Reflexive modules on normal surface singularities and representations of the local fundamental group

We consider the Riemann-Hilbert correspondence on the complement of a normal surface singularity (X,x). Through a closure operation we obtain a correspondence between the category of finite dimensional representations of the local fundamental group and the category of left D_X,x-modules that are reflexive as O_X,x-modules. We show that under this correspondence profinite representations correspond to invariant modules and that these admit a canonical structure as left D_X,x-modules. We prove that the fundamental module is an invariant module if and only if (X,x) is a quotient singularity. Finally we investigate some algebraisation aspects.     

Regimes of radiative and nonradiative transitions in transport through an electronic system in a photon cavity reaching a steady state

We analyze how a multilevel many‐electron system in a photon cavity approaches the steady state when coupled to external leads. When a plunger gate is used to lower cavity photon dressed one‐ and two‐electron states below the bias window defined by the external leads, we can identify one regime with nonradiative transitions dominating the electron transport, and another regime with radiative transitions. Both transitions trap the electrons in the states below the bias bringing the system into a steady state. The order of the two regimes and their relative strength depends on the location of the bias window in the energy spectrum of the system and the initial conditions.

     

Cavity‐photon contribution to the effective interaction of electrons in parallel quantum dots

A single cavity photon mode is expected to modify the Coulomb interaction of an electron system in the cavity. Here we investigate this phenomena in a parallel double quantum dot system. We explore properties of the closed system and the system after it has been opened up for electron transport. We show how results for both cases support the idea that the effective electron‐electron interaction becomes more repulsive in the presence of a cavity photon field. This can be understood in terms of the cavity photons dressing the polarization terms in the effective mutual electron interaction leading to nontrivial delocalization or polarization of the charge in the double parallel dot potential. In addition, we find that the effective repulsion of the electrons can be reduced by quadrupolar collective oscillations excited by an external classical dipole electric field.     

The management of high seas fisheries

The intergovernmental United Nations Conference on Highly Migratory and Straddling Stocks, initiated in 1993 and finished in 1995, addressed the conservation and management of fishery resources located both within the coastal state 200 mile Exclusive Economic Zone (EEZ) and the adjacent high seas. These types of marine resources continue to be a source for international conflicts and debates. The original United Nations Law of the Sea of 1982 failed to address transboundary fisheries in a proper way. In particular, the agreement did not recognize the emergence of the complicated straddling stock issue. In the new United Nations Law of the Sea agreement of 1995, a consensus was reached that the management of the straddling and highly migratory fish stocks should be carried out through regional fisheries management organizations. We present a review of the straddling stock issues in the international agreement emerging from the negotiations within the United Nations. The review is contrasted with and clarified by game theoretic analyses. We also discuss one international fishery exemplifying the case, the Norwegian springspawning herring. The main conclusion is that the local problems, faced during the stage of setting up regional fisheries organizations for the management of straddling and highly migratory fish stocks, are expected to be much more complicated and difficult to solve as compared to the cases of shared fish stocks. In the current paper, we present two reasons for this increased complexity. The first is the larger number of players as compared to the case of shared fish stocks and the second is the possibility of new members entering the regional fisheries organizations.     

The quadrupole moment of the 3/2+ nuclear ground state of 197Au from electric field gradient relativistic coupled cluster and density-functional theory of small molecules and the solid state

An attempt is made to improve the currently accepted muonic value for the 197Au nuclear quadrupole moment [+0.547(16)x10(-28) m2] for the 3/2+ nuclear ground state obtained by Powers et al. [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of +0.60x10(-28) m2 is obtained. Recent Fourier transform microwave measurements for gas-phase AuF, AuCl, AuBr, and AuI give accurate bond distances and nuclear quadrupole coupling constants for the 197Au isotope. However, four-component relativistic density-functional calculations for these molecules yield unreliable results for the 197Au nuclear quadrupole moment. Relativistic singles-doubles coupled cluster calculations including perturbative triples [CCSD(T) level of theory] for these diatomic systems are also inaccurate because of large cancellation effects between different field gradient contributions subsequently leading to very small field gradients. Here one needs very large basis sets and has to go beyond the standard CCSD(T) procedure to obtain any reliable field gradients for gold. From recent microwave experiments by Gerry and co-workers [Inorg. Chem. 40, 6123 (2001)] a significantly enhanced (197)Au nuclear quadrupole coupling constant in (CO)AuF compared to free AuF is observed. Here, these cancellation effects are less important, and relativistic CCSD(T) calculations finally give a nuclear quadrupole moment of +0.64x10(-28) m2 for 197Au. It is argued that it is currently very difficult to improve on the already published muonic value for the 197Au nuclear quadrupole moment.     

Synthesis of both enantiomers of the docosahexaenoic acid ester of 13-hydroxyoctadecadienoic acid (13-DHAHLA)

Recently, several different classes of endogenous lipids have been reported that display antidiabetic and anti-inflammatory effects. Due to their minute presence in human samples, access to synthetic material of each enantiomer becomes necessary for exact structural elucidation and extensive biological evaluation. Herein we report the multi-milligram synthesis of both enantiomers of the docosahexaenoic acid ester of 13-hydroxyoctadecadienoic acid (13-DHAHLA) from commercially available starting materials.     

Multi-mode transport through a quantum nanowire with two embedded dots

We investigate the conductance of a quantum wire with two embedded quantum dots using a T-matrix approach based on the Lippmann-Schwinger formalism. The quantum dots are represented by a quantum well with Gaussian shape and the wire is two-dimensional with parabolic confinement in the transverse direction. In a broad wire the transport can assume a strong nonadiabatic character and the conductance manifests effects caused by intertwined inter- and intra-dot processes that are identified by analysis of the “nearfield” probability distribution of the transported electrons.     

Local and superlinear convergence for truncated iterated projections methods

Least change secant updates can be obtained as the limit of iterated projections based on other secant updates. We show that these iterated projections can be terminated or truncated after any positive number of iterations and the local and the superlinear rate of convergence are still maintained. The truncated iterated projections method is used to find sparse and symmetric updates that are locally and superlinearly convergent. A part of this paper was presented at the Third International Workshop on Numerical Analysis, IIMAS, University of Mexico, January 1981 and ORSA-TIMS National Meeting, Houston, October 1981.