On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

The top 100 questions of importance to the future of global agriculture

Despite a significant growth in food production over the past half-century, one of the most important challenges facing society today is how to feed an expected population of some nine billion by the middle of the 20th century. To meet the expected demand for food without significant increases in prices, it has been estimated that we need to produce 70-100 per cent more food, in light of the growing impacts of climate change, concerns over energy security, regional dietary shifts and the Millennium Development target of halving world poverty and hunger by 2015. The goal for the agricultural sector is no longer simply to maximize productivity, but to optimize across a far more complex landscape of production, rural development, environmental, social justice and food consumption outcomes. However, there remain significant challenges to developing national and international policies that support the wide emergence of more sustainable forms of land use and efficient agricultural production. The lack of information flow between scientists, practitioners and policy makers is known to exacerbate the difficulties, despite increased emphasis upon evidence-based policy. In this paper, we seek to improve dialogue and understanding between agricultural research and policy by identifying the 100 most important questions for global agriculture. These have been compiled using a horizon-scanning approach with leading experts and representatives of major agricultural organizations worldwide. The aim is to use sound scientific evidence to inform decision making and guide policy makers in the future direction of agricultural research priorities and policy support. If addressed, we anticipate that these questions will have a significant impact on global agricultural practices worldwide, while improving the synergy between agricultural policy, practice and research. This research forms part of the UK Government's Foresight Global Food and Farming Futures project.

Solvation dynamics in monohydroxy alcohols: Agreement between theory and different experiments

Recently three different experimental studies on ultrafast solvation dynamics in monohydroxy straight-chain alcohols (C-1-C-4) have been carried out, with an aim to quantify the time constant (and the amplitude) of the ultrafast component. The results reported are, however, rather different from different experiments. In order to understand the reason for these differences, we have carried out a detailed theoretical study to investigate the time dependent progress of solvation of both an ionic and a dipolar solute probe in these alcohols. For methanol, the agreement between the theoretical predictions and the experimental results [Bingemann and Ernsting J. Chem. Phys. 1995, 102, 2691 and Horng et al. J: Phys, Chern, 1995, 99, 17311] is excellent. For ethanol, propanol, and butanol, we find no ultrafast component of the time constant of 70 fs or so. For these three liquids, the theoretical results are in almost complete agreement with the experimental results of Horng et al. For ethanol and propanol, the theoretical prediction for ionic solvation is not significantly different from that of dipolar solvation. Thus, the theory suggests that the experiments of Bingemann and Ernsting and those of Horng et al. studied essentially the polar solvation dynamics. The theoretical studies also suggest that the experimental investigations of Joo et al. which report a much faster and larger ultrafast component in the same series of solvents (J. Chem. Phys. 1996, 104, 6089) might have been more sensitive to the nonpolar part of solvation dynamics than the polar part. In addition, a discussion on the validity of the present theoretical approach is presented. In this theory the ultrafast component arises from almost frictionless inertial motion of the individual solvent molecules in the force field of its neighbors.

Intrinsic large gap quantum anomalous Hall insulators in LaX (X = Br,Cl,I)

We report a theoretical prediction of a new class of bulk and intrinsic quantum anomalous Hall (QAH) insulators LaX (X=Br, Cl, and I) via relativistic first-principles calculations. We find that these systems are innate long-ranged ferromagnets which, with the help of intrinsic spin-orbit coupling, become QAH insulators. A low-energy multiband tight-binding model is developed to understand the origin of the QAH effect. Finally, integer Chern number is obtained via Berry phase computation for each two-dimensional plane. These materials have the added benefit of a sizable band gap of as large as similar to 25 meV, with the flexibility of enhancing it to above 75 meV via strain engineering. The synthesis of LaX materials will provide the impurity-free single crystals and thin-film QAH insulators for versatile experiments and functionalities.

Moduli spaces of vector bundles on a singular rational ruled surface

We study moduli spaces M-X (r, c(1), c(2)) parametrizing slope semistable vector bundles of rank r and fixed Chern classes c(1), c(2) on a ruled surface whose base is a rational nodal curve. We showthat under certain conditions, these moduli spaces are irreducible, smooth and rational (when non-empty). We also prove that they are non-empty in some cases. We show that for a rational ruled surface defined over real numbers, the moduli space M-X (r, c(1), c(2)) is rational as a variety defined over R.