Partition theory: A very simple illustration

We illustrate the main features of a recently proposed method based on ensemble density functional theory to divide rigorously a complex molecular system into its parts [M.H. Cohen and A. Wasserman, J. Phys. Chem. A 111, 2229 (2007)]. The illustrative system is an analog of the hydrogen molecule for which analytic expressions for the densities of the parts (hydrogen "atoms") are found along with the "reactivity potential" that enters the theory. While previous formulations of Chemical Reactivity Theory lead to zero, or undefined, values for the chemical hardness of the isolated parts, we demonstrate they can acquire a finite and positive hardness within the present formulation.Comment: 8 pages, 8 figure

Cosmology in the Randall-Sundrum Brane World Scenario

The cosmology of the Randall-Sundrum scenario for a positive tension brane in a 5-D Universe with localized gravity has been studied extensively recently. Here we extend it to more general situations. We consider the time-dependent situation where the two sides of the brane are different AdS/Schwarzschild spaces. We show that the expansion rate in these models during inflation could be larger than in brane worlds with compactified extra dimensions of fixed size. The enhanced expansion rate could lead to the production of density perturbations of substantially larger amplitude.Comment: 11 pages, revte

Post-mission Viking data anaysis

Three Mars data analysis projects from the Viking Mars program were identified initially, and three more came into being as the work proceeded. All together, these six pertained to: (1) the veritical distribution of scattering particles in the Martian atmosphere at various locations in various seasons, (2) the physical parameters that define photometric properties of the Martian surface and atmosphere, (3) patterns of dust-cloud and global dust-storm development, (4) a direct comparison of near-simultaneous Viking and ground-based observations, (5) the annual formation and dissipation of polar frost caps, and (6) evidence concerning possible present-day volcanism or venting. A list of publications pertaining to the appropriate projects is included

On the effectiveness of run-time checks

Run-time checks are often assumed to be a cost-effective way of improving the dependability of software components, by checking required properties of their outputs and flagging an output as incorrect if it fails the check. However, evaluating how effective they are going to be in a future application is difficult, since the effectiveness of a check depends on the unknown faults of the program to which it is applied. A programming contest, providing thousands of programs written to the same specifications, gives us the opportunity to systematically test run-time checks to observe statistics of their effects on actual programs. In these examples, run-time checks turn out to be most effective for unreliable programs. For more reliable programs, the benefit is relatively low as compared to the gain that can be achieved by other (more expensive) measures, most notably multiple-version diversity

Interpretation of the angular dependence of the de Haas-van Alphen effect in MgB_2

We present detailed results for the amplitude and field dependence of the de Haas-van Alphen (dHvA) signal arising from the electron-like $\pi$ sheet of Fermi surface in MgB_2. Our data and analysis show that the dip in dHvA amplitude when the field is close to the basal plane is caused by a beat between two very similar dHvA frequencies and not a spin-zero effect as previously assumed. Our results imply that the Stoner enhancement factors in MgB_2 are small on both the Sigma and Pi sheets.Comment: 4 pages with figures. Submitted to PR

Regularization independent of the noise level: an analysis of quasi-optimality

The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators and we prove that the quasi-optimality criterion determines estimators which are rate-optimal {\em on average}. Its practical performance is illustrated with a calibration problem from mathematical finance.Comment: 18 pages, 3 figure

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He$^+$ scattering.Comment: 5 pages, 2 figures, J. Chem. Phys. accepte

Forms of Knowledge of Advanced Mathematics for Teaching

In this paper, we explore in more detail why knowing advanced mathematics might be beneficial for teachers, specifically in relation to their classroom practice. Rather than by listing courses or specific advanced topics, as though those were the agents of change, we do so by considering advanced mathematical content for teachers in terms of more general forms of knowledge. In particular, we identify five forms of knowledge of advanced mathematics for teaching: peripheral, evolutionary, axiomatic, logical, and inferential. These categories were derived from analysis of an extensive mapping process linking K-12 content to relevant advanced mathematics. We connect these forms of knowledge to particular practices that teachers engage in so as to clarify the perceived relations to classroom practices. We view such work as important to and productive for teacher educators, particularly in conceptualizing and structuring mathematics courses for teachers so that content that truly informs the work of K-12 teaching can be highlighted, and in a manner that facilitates teachers’ formation of those connections