Hankel and Toeplitz transforms on H 1: continuity, compactness and Fredholm properties

We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H 1 and give a new proof of the old result stating that the Hankel operator H a is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H a to be compact on H 1. The Fredholm properties of Toeplitz operators on H 1 are studied for symbols in a Banach algebra similar to C + H ∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H 1 and H 2.

Haptics in medicine and clinical skill acquisition

THE clinical skills of medical professionals rely strongly on the sense of touch, combined with anatomical and diagnostic knowledge. Haptic exploratory procedures allow the expert to detect anomalies via gross and fine palpation, squeezing, and contour following. Haptic feedback is also key to medical interventions, for example when an anaesthetist inserts an epidural needle, a surgeon makes an incision, a dental surgeon drills into a carious lesion, or a veterinarian sutures a wound. Yet, current trends in medical technology and training methods involve less haptic feedback to clinicians and trainees. For example, minimally invasive surgery removes the direct contact between the patient and clinician that gives rise to natural haptic feedback, and furthermore introduces scaling and rotational transforms that confuse the relationship between movements of the hand and the surgical site. Similarly, it is thought that computer-based medical simulation and training systems require high-resolution and realistic haptic feedback to the trainee for significant training transfer to occur. The science and technology of haptics thus has great potential to affect the performance of medical procedures and learning of clinical skills. This special section is about understanding

Parental death as a vital conjuncture? Intergenerational care and responsibility following bereavement in Senegal

This article explores the ways that parental death represents a 'vital conjuncture' for Serer young people that reconfigures and potentially transforms intergenerational caring responsibilities in different spatial and temporal contexts. Drawing on semi-structured interviews with young people (aged 15-27), family members, religious and community leaders and professionals in rural and urban Senegal, I explore young people's responses to parental death. 'Continuing bonds' with the deceased were expressed through memories evoked in homespace, shared family practices and gendered responsibilities to 'take care of' bereaved family members, to cultivate inherited farmland and to fulfil the wishes of the deceased. Parental death could reconfigure intergenerational care and lead to shifts in power dynamics, as eldest sons asserted their position of authority. While care-giving roles were associated with agency, the low social status accorded to young women's paid and unpaid domestic work undermined their efforts. The research contributes to understandings of gendered nuances in the experience of bereavement and continuing bonds and provides insight into intra-household decision-making processes, ownership and control of assets. Analysis of the culturally specific meanings of relationships and a young person's social location within hierarchies of gender, age, sibling birth order and wider socio-cultural norms and practices is needed.

A carbamazepine-indomethacin (1:1) cocrystal produced by milling

An X-ray amorphous mixture of carbamazepine and indomethacin transforms upon annealing to produce a novel 1:1 cocrystal, whose structure has been determined from laboratory powder X-ray diffraction (PXRD) data.

A carbamazepine-indomethacin (1 : 1) cocrystal produced by milling

An X-ray amorphous mixture of carbamazepine and indomethacin transforms upon annealing to produce a novel 1 : 1 cocrystal, whose structure has been determined from laboratory powder X-ray diffraction (PXRD) data

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Sparse shape representation using the Laplace-Beltrami eigenfunctions and its application to modeling subcortical structures

We present a new sparse shape modeling framework on the Laplace-Beltrami (LB) eigenfunctions. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes by forming a Fourier series expansion. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we propose to filter out only the significant eigenfunctions by imposing l1-penalty. The new sparse framework can further avoid additional surface-based smoothing often used in the field. The proposed approach is applied in investigating the influence of age (38-79 years) and gender on amygdala and hippocampus shapes in the normal population. In addition, we show how the emotional response is related to the anatomy of the subcortical structures.

Fourier transform infrared spectra of H2CS and D2CS

Infrared spectra of thoformaldehyde, H2CS and D2CS, were observed in the gas phase at a resolution of better than 0.1 cm−1 from 4000 to 400 cm−1 using a Nicolet FTIR system. Vibrational band origins and rotational constants were determined for ν2, ν3, ν4, and ν6 of H2CS and for ν1, ν2, ν3, ν4, and ν6 of D2CS. The ν3, ν4, and ν6 bands of H2CS were analyzed as a set of three Coriolis interacting bands, and three Coriolis constants were determined; similarly the ν4 and ν6 bands of D2CS were analyzed as a pair of interacting bands and one Coriolis constant was determined. A general harmonic force field was determined, without constraints, to fit the vibrational wavenumbers, Coriolis constants, and centrifugal distortion constants. A zero-point (rz) structure was determined from the ground-state rotational constants, and the equilibrium (re) bond lengths were estimated.

Remote gas detection and quantitative analysis from infrared emission spectra obtained by Fourier transform infrared spectroscopy

Techniques for obtaining quantitative values of the temperatures and concentrations of remote hot gaseous effluents from their measured passive emission spectra have been examined in laboratory experiments. The high sensitivity of the spectrometer in the vicinity of the 2397 cm-1 band head region of CO2 has allowed the gas temperature to be calculated from the relative intensity of the observed rotational lines. The spatial distribution of the CO2 in a methane flame has been reconstructed tomographically using a matrix inversion technique. The spectrometer has been calibrated against a black body source at different temperatures and a self absorption correction has been applied to the data avoiding the need to measure the transmission directly. Reconstruction artifacts have been reduced by applying a smoothing routine to the inversion matrix.

Assembling spatially explicit landscape models of pollen and spore dispersal by wind for risk assessment

Models of windblown pollen or spore movement are required to predict gene flow from genetically modified (GM) crops and the spread of fungal diseases. We suggest a simple form for a function describing the distance moved by a pollen grain or fungal spore, for use in generic models of dispersal. The function has power-law behaviour over sub-continental distances. We show that air-borne dispersal of rapeseed pollen in two experiments was inconsistent with an exponential model, but was fitted by power-law models, implying a large contribution from distant fields to the catches observed. After allowance for this 'background' by applying Fourier transforms to deconvolve the mixture of distant and local sources, the data were best fit by power-laws with exponents between 1.5 and 2. We also demonstrate that for a simple model of area sources, the median dispersal distance is a function of field radius and that measurement from the source edge can be misleading. Using an inverse-square dispersal distribution deduced from the experimental data and the distribution of rapeseed fields deduced by remote sensing, we successfully predict observed rapeseed pollen density in the city centres of Derby and Leicester (UK).

Fourier transform, null variety, and Laplacian's eigenvalues

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.