Worst case behavior of the steepest edge simplex method

At each nondegenerate iteration of the steepest-edge simplex method one moves from a vertex of the polyhedron, P, of feasible points to an adjacent vertex along an edge that is steepest with respect to the linear objective function ψ. In this paper we show how to construct a sequence of linear programs (P_n,ψ_n) in n variables for which the number of iterations required by the steepest edge simplex method is 2ⁿ−1.     

Realistic quantitative descriptions of electron transfer reactions: diabatic free-energy surfaces from first-principles molecular dynamics

A general approach to calculate the diabatic surfaces for electron-transfer reactions is presented, based on first-principles molecular dynamics of the active centers and their surrounding medium. The excitation energy corresponding to the transfer of an electron at any given ionic configuration (the Marcus energy gap) is accurately assessed within ground-state density-functional theory via a novel penalty functional for oxidation-reduction reactions that appropriately acts on the electronic degrees of freedom alone. The self-interaction error intrinsic to common exchange-correlation functionals is also corrected by the same penalty functional. The diabatic free-energy surfaces are then constructed from umbrella sampling on large ensembles of configurations. As a paradigmatic case study, the self-exchange reaction between ferrous and ferric ions in water is studied in detail.     

Synthesis, structure, and reactivity of Group 4 metallacycles incorporating a Me2C-linked cyclopentadienyl-carboranyl ligand

Group 4 metallacycles [eta5:sigma-Me2C(C5H4)(C2B10H10)]Ti[eta2-N(Me)CH2CH2N(Me)] (1a), [eta5:sigma-Me2C(C5H4)(C2B10H10)]Zr[eta2-N(Me)CH2CH2N(Me)](HNMe2) (1b) and [eta5:sigma-Me2C(C5H4)(C2B10H10)]M[eta2-N(Me)CH2CH2CH2N(Me)] (M = Ti (2a), Zr (2b), Hf (2c)) were synthesized by reaction of [eta5:sigma-Me2C(C5H4)(C2B10H10)]M(NMe2)(2) (M = Ti, Zr, Hf) with MeNH(CH2)(n)NHMe (n = 2, 3). These metal complexes reacted with unsaturated molecules such as 2,6-Me2C6H3NC, PhNCO and PhCN to give exclusively M-N bond insertion products. The M-C(cage) bond remained intact. Such a preference of M-N over M-C(cage) insertion is suggested to most likely be governed by steric factors, and the mobility of the migratory groups plays no obvious role in the reactions. This work also shows that the insertion of unsaturated molecules into the metallacycles is a useful and effective method for the construction of very large ring systems.     

Precise mass measurement of a double-stranded 500 base-pair (309 kDa) polymerase chain reaction product by negative ion electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd.     

Thermal characteristics of bitumen pyrolysis

The pyrolysis behavior of bitumen was investigated using a thermogravimetric analyzer–mass spectrometer system (TG–MS) and a differential scanning calorimeter (DSC) as well as a pyrolysis-gas chromatograph/mass spectrometer system (Py-GC/MS). TG results showed that there were three stages of weight loss during pyrolysis—less than 110, 110–380, and 380–600 °C. Using distributed activation energy model, the average activation energy of the thermal decomposition of bitumen was calculated at 79 kJ mol⁻¹. The evolved gas from the pyrolysis showed that organic species, such as alkane and alkene fragments had a peak maximum temperature of 130 and 480 °C, respectively. Benzene, toluene, and styrene released at 100 and 420 °C. Most of the inorganic compounds, such as H₂, H₂S, COS, and SO₂, released at about 380 °C while the CO₂ had the maximum temperature peaks at 400 and 540 °C, respectively. FTIR spectra were taken of the residues of the different stages, and the results showed that the C–H bond intensity decreased dramatically at 380 °C. Py-GC/MS confirmed the composition of the evolved gas. The DSC revealed the endothermic nature of the bitumen pyrolysis.     

An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems

In this paper we develop a numerical method for two-dimensionaltime-dependent reaction-diffusion problems. This method, whichcan immediately be generalized to higher dimensions, is shownto be uniformly convergent with respect to the diffusion problems.This method, which can immediately be generalized to higherdimensions, is shown to be uniformly convergent with respectto the diffusion parameter.