The relationship between potential elemental proxies (Mg/Ca, Sr/Ca and Mn/Ca ratios) and environmental factors was investigated for the bivalve Pecten maximus in a detailed field study undertaken in the Menai Strait, Wales, U.K. An age model constructed for each shell by comparison of measured and predicted oxygen-isotope ratios allowed comparison on a… (More)
 We present new annually resolved d 18 O, d 13 C, Mg/Ca, and Sr/Ca ratio records for two shells of the fast growing Mediterranean fan mussel Pinna nobilis, collected from proximal Spanish coast sea grass meadows. The relationship between the potential geochemical proxies and ontogenetic and environmental controlling factors is investigated. Specifically,… (More)
The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating w.r.t. the Tang frame along infinite curves in Euclidean spaces of arbitrary dimension is investigated. If the reference curve is not straight and its curvatures vanish at infinity, we prove that the essential spectrum as a set coincides with the spectrum of the straight tube of the… (More)
We present a numerical study for the first Dirichlet eigenvalue of certain classes of planar regions. Based on this, we propose new types of bounds and establish several conjectures regarding the dependence of this eigenvalue on the perimeter and the area.
We consider the Laplace operator with Dirichlet boundary conditions on a domain in R d and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero. This generalizes our previous results in two dimensions and, as in that case, allows us to obtain an… (More)
The Mg/Ca ratios of biogenic calcite is commonly seen as a valuable palaeo-proxy for reconstructing past ocean temperatures. The temperature dependence of Mg/Ca ratios in bivalve calcite has been the subject of contradictory observations. The palaeoceanographic use of a geochemical proxy is dependent on initial, rigorous calibration and validation of… (More)
We define a sequence of real functions which coincide with Li's coefficients at one and which allow us to extend Li's criterion for the Riemann Hypothesis to yield a necessary and sufficient condition for the existence of zero–free strips inside the critical strip 0 < ℜ(z) < 1. We study some of the properties of these functions, including their oscillatory… (More)
We perform a numerical optimization of the first ten nontrivial eigenvalues of the Neumann Laplacian for planar Euclidean domains. The optimization procedure is done via a gradient method, while the computation of the eigenvalues themselves is done by means of an efficient meshless numerical method allowing for the computation of the eigenvalues for large… (More)
We prove some new upper and lower bounds for the first Dirichlet eigenvalue of a triangle in terms of the lengths of its sides.
We show that as the ratio between the first Dirichlet eigenvalues of a convex domain and of the ball with the same volume becomes large, the same must happen to the corresponding ratio of isoperimetric constants. The proof is based on the generalization to arbitrary dimensions of Pólya and Szegö's 1951 upper bound for the first eigenvalue of the Dirichlet… (More)