0.0024T and epsilon(2) - 4.11 + 0.086T and for film 2: epsilon(1) = - 24.09 + 0.0013T and epsilon(2) = 7.66 + 0.067T where T is the temperature in Kelvin. An understanding of the results is offered in terms of temperature-dependent intrinsic intragrain inelastic scattering and temperature-independent contributions: elastic and inelastic grain boundary scattering and optical interband (or localised charge) absorption. The relative contribution of each is estimated. A key conclusion is that the interband (or localised charge) absorption is only similar to 10%. Most importantly, the intrinsic scattering rate, 1/tau, decreases linearly with fall in temperature, T, in a regime where current theory predicts dependence on frequency, omega, to dominate. The coupling constant, lambda, between the charge carriers and the thermal excitations has a value of 1.7, some fivefold greater than the far infrared value. These results imply a need to restate the phenomenology of the normal state of high temperature superconductors and seek a corresponding theoretical understanding.

Evaluation of infilled frames: an updated in-plane-stiffness macro-model considering the effects of vertical loads

The influence of masonry infills on the in-plane behaviour of RC framed structures is a central topic in the seismic evaluation and retrofitting of existing buildings. Many models in the literature use an equivalent strut member in order to represent the infill but, among the parameters influencing the equivalent strut behaviour, the effect of vertical loads acting on the frames is recognized but not quantified. Nevertheless a vertical load causes a non-negligible variation in the in-plane behaviour of infilled frames by influencing the effective volume of the infill. This results in a change in the stiffness and strength of the system. This paper presents an equivalent diagonal pin-jointed strut model taking into account the stiffening effect of vertical loads on the infill in the initial state. The in-plane stiffness of a range of infilled frames was evaluated using a finite element model of the frame-infill system and the cross-section of the strut equivalent to the infill was obtained for different levels of vertical loading by imposing the equivalence between the frame containing the infill and the frame containing the diagonal strut. In this way a law for identifying the equivalent strut width depending on the geometrical and mechanical characteristics of the infilled frame was generalized to consider the influence of vertical loads for use in the practical applications. The strategy presented, limited to the initial stiffness of infilled frames, is preparatory to the definition of complete non-linear cyclic laws for the equivalent strut.

Autism in the air: using Point of View Video Priming and Natural Environment Teaching to help children with autism travel by plane

This paper describes a study that used video materials and visits to an airport to prepare children on the autism spectrum for travel by plane. Twenty parents and carers took part in the study with children aged from 3 to 16 years. The authors explain that the methods they used were based on Applied Behaviour Analysis (ABA) research; a video modeling technique called Point-Of-View Video-priming and during visits to an airport they used procedures known as Natural Environment Teaching. The findings suggest that using video and preparing children by taking them through what is likely to happen in the real environment when they travel by plane is effective and the authors suggest these strategies could be used to support children with autism with other experiences they need or would like to engage in such as visits to the dentist or hairdressers and access to leisure centres and other public spaces.

The linear elastic in-plane bending of curved hollow profiles having a thin-walled rectangular section

This paper presents a simple solution for the flexibility calculation of curved profiles having a rectangular thin-walled cross-section. Some assumptions related to geometric details about the shape of the deformed structure are included in the present analysis, aiming at an economic and accurate solution. Results concerning the distortion of the transverse section are compared with the corresponding data from the solution with a thin shell finite element analysis. A flexibility factor for the structure analysed here is presented as a graphical result.

Destructive Groups: The Role of Projective Identification in Suicidal Groups of Young People

Group suicidal behaviour by young people has been attracting increasing worldwide attention, but the subject has rarely been studied from a clinical or psychodynamic perspective. Although etiological factors are not well understood, unconscious as well as conscious group processes likely contribute to self-destructive actions. In this article we discuss the role of projective identification in the development of suicidal behavior by individuals who are part of a destructive group. We consider how these factors may operate, illustrated through a case description of a young man involved with a group of high school students that included at least four who made serious suicide attempts. Recognition and understanding of these forms of communication have important implications for clinical practice and suicide prevention.

Projective Identification and the Fear of Failing: Making Sense of Practice Educators' Experiences of Failing Social Work Students in Practice Learning Settings

The paper focuses on emotions and processes that may arise for practice educators when working with a struggling or failing student in a practice learning setting.1 The paper firstly documents a previously undertaken thematic review of the literature, which explored why practice educators appeared to find it difficult to fail students in practice learning settings. Secondly, the paper draws on two UK qualitative studies that highlighted the emotional distress experienced by practice educators when working with a marginal or failing student. The paper documents key findings using a case study approach from both studies. We argue that the concept of projective identification offers a plausible and illuminating account of the states of mind experienced by practice educators and in making explicit, unconscious states of mind, our aim is that practice educators will feel confident to make appropriate assessment decisions when required.

Floating on the same plane: metropolis, money and the culture of abstraction

This article argues that the emergence of a trans-disciplinary discourse of ‘visual culture’ must be understood as, above all, a constitutively urban phenomenon. More specifically, it is in the historically new form of the capitalist metropolis, as described most famously by Simmel, that the ‘hyper-stimulus’ of modern visual culture has its social and spatial conditions. Paradoxically, however, it is as a result of this that visual culture studies is also intrinsically ‘haunted’ by a certain spectre of the invisible: one rooted in those forms of ‘real abstraction’ which Marx identifies with the commodity and the money form. Considering, initially, the canonical urban visual forms of the collage and the spectacle, these are each read in a certain relation to Simmel’s account of metropolitan life and of the money form, and, through this, to what the author claims are those forms of social and spatial abstraction that must be understood to animate them. Finally, the article returns to the entanglement of the visible and invisible entailed by this, and concludes by making some tentative suggestions about something like a paradoxical urban ‘aesthetic’ of abstraction on such a basis.

Ultra compact inline E-plane waveguide extracted pole bandpass filters

This letter presents an ultra compact extracted pole E-plane filter. The proposed structure can achieve up to 65% size reduction in comparison with a standard extracted pole filter designed at 9.5 GHz centre frequency with a 3% fractional bandwidth. The filter has been fabricated and tested using E-plane waveguide technology. Measurements on a fabricated filter confirm the accuracy of the design method.

Optically reconfigurable E-plane waveguide resonators and filters

This paper presents an optically reconfigurable E-plane waveguide resonator and filter. N-type silicon dice doped with phosphorus is used as the switching element and is connected to the edge of a metallic fin. Illumination of the silicon dice allows realization of a different length of the fin, thus creating a shift in resonant frequency of the structure. Frequency tuning range up to about 5.2% is achieved for the resonator as well as the filter. Measurements on a fabricated optically reconfigurable resonator confirm the accuracy of the design procedure. Measured responses show good agreement with simulation.