SETAR model selection-A bootstrap approach

Summary  The aim of this paper is to propose new selection criteria for the orders of selfexciting threshold autoregressive (SETAR) models. These criteria use bootstrap methodology; they are based on a weighted mean of the apparent error rate in the sample and the average error rate obtained from bootstrap samples not containing the point being predicted. These new criteria are compared with the traditional ones based on the Akaike information criterion (AIC). A simulation study and an example on a real data set end the paper.     

Chemo- and regioselectivity in the reactions of polyfunctional pyrroles

The chemo- and regioselectivity of the reduction, oxidation and Wittig reaction of polyfunctional pyrroles, containing a variety of reactive centres was investigated. The reaction of 3,5-dichloropyrrole-2,4-dicarboxaldehydes with potassium permanganate leads to regioselective oxidation of the 2-formyl group, while the Wittig reaction with 1 equiv of a triphenylphosphorane produced the 2-alkenyl substituted pyrroles.     

Stereoselective Control by Face‐to‐Face Versus Edge‐to‐Face Aromatic Interactions: The Case of C3‐TiIV Amino Trialkolate Sulfoxidation Catalysts

The stereoselective oxidation of differently functionalised benzyl phenyl sulfides has been examined by using enantiopure Ti^IV trialkanolamine complexes. These complexes efficiently catalyse the sulfoxidation with good stereoselectivities. The data highlight the contribution to the stereoselectivity of steric effects and non‐covalent π–π interactions between the aromatic rings of the Ti^IV complex and those pertaining to the substrates. Enantiomeric excesses have been correlated with the electrostatic potential surfaces (EPS) of the reacting sulfides. The overall study leads to a mechanistic interpretation that explains the stereoselectivity of the system and dissects the role of aromatic and steric interactions in the stereoselective process.     

Weak bimonoids in duoidal categories

Weak bimonoids in duoidal categories are introduced. They provide a common generalization of bimonoids in duoidal categories and of weak bimonoids in braided monoidal categories. Under the assumption that idempotent morphisms in the base category split, they are shown to induce weak bimonads (in four symmetric ways). As a consequence, they have four separable Frobenius base (co)monoids, two in each of the underlying monoidal categories. Hopf modules over weak bimonoids are defined by weakly lifting the induced comonad to the Eilenberg–Moore category of the induced monad. Making appropriate assumptions on the duoidal category in question, the fundamental theorem of Hopf modules is proven which says that the category of modules over one of the base monoids is equivalent to the category of Hopf modules if and only if a Galois-type comonad morphism is an isomorphism.     

Uniqueness of selfdual periodic Chern–Simons vortices of topological-type

In analogy with the abelian Maxwell–Higgs model (cf. Jaffe and Taubes in Vortices and monopoles, 1980) we prove that periodic topological-type selfdual vortex-solutions for the Chern–Simons model of Jackiw–Weinberg [Phys Rev Lett 64:2334–2337, 1990] and Hong et al. Phys Rev Lett 64:2230–2233, 1990 are uniquely determined by the location of their vortex points, when the Chern–Simons coupling parameter is sufficiently small. This result follows by a uniqueness and uniform invertibility property established for a related elliptic problem (see Theorem 3.6 and 3.7). Research supported by M.I.U.R. project: Variational Methods and Nonlinear Differential Equations.     

Model reactions for abiotic mercury(II) methylation: Kinetics of methylation of mercury(II) by mono-, di-, and tri-methyltin in seawater

The usual presence of mercury(II) with monodi-, and tri-methyltin in water, sediments, and plants in estuarine environments suggests possible abiotic formation of methylmercury via methyl transfer from methyltin compounds. Kinetics studies of reactions between mercury(II) and methyltin compounds under pseudo-first-order conditions in seawater show that relative rate of methylmercury formation under the same conditions are: monomethyltin <trimethyltin> dimethyltin. This order is explainable mainly by the speciation and charge of methyltin compounds in seawater and by the existence of mercury(II) as a tetrachloro anion. A factorial experiment with the variables pH and salinity (seawater diluted with deionized water) showed that pH, but not salinity, is significant at the 95% confidence level; and that reaction rates increase as pH increases. These results suggest the possibility of abiotic methylation of mercury(II) in seawater. Additional experiments in seawater demonstrated an absence of methylation of mercury(II) (14 days) and mercury(0) (35 days) by methyl iodide.     

Synthesis of 7-methyl-4,6,6a,7,10,10a-hexa-hydroindolo[4,3-fg]quinazoline derivatives

The synthesis of a series of compounds indolo[4,3-fg]quinazoline related to ergoline (indolo[4,3-fg]quinoline) is reported. The key step of the synthetic sequence is the ring cleavage of the ketone IV. The stereochemistry of the chiral centers is established by the chirality of dihydrolysergic acid I.