The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

Simultaneous analysis of v1, v4, 2v2, v2+v5, and 2v5 bands of 12CH3F

The Fourier-transform spectrum of CH3F from 2800 to 3100 cm−1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm−1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν1(A1), ν4(E), 2ν2(A1), ν2 + ν5(E), 2ν50(A1), and 2ν5±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm−1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.

The method of predicate least squares refinement

Parameters to be determined in a least squares refinement calculation to fit a set of observed data may sometimes usefully be `predicated' to values obtained from some independent source, such as a theoretical calculation. An algorithm for achieving this in a least squares refinement calculation is described, which leaves the operator in full control of the weight that he may wish to attach to the predicate values of the parameters.

Heterosis for yield and its physiological determinants in wheat

Heterosis in hybrid wheat varieties produced using a chemical hybridising agent was assessed in field experiments. Hyno Esta and its parents were compared in factorial combinations of four-seed rates (25-300 seeds m(-2)) and two nitrogen fertilizer rates (0 and 200 kg N ha(-1)) in 2001/02 and again in 2002/03. Hyno Rista and Hyno Renta and their parents were compared at two-seed rates in 2001/02. Hyno Rista and its parents were added factorially to the Hyno Esta experiment in 2002/03, while Hyno Renta and Hybred and their parents were compared at two seed rates in 2002/03. Mid parent heterosis for grain yield was found in three hybrids and two of these showed high parent heterosis. High parent heterosis in Hyno Esta over a range of sowing densities was mostly exhibited in total biomass but also, in one of two years, in harvest index. High parent heterosis in Hyno Renta was associated more with harvest index than with biomass. The heterosis for biomass in Hyno Esta resulted from greater interception of photosynthetically active radiation (PAR) than the male parent, with better radiation use efficiency than the female parent. In both seasons Hyno Esta achieved grain numbers per ear at least as high as the high parent for this trait (Audace), and combined this with mean grain weights at least as heavy as the high parent for mean grain weight (Estica). Much of the increased biomass and grain yield in the hybrid came late in the season as high parent heterosis was expressed for both maximum grain filling rate and grain filling duration. Heterosis was higher when nitrogen was applied than when withheld; only greater at lower seed rates when expressed in proportionate terms (e.g. as a percentage of the parents), rather than in absolute terms (e.g. t ha(-1)); and greater in the year with the cooler and wetter summer.

Extreme host plant conservatism during at least 20 million years of host plant pursuit by oak gallwasps

Diversification of insect herbivores is often associated with coevolution between plant toxins and insect countermeasures, resulting in a specificity that restricts host plant shifts. Gall inducers, however, bypass plant toxins and the factors influencing host plant associations in these specialized herbivores remain unclear. We reconstructed the evolution of host plant associations in Western Palaearctic oak gallwasps (Cynipidae: Cynipini), a species-rich lineage of specialist herbivores on oak (Quercus). (1) Bayesian analyses of sequence data for three genes revealed extreme host plant conservatism, with inferred shifts between major oak lineages (sections Cerris and Quercus) closely matching the minimum required to explain observed diversity. It thus appears that the coevolutionary demands of gall induction constrain host plant shifts, both in cases of mutualism (e.g., fig wasps, yucca moths) and parasitism (oak gallwasps). (2) Shifts between oak sections occurred independently in sexual and asexual generations of the gallwasp lifecycle, implying that these can evolve independently. (3) Western Palaearctic gallwasps associated with sections Cerris and Quercus diverged at least 20 million years ago (mya), prior to the arrival of oaks in the Western Palaearctic from Asia 5-7 mya. This implies an Asian origin for Western Palaearctic gallwasps, with independent westwards range expansion by multiple lineages.

Direct time-resolved study of the gas-phase reactions of germylene with ethyl- and diethylgermane: absolute rate constants, temperature dependences, and mechanism

Time-resolved studies of germylene, GeH2, generated by the 193 nm laser flash photolysis of 3,4-dimethyl-1-germacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reactions with ethyl- and diethylgermanes in the gas phase. The reactions were studied over the pressure range 1-100 Torr with SF6 as bath gas and at five temperatures in the range 297-564 K. Only slight pressure dependences were found for GeH2 + EtGeH3 (399, 486, and 564 K). The high pressure rate constants gave the following Arrhenius parameters: for GeH2 + EtGeH3, log A = -10.75 +/- 0.08 and E-a = -6.7 +/- 0.6 kJ mol(-1); for GeH2 + Et2GeH2, log A = -10.68 +/- 0.11 and E-a = -6.95 +/- 0.80 kJ mol(-1). These are consistent with fast, near collision-controlled, association processes at 298 K. RRKM modeling calculations are, for the most part, consistent with the observed pressure dependence of GeH2 + EtGeH3. The ethyl substituent effects have been extracted from these results and are much larger than the analogous methyl substituent effects in the SiH2 + methylsilane reaction series. This is consistent with a mechanistic model for Ge-H insertion in which the intermediate complex has a sizable secondary barrier to rearrangement.

Gas phase kinetic and quantum chemical studies of the reactions of silylene with the methylsilanes. Absolute rate constants, temperature dependences, RRKM modelling and potential energy surfaces

Time resolved studies of silylene, SiH2, generated by the 193 nm laser. ash photolysis of phenylsilane, have been carried out to obtain rate coefficients for its bimolecular reactions with methyl-, dimethyl- and trimethyl-silanes in the gas phase. The reactions were studied over the pressure range 3 - 100 Torr with SF6 as bath gas and at five temperatures in the range 300 - 625 K. Only slight pressure dependences were found for SiH2 + MeSiH3 ( 485 and 602 K) and for SiH2 + Me2SiH2 ( 600 K). The high pressure rate constants gave the following Arrhenius parameters: [GRAPHICS] These are consistent with fast, near to collision-controlled, association processes. RRKM modelling calculations are consistent with the observed pressure dependences ( and also the lack of them for SiH2 + Me3SiH). Ab initio calculations at both second order perturbation theory (MP2) and coupled cluster (CCSD(T)) levels, showed the presence of weakly-bound complexes along the reaction pathways. In the case of SiH2 + MeSiH3 two complexes, with different geometries, were obtained consistent with earlier studies of SiH2 + SiH4. These complexes were stabilised by methyl substitution in the substrate silane, but all had exceedingly low barriers to rearrangement to product disilanes. Although methyl groups in the substrate silane enhance the intrinsic SiH2 insertion rates, it is doubtful whether the intermediate complexes have a significant effect on the kinetics. A further calculation on the reaction MeSiH + SiH4 shows that the methyl substitution in the silylene should have a much more significant kinetic effect ( as observed in other studies).

Total synthesis of (+/-) maculalactone A, maculalactone B and maculalactone C and the determination of the absolute configuration of natural (+) maculalactone A by asymmetric synthesis

Maculalactones A, B and C from the marine cyanobacterium Kyrtuthrix maculans are amongst the only compounds based on the tribenzylbutyrolactone skeleton known in nature and (+) maculalactone A from the natural source possesses significant biological activity against various marine herbivores and marine settlers. We now report a concise synthesis of racemic maculalactone A in five steps from inexpensive starting materials. Maculalactones B and C were synthesized by a minor modification to this procedure, and the synthetic design also permitted an asymmetric synthesis of maculalactone A to be achieved in around 85% ee. The (+) and (-) enantiomers of maculalactone A were assigned, respectively, to the S and R configurations on the basis of the chiral selectivity expected for catecholborane reduction of an unsymmetrical ketone in the presence of Corey's oxazoborolidine catalyst. Surprisingly, it appeared that natural (+) maculalactone A was biosynthesized in K. maculans in a partially racemic form, comprising ca. 90-95% of the (S) enantiomer and 5-10% of its (R) enantiomer. Coincidentally therefore, the percentage enantiomeric excess of the product obtained from asymmetric synthesis almost exactly matched that found in nature. (C) 2004 Elsevier Ltd. All rights reserved.