On the ADI method for the Sylvester Equation and the optimal-H2\mathcal{H}_2 points

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal in the sense that for the Lyapunov equation, they yield a residual which is orthogonal to the rational Krylov projection subspace. Via several examples, we show that the pseudo H2-optimal shifts consistently yield nearly optimal low rank approximations to the solutions of the Lyapunov equations

Gamma-ray Novae: Rare or Nearby?

Classical Novae were revealed as a surprise source of gamma-rays in Fermi LAT observations. During the first 8 years since the LAT was launched, 6 novae in total have been detected to > 5 sigma in gamma-rays, in contrast to the 69 discovered optically in the same period. We attempt to resolve this discrepancy by assuming all novae are gamma-ray emitters, and assigning peak one-day fluxes based on a flat distribution of the known emitters to a simulated population. To determine optical parameters, the spatial distribution and magnitudes of bulge and disc novae in M31 are scaled to the Milky Way, which we approximate as a disc with a 20 kpc radius and elliptical bulge with semi major axis 3 kpc and axis ratios 2:1 in the xy plane. We approximate Galactic reddening using a double exponential disc with vertical and radial scale heights of r_d = 5 kpc and z_d = 0.2 kpc, and demonstrate that even such a rudimentary model can easily reproduce the observed fraction of gamma-ray novae, implying that these apparently rare sources are in fact nearby and not intrinsically rare. We conclude that classical novae with m_R < 12 and within ~8 kpc are likely to be discovered in gamma-rays using the Fermi LAT.Comment: Accepted by MNRAS, 10 pages, 7 figure

Polymerization catalysis for the precision synthesis of chiral and sustainable polymers

2011 Spring.Includes bibliographical references.Polymerization catalysis for the precision synthesis of chiral and sustainable polymers is described in this dissertation. The central theme of chiral polymers has revolved around the employment of newly synthesized enantiomeric zirconocenium ester enolate catalysts. These catalysts have been utilized in the asymmetric coordination polymerization of prochiral functionalized vinyl monomers towards optically-active, solution stable, one-handed helical polymers. These enantiomeric catalysts have also been used in the successful kinetic resolution polymerization of a racemic methacrylamide monomer. The stereospecific polymerization of chiral oxazolidinone functionalized alkenes has been performed, producing highly isotactic polymers that assume helical or random-coil secondary conformations, dictated by the proximity of the chiral oxazolidinone to the main-chain of the polymer. Investigating applications of helical polymers, two pseudo-enantiomeric helical poly(phenyl acetylene)s bearing chiral organocatalyst side-groups have been synthesized and the effects of the helix-sense and helicity on the enantioselectivity of these catalysts was subsequently examined. Towards sustainable polymers, renewable butyrolactone-based vinylidene monomers are of particular interest in exploring the prospects of substituting the petroleum-based methacrylate monomers for specialty chemicals production. The polymerization of such monomers by group III and IV transition metal catalysts has been investigated resulting in the synthesis of sustainable polymers with controlled molecular weights. These butyrolactone-based monomers have also been successfully polymerized in a rapid and living fashion, using ambiphilic silicon propagating species

Perylene as an Organic Photocatalyst for the Radical Polymerization of Functionalized Vinyl Monomers through Oxidative Quenching with Alkyl Bromides and Visible Light

The generation of carbon-centered radicals from alkyl bromides through an oxidative quenching pathway using perylene as an organic visible-light photocatalyst is described. This methodology is used to initiate the radical polymerization of methyl methacrylate and other functionalized vinyl monomers. The polymers possess bromide chain-end groups that can be used to reinitiate polymerization to produce block copolymers. Control over the polymerization propagation can be achieved through pulsed light sequences while the ability to use natural sunlight to promote carbon–carbon bond formation produces polymers with dispersity as low as 1.29

Iterator-based temporal logic task planning

Temporal logic task planning for robotic systemssuffers from state explosion when specifications involve largenumbers of discrete locations. We provide a novel approach,particularly suited for tasks specifications with universallyquantified locations, that has constant time with respect tothenumber of locations, enabling synthesis of plans for an arbitrarynumber of them. We propose a hybrid control framework thatuses an iterator to manage the discretised workspace hidingitfrom a plan enacted by a discrete event controller. A downsideof our approach is that it incurs in increased overhead whenexecuting a synthesised plan. We demonstrate that the overheadis reasonable for missions of a fixed-wing Unmanned AerialVehicle in simulated and real scenarios for up to700 000locations

Prospects for probing the gluon density in protons using heavy quarkonium hadroproduction

We examine carefully bottomonia hadroproduction in proton colliders, especially focusing on the LHC, as a way of probing the gluon density in protons. To this end we develop some previous work, getting quantitative predictions and concluding that our proposal can be useful to perform consistency checks of the parameterization sets of different parton distribution functions.Comment: LaTeX, 14 pages, 6 EPS figure

Local Amplification of Platelet Function by 8-Epi Prostaglandin F2α Is Not Mediated by Thromboxane Receptor Isoforms

8-epi-Prostaglandin (PG) F2alpha may be formed by cyclooxygenases 1 and 2 or by a free radical catalyzed process as an isoprostane. Concentrations of 8-epi-PGF2alpha in the range 1 nM to 1 microM induce a dose-dependent increase in platelet shape change, in calcium release from intracellular stores [Ca2+]iand in inositol phosphates; it also causes irreversible platelet aggregation, dependent on thromboxane generation, when incubated with subthreshold concentrations of ADP, thrombin, collagen, and arachidonic acid. Much higher concentrations of 8-epi-PGF2alpha (10-20 microM) alone induce weak, reversible aggregation. Although these effects are prevented by pharmacological thromboxane receptor antagonists, they are unlikely to be mediated by thromboxane receptors. Thus, 8-epi-PGF2alpha does not compete for binding at the stably expressed placental or endothelial isoforms of the thromboxane receptor or for binding of thromboxane ligands to human platelets. Furthermore, the response to 8-epi PGF2alpha exhibits structural specificity versus 8-epi PGF3alpha and PGF2alpha. Concentrations in the range that evoke its effects on platelets do not desensitize the aggregation response stimulated by thromboxane or PGH2 analogs. Unlike primary prostaglandins, which are rapidly metabolized to inactive products, 8-epi PGF2alpha circulates in plasma. However, the systemic concentrations found in healthy volunteers (median 48 pmol/liter) and in patients with hepatic cirrhosis (median 147 pmol/liter), a syndrome of oxidant stress in vivo, fall well below those which modulate platelet function. 8-Epi PGF2alpha may amplify the response to platelet agonists in syndromes where oxidant stress and platelet activation coincide. Despite blockade by thromboxane antagonists, 8-epi PGF2alpha does not activate either of the thromboxane receptor isoforms described in platelets. Activation of a distinct receptor would be consistent with the enzymatic formation of 8-epi PGF2alpha by cyclooxygenases. However, incidental activation of such a receptor by systemic concentrations of 8-epi PGF2alpha is unlikely to occur, even in syndromes of excessive free radical generation in vivo

Synthesis and Ring-Opening Metathesis Polymerization of Second-Generation Dendronized Poly(ether) Monomers Initiated by Ruthenium Carbenes

The Ring-Opening Metathesis Polymerization (ROMP) of second-generation dendronized monomers is described. Using the highly active and fast-initiating third-generation ruthenium complex [(H_2IMes)(pyr)_2Cl_2RuCHPh], moderate to high molecular weight polymers (430-2230 kDa) are efficiently synthesized with low dispersities (Ð = 1.01-1.17). This study highlights the power of the metathesis approach toward polymer synthesis in a context where monomer structure can significantly impede polymerization