2,128 research outputs found
Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs
We prove persistence of absolutely continuous spectrum for the Anderson model
on a general class of tree-like graphs.Comment: Some clarifications were added in the introduction and an extra
appendix was adde
A comment on "What catch data can tell us about the status of global fisheries"
There is considerable interest in the state of the world’s natural fishery resources. The paper by Froese et al. (2012) is a recent example of applying a set of ad hoc decision rules to a time series of catch data in order to assign the world’s fisheries to categories of exploitation and hence make generalisations about their current status. They conclude that the percentage of stocks that are over-exploited is worse than previously reported in FAO (2010). The approach used by Froese et al. is based on an algorithm proposed by Froese and Kesner-Reyes (2002) which has been heavily criticised both on theoretical grounds and from simulation studies (Branch et al. 2011; Daan et al. 2011; Wilberg and Miller 2007). In their recent paper, Froese et al. (2012) produce additional analyses to support their method which assumes that maximum sustainable yield (MSY) lies in the interval (0.5Cmax, Cmax), where Cmax is the maximum observed catch in the time series. Unfortunately, these analyses do not support their contention that MSY for a particular stock is related to maximum catch in a predictable way and renders their conclusions unsaf
Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg
We report smooth relativistic Hartree-Fock pseudopotentials (also known as
averaged relativistic effective potentials or AREPs) and spin-orbit operators
for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely
non-local behaviour resulting from the exchange interaction in a controlled
manner, and represent the resulting pseudopotentials in an analytic form
suitable for use within standard quantum chemistry codes. These
pseudopotentials are suitable for use within Hartree-Fock and correlated wave
function methods, including diffusion quantum Monte Carlo calculations.Comment: 13 pages, 3 figure
Multiconfiguration Dirac-Hartree-Fock energy levels and transition probabilities for 3d^5 in Fe IV
Multiconfiguration Dirac-Hartree-Fock electric quadrupole (E2) and magnetic
dipole (M1) transition probabilities are reported for transitions between
levels of 3d^5 in [Fe IV]. The accuracy of the ab initio energy levels and the
agreement in the length and velocity forms of the line strength for the E2
transitions are used as indicators of accuracy. The present E2 and M1
transition probabilities are compared with earlier Breit-Pauli results and
other theories. An extensive set of transition probabilites with indicators of
accuracy are reported in Appendices A and B. Recommended values of A(E2) +
A(M1) are listed in Appendix C.Comment: 16 pages, three appendices containing accuracy indicators and
recommended values for E2 and M1 transition rate
Beyond density functional theory: the domestication of nonlocal potentials
Due to efficient scaling with electron number N, density functional theory
(DFT) is widely used for studies of large molecules and solids. Restriction of
an exact mean-field theory to local potential functions has recently been
questioned. This review summarizes motivation for extending current DFT to
include nonlocal one-electron potentials, and proposes methodology for
implementation of the theory. The theoretical model, orbital functional theory
(OFT), is shown to be exact in principle for the general N-electron problem. In
practice it must depend on a parametrized correlation energy functional.
Functionals are proposed suitable for short-range Coulomb-cusp correlation and
for long-range polarization response correlation. A linearized variational
cellular method (LVCM) is proposed as a common formalism for molecules and
solids. Implementation of nonlocal potentials is reduced to independent
calculations for each inequivalent atomic cell.Comment: Accepted for publication in Modern Physics Letters B (2004
Carleman estimates and absence of embedded eigenvalues
Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove
that there is no embedded eigenvalue. The main tool is an Lp Carleman type
estimate, which builds on delicate dispersive estimates established in a
previous paper. The arguments extend to variable coefficient operators with
long range potentials and with gradient potentials.Comment: 26 page
What catch data can tell us about the status of global fisheries
The only available data set on the catches of global fisheries are the official landings reported annually by the Food and Agriculture Organization of the United Nations (FAO). Attempts to detect and interpret trends in these data have been criticized as being both technically and conceptually flawed. Here, we explore and refute these claims. We show explicitly that trends in catch data are not an artifact of the applied method and are consistent with trends in biomass data of fully assessed stocks. We also show that, while comprehensive stock assessments are the preferred method for evaluating single stocks, they are a biased subsample of the stocks in a given area, strongly underestimating the percentage of collapsed stocks. We concur with a recent assessment-based analysis by FAO that the increasing trends in the percentage of overexploited, depleted, and recovering stocks and the decreasing trends in underexploited and moderately exploited stocks give cause for concern. We show that these trends are much more pronounced if all available data are considered
On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials
We consider discrete one-dimensional random Schroedinger operators with
decaying matrix-valued, independent potentials. We show that if the l^2-norm of
this potential has finite expectation value with respect to the product measure
then almost surely the Schroedinger operator has an interval of purely
absolutely continuous (ac) spectrum. We apply this result to Schroedinger
operators on a strip. This work provides a new proof and generalizes a result
obtained by Delyon, Simon, and Souillard.Comment: (1 figure
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