AN ENCOMPASSING APPROACH TO MODELING FISHERY DYNAMICS: MODELING DYNAMIC NONLINEAR SYSTEMS

Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data-based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data.     

Aromatic antimony compounds. Transition metal complexes of 2,5-dimethylstibacyclopentadienyl

Hydrostannation of 2,4-hexadiyne with dibutyltin dihydride gave 1,1-dibutyl-2,5-dimethylstannole, which was converted to 2,5-dimethylstibacymantrene and to bis(2,5-dimethylstibacyclopentadienyl)iron.     

Photolysis of hexamethyldisilane at 206 nm

The photolysis of Me₆Si₂ at 206 nm results in two main decomposition processes: simple Si---Si bond breaking with a quantum yield of Φ = 0.21 ± 0.03, and Me₃SiH elimination with the concomitant formation of Me₂SiCH₂ with Φ = 0.18 ± 0.01. There is also a minor decomposition channel with a very small quantum yield, Φ = (5.6 ± 0.2) × 10⁻³, which results in the formation of Me₄Si and Me₂Si. The main fate of the excited Me₆Si₂ molecule produced during photolysis is stabilization by collisional deactivation. The end products observed indicate that the reaction pathways followed by the main intermediates, Me₃Si and Me₂SiCH₂, are the same as those found in the photolysis of Me₄Si (Ahmed et al., J. Photochem. Photobiol. A: Chem. 86 (1995) 33).     

Direct observation of eta 2-imine formation through beta-H abstraction between amide ligands. Neutron and X-ray diffraction structure of a dihydride imine ditantalum complex

Reactions of Ta(NMe2)5 with D2SiR'Ph (R' = Me, Ph) were found to give a dideuteride eta 2-imine complex (Me2N)3Ta(mu-D)2(mu-N-eta 2-N,C-CH2NMe)Ta(NMe2)3(1-d2) through C-H activation of an amide ligand via beta-H abstraction, and the structure of 1 was confirmed by single crystal neutron and X-ray diffraction.     

Counterexamples in optimal quadrature

It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an -approximation can be an arbitrary function of , i.e., there is no hardest quadrature problem.     

Objective function approximations in mathematical programming

Mathematical programming applications often require an objective function to be approximated by one of simpler form so that an available computational approach can be used. An a priori bound is derived on the amount of error (suitably defined) which such an approximation can induce. This leads to a natural criterion for selecting the best approximation from any given class. We show that this criterion is equivalent for all practical purposes to the familiar Chebyshev approximation criterion. This gains access to the rich legacy on Chebyshev approximation techniques, to which we add some new methods for cases of particular interest in mathematical programming. Some results relating to post-computational bounds are also obtained.This paper was partially supported by the National Science Foundation and by the Office of Naval Research, and was the basis for a plenary lecture delivered at the IX International Symposium on Mathematical Programming in Budapest, Hungary, August 1976.     

Synthesis of an Azasteroid Using an Acyl Iminium Ion-Initiated Tandem Cyclization

An acyl iminium ion-initiated tandem cyclization gave an unexpected dienone product, a seco-azasteroid (2). The factors governing the formation of 2 were investigated in an attempt to optimize its formation. The reaction was applied to a more elaborate system, resulting in the synthesis of the full steroid skeleton of 13-azaandrosta-1,4-diene-3,17-dione (3), which contains the unusual substitution of a chlorine atom for the axial 19-methyl.     

Transference numbers for ultra concentrated solutions of aqueous hydrochloric acid at 25°C

Transference numbers of HCl(aq) solutions at 25°C, from 0.01 to 13.6 mol-kg^–1(m) have been obtained by measuring the emf of cells with transference using hydrogen gas/platinum electrodes. Good agreement is obtained at concentrations up to 1 m with all previous data, and our results strongly corroborate those of King and Spiro over the 2–8m concentration range. The transference numbers of the hydronium ion fit the empirical equation, _H ^HCl = 0.821 + 0.0457m ^1/2 – 2.476×10^–2m – 1.90×10^–4 m ² – 1.45×10^–5 m ³ the maximum deviation in T _H ^HCl being 0.003.     

Copper(II)-catalyzed aerobic oxidation of primary alcohols to aldehydes in ionic liquid [bmpy]PF6

A room-temperature aerobic oxidation of primary alcohols to aldehydes catalyzed by the three-component system acetamido-TEMPO/Cu(ClO(4))(2)/DMAP in the ionic liquid [bmpy]PF(6) has been developed, and the catalysts can be recycled and reused for five runs without any significant loss of catalytic activity. [reaction: see text]