English relative clauses in science and engineering journal papers: A comparative corpus-based study for pedagogical purposes

11Yscopu

Differential equations having orthogonal polynomial solutions

AbstractNecessary and sufficient conditions for an orthogonal polynomial system (OPS) to satisfy a differential equation with polynomial coefficients of the form (∗) LN[y] = ∑i=1Nli(x)y(i)(x) = λny(x) were found by H.L. Krall. Here, we find new necessary conditions for the equation (∗) to have an OPS of solutions as well as some other interesting applications. In particular, we obtain necessary and sufficient conditions for a distribution w(x) to be an orthogonalizing weight for such an OPS and investigate the structure of w(x). We also show that if the equation (∗) has an OPS of solutions, which is orthogonal relative to a distribution w(x), then the differential operator LN[·] in (∗) must be symmetrizable under certain conditions on w(x)

Petrography and Geochemistry of Metals in Almahata Sitta Ureilites

Ureilites are ultramafic achondrites, predominantly composed of olivine and pyroxenes with accessory carbon, metal and sulfide. The majority of ureilites are believed to represent the mantle of the ureilite parent body (UPB) [1]. Although ureilites have lost much of their original metal [2], the metal that remains retains a record of the formative processes. Almahata Sitta is predominantly composed of unbrecciated ureilites with a wide range of silicate compositions [3,4]. As a fall it presents a rare opportunity to examine fresh ureilite metal in-situ, and analyzing their highly siderophile element (HSE) ratios gives clues to their formation. Bulk siderophile element analyses of Almahata Sitta fall within the range observed in other ureilites [5]. We have examined the metals in seven ureilitic samples of Almahata Sitta (AS) and one associated chondrite fragment (AS#25)

Weak localisation in bilayer graphene

We have performed the first experimental investigation of quantum interference corrections to the conductivity of a bilayer graphene structure. A negative magnetoresistance - a signature of weak localisation - is observed at different carrier densities, including the electro-neutrality region. It is very different, however, from the weak localisation in conventional two-dimensional systems. We show that it is controlled not only by the dephasing time, but also by different elastic processes that break the effective time-reversal symmetry and provide invervalley scattering.Comment: 4 pages, 4 figures (to be published in PRL

Atomic Scale Depth Profile of Space Weathering in an Itokawa Olivine Grain

No abstract available

Estimating outflow facility parameters for the human eye using hypotensive pressure-time data

We have previously developed a new theory for pressure dependent outflow from the human eye, and tested the model using experimental data at intraocular pressures above normal eye pressures. In this paper, we use our model to analyze a hypotensive pressure-time dataset obtained following application of a Honan balloon. Here we show that the hypotensive pressure-time data can be successfully analyzed using our proposed pressure dependent outflow model. When the most uncertain initial data point is removed from the dataset, then parameter estimates are close to our previous parameter estimates, but clearly parameter estimates are very sensitive to assumptions. We further show that (i) for a measured intraocular pressure-time curve, the estimated model parameter for whole eye surface hydraulic conductivity is primarily a function of the ocular rigidity, and (ii) the estimated model parameter that controls the rate of decrease of outflow with increasing pressure is primarily a function of the convexity of the monotonic pressure-time curve. Reducing parameter uncertainty could be accomplished using new technologies to obtain higher quality datasets, and by gathering additional data to better define model parameter ranges for the normal eye. With additional research, we expect the pressure dependent outflow analysis described herein may find applications in the differential diagnosis, prognosis and monitoring of the glaucomatous eye

A high order qq-difference equation for qq-Hahn multiple orthogonal polynomials

A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when $q\to1$ are studied. Indeed, the difference equation for Hahn multiple orthogonal polynomials given in \cite{Lee} is corrected and obtained as a limiting case

Quantum Monte Carlo treatment of elastic exciton-exciton scattering

We calculate cross sections for low energy elastic exciton-exciton scattering within the effective mass approximation. Unlike previous theoretical approaches, we give a complete, non-perturbative treatment of the four-particle scattering problem. Diffusion Monte Carlo is used to calculate the essentially exact energies of scattering states, from which phase shifts are determined. For the case of equal-mass electrons and holes, which is equivalent to positronium-positronium scattering, we find a_s = 2.1 a_x for scattering of singlet-excitons and a_s= 1.5 a_x for triplet-excitons, where a_x is the excitonic radius. The spin dependence of the cross sections arises from the spatial exchange symmetry of the scattering wavefunctions. A significant triplet-triplet to singlet-singlet scattering process is found, which is similar to reported effects in recent experiments and theory for excitons in quantum wells. We also show that the scattering length can change sign and diverge for some values of the mass ratio m_h/m_e, an effect not seen in previous perturbative treatments.Comment: 6 pages, 6 figures. Revision has updated figures, improved paper structure, some minor correction