Towards a radiocarbon chronology of the Late-Glacial: Sample selection strategies

This paper outlines a dating program designed to test the reproducibility of radiocarbon dates on different materials of Late-Glacial age (plant macrofossils, fossil beetle remains, and the "humic" and "humin" chemical fractions of limnic sediments) using a combination of radiometric (beta counting) and accelerator mass spectrometry (AMS) techniques. The results have implications for the design of sampling strategies and for the development of improved dating protocols, both of which are important if a high-precision C-14 chronology for the Late- Glacial is to be achieved

Reliable computation of the points of intersection of nn spheres in RnR^n

The problem of determining the points of intersection of n spheres in R n has many applications. Examples in 3-D include problems in navigation, in positioning of specific atoms in crystal structures, in reconstructing torso geometries in experimental cardiology, in the `Pentacle Problem,' and in many other problems of distance geometry. The problem is easily formulated as a system of n nonlinear equations in the coordinates of the unknown point(s) of intersection and it is of interest to determine an efficient and reliable method of solution. It is shown that apart from a few square roots the problem is usually easily and robustly solved without iteration by employing standard techniques from linear algebra. In some applications, however, the radii of the spheres may not be known accurately and this can lead to difficulties, particularly when the required point is close to lying in the affine subspace defined by the n centres of the spheres. In such cases it is more appropriate to formulate a nonlinear least squares problem in order to identify a `best approximate solution.' The special structure of this nonlinear least squares problem allows a solution to be calculated through an efficient safeguarded Newton iteration

Animal and celestial motion: the role of an external springboard: De Motu Animalium 2–3

This contribution comments on Aristotle’s De Motu Animalium 2–3 (MA 2–3). In these chapters Aristotle first claims that animal self-motion requires something eternal to the animal that is unmoved. He then poses the question whether, if something moves the whole heavens, there must be something that is unmoved and external. It is perplexing that Aristotle brings up this question in the discussion of animal self-movement. The contribution suggests that the realization that there must be an unmoved mover in the case of heavenly motion motivates the search for something to play that role in the case of animal self-motion

Optically tailored access to metastable electronic states

On irradiating a molecular system with a laser beam of ultraviolet or visible frequency, photon absorption occurs when an electronic state is at a suitable energy level relative to an initial state. Despite meeting this criterion, interesting metastable states can remain inaccessible because of symmetry constraints. In this Letter a mechanism, based on the input of an off-resonant beam, is shown to enable the population of such states. This is achievable because the laser-modified process involves different selection rules compared to conventional photon absorption. The effects of applying the stimulus beam to either a one- or two-photon process are examined

On the calculation of minimum variance estimators for unobservable dependent variables

The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored

Numerical experiments in semi-infinite programming

A quasi-Newton algorithm for semi-infinite programming using an L∞ exact penalty function is described, and numerical results are presented. Comparisons with three Newton algorithms and one other quasi-Newton algorithm show that the algorithm is very promising in practice