Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Mental health impacts of flooding: a controlled interrupted time series analysis of prescribing data in England.

BACKGROUND: There is emerging evidence that people affected by flooding suffer adverse impacts on their mental well-being, mostly based on self-reports. METHODS: We examined prescription records for drugs used in the management of common mental disorder among primary care practices located in the vicinity of recent large flood events in England, 2011-2014. A controlled interrupted time series analysis was conducted of the number of prescribing items for antidepressant drugs in the year before and after the flood onset. Pre-post changes were compared by distance of the practice from the inundated boundaries among 930 practices located within 10 km of a flood. RESULTS: After control for deprivation and population density, there was an increase of 0.59% (95% CI 0.24 to 0.94) prescriptions in the postflood year among practices located within 1 km of a flood over and above the change observed in the furthest distance band. The increase was greater in more deprived areas. CONCLUSIONS: This study suggests an increase in prescribed antidepressant drugs in the year after flooding in primary care practices close to recent major floods in England. The degree to which the increase is actually concentrated in those flooded can only be determined by more detailed linkage studies

Gold(I)-catalysed one-pot synthesis of chromans using allylic alcohols and phenols

A gold(I)-catalysed reaction of allylic alcohols and phenols produces chromans regioselectively via a one-pot Friedel–Crafts allylation/intramolecular hydroalkoxylation sequence. The reaction is mild, practical and tolerant of a wide variety of substituents on the phenol

Simplified analytical model for tapered sandwich beams using variable stiffness materials

A simplified layer-wise sandwich beam model to capture the effects of a combination of geometric taper and variable stiffness of the core on the static response of a sandwich beam is developed. In the present model, the face sheets are assumed to behave as Euler beams and the core is modelled with a first-order shear deformation theory. With geometrical compatibility enforced at both upper and lower skin/core interfaces, the beam’s field functions are reduced to only three, namely the extensional, transverse and rotational displacements at the mid-plane of the core. The minimum total potential energy method is used in combination with the Ritz technique to obtain an approximate solution. Geometrically nonlinear effects are considered in the present formulation by introducing von Kármán strains into the face sheets and core. Two types of sandwich beams, uniform and tapered, with different boundary conditions are studied. Results show that the proposed model provides accurate prediction of displacements and stresses, compared to three-dimensional finite element analysis. It is found that due to the axial stiffness variation in the core, displacements of beams and stresses of face sheets and core are significantly affected. The potential design space is shown to be expanded by utilizing variable stiffness materials in sandwich constructions. </jats:p

Discrete element modelling of material non-coaxiality in simple shear flows

We investigate the quasi-static simple shear flow of a two-dimensional assembly of cohesionless particles using discrete element method (DEM) simulations. We focus on the unsteady flow regime where the solid would experience significant evolution of stresses, mobilised shear strength and dilation. We construct the DEM model using a discretised-wall confined granular cell where the apparent boundary is allowed to dilate or contract synchronously with the confined solid. A rather uniform simple shear field is achieved across the whole assembly, which benefits rheological studies in generalising constitutive laws for continuum methods. We examine two aspects of the simple shear behaviour: macroscopic stress and strain rate evolution, particularly the non-coaxiality between the principal directions of the two; and micromechanics such as evolution of fabric. For an initially anisotropic specimen sheared under constant normal pressure, the direction of principal stress rotates towards that of the principal strain rate, gradually reducing the degree of non-coaxiality from about 45° to fluctuating around 0°. The rate in approaching coaxiality is slower in samples with larger initial porosity, stress ratio and mean stress. Generally, a faster rate in approaching coaxiality in simple shear is observed in a more dilatant sample, which often shows a larger degree of mobilised fabric anisotropy, suggesting the possible important role of instantaneous internal friction angle. The evolution of principal fabric direction resembles that of the principal stress direction

Gold(I)-Catalysed Direct Thioetherifications Using Allylic Alcohols: an Experimental and Computational Study

A gold(I)-catalysed direct thioetherification reaction between allylic alcohols and thiols is presented. The reaction is generally highly regioselective (S(N)2′). This dehydrative allylation procedure is very mild and atom economical, producing only water as the by-product and avoiding any unnecessary waste/steps associated with installing a leaving or activating group on the substrate. Computational studies are presented to gain insight into the mechanism of the reaction. Calculations indicate that the regioselectivity is under equilibrium control and is ultimately dictated by the thermodynamic stability of the products