Rounding Error Analysis in Solving M-Matrix Linear Systems of Block Hessenberg Form

The problem of solving large M-matrix linear systems with sparse coefficient matrix in block Hessenberg form is here addressed. In previous work of the authors a divide-and-conquer strategy was proposed and a backward error analysis of the resulting algorithm was presented showing its effectiveness for the solution of computational problems of queueing theory and Markov chains. In particular, it was shown that for block Hessenberg M-matrices the algorithm is weakly backward stable in the sense that the computed solution is the exact solution of a nearby linear system, where the norm of the perturbation is proportional to the condition number of the coefficient matrix. In this note a better error estimate is given by showing that for block Hessenberg M-matrices the algorithm is even backward stable.     

基于多项式组主项解耦消元法的几何定理机器证明

基于多项式组主项解耦消元法 ,将几何定理的假设条件 (多项式组 PS)化为主项只含主变元的三角型多项式组 DTS,可得到定理命题成立的不含变元的非退化条件 ,即充分必要或更接近充分必要的非退化条件 .由于多项式主系数不含变元 ,已不存在 DTS多项式之间的约化问题 ,故方法有普遍意义 .文中例为西姆松定理的机器证明 .     

Synthetic approach to pentacyclic quassinoids from communic acids, via ambracetal derivatives

Methyl (8R,13S)-8α,13:13,17-diepoxy-14,15-dinorlabdane-19-oate, easily prepared from communic acids, is a suitable intermediate for synthesizing pentacyclic quassinoids, because it enables the elaboration of the A ring and the further construction of the B-C-D ring system of these terpenoids. The cetal group is stable under the reaction conditions utilized during the elimination of the ester group and the introduction of the hydroxyl group on C-3. At the same time, it enables the regeneration of the methylketone and exocyclic double bond presented by methyl 13-oxo-14,15-dinorlabd-8(17)en-19-oate. The latter compound was previously used to construct the B-C-D-ring of these quassinoids.     

In Situ Solid‐State Generation of (BN)2‐Pyrenes and Electroluminescent Devices

New BN‐heterocyclic compounds have been found to undergo double arene photoelimination, forming rare yellow fluorescent BN‐pyrenes that contain two B? N units. Most significant is the discovery that the double arene elimination can also be driven by excitons generated electrically within electroluminescent (EL) devices, enabling the in situ solid‐state conversion of BN‐heterocycles to BN‐pyrenes and the use of BN‐pyrenes as emitters for EL devices. The in situ exciton‐driven elimination (EDE) phenomenon has also been observed for other BN‐heterocycles.     

Understanding the thermal stability of human serum proteins with the related near-infrared spectral variables selected by Monte Carlo-uninformative variable elimination

Understanding the thermal stability of the proteins in human serum is essential since human serum is the important source of pharmaceutical proteins. Near-infrared (NIR) spectroscopy was applied to the investigation of thermal changes in secondary structure and hydration of human serum proteins. However, as a multicomponent system, the overlap of the broad NIR bands makes the structural analysis very difficult directly using the spectra of serum samples. Therefore, continuous wavelet transform (CWT) was used to improve the resolution of NIR spectra, and Monte Carlo-uninformative variable elimination (MC-UVE) method was applied to the selection of the variables associated with the proteins for the structural analysis. The variables (5956, 5867, 5815, 5747, 4525, 4401, 4359 and 4328 cm^-1) related to protein secondary structures and those (7074, 6951, 6827 and 6700 cm^-1) connected with water species were selected. Then, the thermal stability was analyzed through the intensity variations of the selected variables with temperature from 30 ℃ to 80 ℃. It was found that the variation of the spectral variables related to both α-helix and β-sheetchanges apparently around 60 ℃, indicating the beginning of the thermal denaturation and the transition from α-helix to β-sheet. Moreover, an obvious change was found around 60 ℃ for the content of the water specie S₃, i.e., the water cluster containing three hydrogen bonds. The result demonstrates that MC-UVE can identify the protein-related NIR spectral variables, and the water species may be a marker for investigation of the structural change of proteins in biochemical systems.     

A free-energy perturbation method based on Monte Carlo simulations using quantum mechanical calculations (QM/MC/FEP method): application to highly solvent-dependent reactions

This study describes the framework of the quantum mechanical (QM)/Monte Carlo (MC)/free‐energy perturbation (FEP) method, a FEP method based on MC simulations using quantum chemical calculations. Because a series of structures generated by interpolating internal coordinates between transition state and reactant did not produce smooth free‐energy profiles, we used structures from the intrinsic reaction coordinate calculations. This method was first applied to the Diels–Alder reaction between methyl vinyl ketone and cyclopentadiene and produced ΔG values of 20.1 and 21.4 kcal mol^?1 in aqueous and methanol solutions, respectively. They are very consistent with the experimentally observed values. The other two applications were the free‐energy surfaces for the Cope elimination of N,N‐dimethyl‐3‐phenylbutan‐2‐amine oxide in aqueous, dimethyl sulfoxide, and tetrahydrofuran solutions, and the Kemp decarboxylation of 6‐hydroxybenzo‐isoxazole‐3‐carboxylic acid in aqueous, dimethyl sulfoxide, and CH₃CN solutions. The calculated activation free energies differed by less than 1.8 kcal mol^?1 from the experimental values for these reactions. Although we used droplet models for the QM/MC/FEP simulations, the calculated results for three reactions are very close to the experimental data. It was confirmed that most of the interactions between the solute and solvents can be described using small numbers of solvent molecules. This is because a few solvent molecules can produce large portions of the solute–solvent interaction energies at the reaction centers. When we confirmed the dependency on the droplet sizes of solvents, the QM/MC/FEP for a large droplet with 106 water molecules produced a ΔG value similar to the experimental values, as well as that for a small droplet with 34 molecules. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Density functional studies of influences of Ni triad metals and solvents on oxidative addition of MeI to [M(CH3)2(NH3)2] complexes and C-C reductive elimination from [M(CH3)3(NH3)2I] complexes

Three metal square planar complexes of the type [M(CH₃)₂(NH₃)₂] (M = Ni, Pd, Pt), with a systematic variation in the metals, are chosen to investigating their S_N2-type oxidative addition reactions with methyl iodide by using the B3LYP levels of theory. The oxidative addition was found to take place via a transition state with a nearly linear arrangement of the I-CH₃-M moiety. Solvation effects in these oxidative addition reactions were also investigated. Considering the nature of the metal centre and solvation effects, the following conclusions emerge: (i) addition of MeI is exothermic for all three metals, and Pt is predicted to react with a much lower barrier than either Pd or Ni. The results describe that the MeI addition would be expected to be more favourable with the complex bearing the third-row metal (platinum) as compared to the other triad metals, nickel or palladium, in which case a more strongly bound MeI adduct is formed with a lower activation barriers and the reaction being more exothermic; (ii) the reaction is very difficult to occur in low polar solvents, such as benzene, due to the high barrier which is induced by dissociation of iodide anion from methyl group, but the reaction easily occurs in polar solvents, such as acetonitrile; this is attributed to the ability of polar solvents to solvate and therefore stabilize the related polar intermediate ion pair. Ethane reductive elimination from the M(VI) complexes fac-[M(CH₃)₃(NH₃)₂I] were also studied, indicating that the Ni(IV) and Pd(IV) complexes are very prone to undergo the reductive elimination while the Pt(IV) analogous is less reactive towards the reductive elimination. The results indicate that in contrast to the Me-Me reductive elimination, the S_N2 oxidative addition reaction of MeI to M(II) is much less sensitive to the nature of the metal centre, suggesting that the nucleophilicity of M(II) in [M(CH₃)₂(NH₃)₂] does not change significantly as one moves from M = Ni to Pt.     

Arylation of styrene derivatives using aryliron complexes [CpFe(CO)2Ar] revealed by density functional theory calculations: Fe(II)-assisted group exchange through Fe-C bond cleavage and Fe-X bond formation

The detailed mechanism for arylation of styrene or its α-CF₃ substituted analog using aryliron complex [CpFe(CO)₂Ar] was studied using density functional theory calculations. Results of calculations show that the arylation mechanism mainly involves three steps: (1) a ligand exchange process between a CO and styrene or its derivative; (2) migration of Ar group from Fe to β-C of styrene; (3) β-H (or β-F) elimination and dissociation of the stilbene derivative from the CpFeHCO (or CpFeFCO) moiety. Both of Steps (2) and (3) experience a similar four-memberred cyclic transition state. The d_π-p_π interaction stabilizes the CC π coordinated complexes and the agostic interaction plays an important role in stabilizing intermediates and promoting elimination of the β-H (or β-F if available). For arylation of the α-CF3 substituted styrene, our calculations clarified that the dissociation of ethylene derivatives to give PF (product for β-F elimination) is kinetically and thermodynamically more favorable than to give PH (product for β-H elimination), which is the determined step for the selectivity of the final products.