Reply to “Comment on the Comparative Use of the Electron Density and Its Laplacian”

In our reply to the preceding comment by Richard Bader we show that the statements of the author are not justified and that he contradicts his own previous work.     

Lower bounds and modified LPT algorithm for k -partitioning problems with partition matroid constraint

In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-case performance is analyzed. The lower bounds of optimal solution for the min-max problem are given. Supported by the National Natural Science Foundation of China(10671177).     

Product Vibrational State Distributions of F+CH3OH Reaction on Full-Dimensional Accurate Potential Energy Surface

The hydrogen abstraction reaction of methanol with fluorine atoms can produce HF and CH\begin{document}$ _3 $\end{document}O or CH\begin{document}$ _2 $\end{document}OH radicals, which are important in the environment, combustion, radiation, and interstellar chemistry. In this work, the dynamics of this typical reaction is investigated by the quasi-classical trajectory method based on a recently developed globally accurate full-dimensional potential energy surface. Particularly, the vibrational state distributions of the polyatomic products CH\begin{document}$ _3 $\end{document}O and CH\begin{document}$ _2 $\end{document}OH are determined by using the normal mode analysis method. It is found that CH\begin{document}$ _3 $\end{document}O and CH\begin{document}$ _2 $\end{document}OH are dominantly populated in the ground state when the reactants are at the ground ro-vibrational state. The OH stretching mode, torsional mode, H\begin{document}$ _2 $\end{document}CO out-of-plane bending mode and their combination bands in the CH\begin{document}$ _2 $\end{document}OH product can be effectively excited once the OH stretching mode of the reactant CH\begin{document}$ _3 $\end{document}OH is excited to the first vibrationally excited state. Most of the available energy flows into the HF vibrational energy and the translational energy in both channels, while the radical products, CH\begin{document}$ _3 $\end{document}O or CH\begin{document}$ _2 $\end{document}OH, receive a small amount of energy, consistent with experiment, which is an indication of its spectator nature.     

Revisiting Aromaticity and Chemical Bonding of Fluorinated Benzene Derivatives

The electron delocalization of benzene (C₆H₆) and hexafluorobenzene (C₆F₆) was analyzed in terms of the induced magnetic field, nucleus-independent chemical shift (NICS), and ring current strength (RCS). The computed out-of-plane component of the induced magnetic field at a distance (r) greater than or equal to 1.0 Å above the ring center correlates well (R²>0.99) with the RCS value. According to these criteria, fluorination has two effects on the C₆ skeleton; concomitantly, the resonant effects diminish the π electron delocalization and the inductive effects decrease the charge density at the ring center and therefore reduce the magnitude of the paratropic current generated in this region. The equilibrium between both effects decreases aromaticity in the fluorinated benzene derivatives. These results can be extrapolated to determine the aromaticity of any derivative within the series of fluorinated benzene derivatives (C₆H_(6−n)F_n, where n=1–5).     

Enhancing micro-perforated panel attenuation by partitioning the adjoining cavity

The sound attenuation performance of micro-perforated panels (MPP) with adjoining air cavity is investigated for a plenum. The sound field inside of a plenum is compared for two cases. In the first case, the plenum is treated with an MPP and adjoining air cavity without any partitioning. For the second case, the adjoining air cavity is partitioned into a number of sub-cavities. The resulting sound pressure fields indicate that partitioning the adjoining air cavity increases the overall sound attenuation due to the MPP by approximately 4 dB. The explanation for this phenomenon was investigated by measuring the sound pressure level on planes in front of the MPP. Additionally, boundary element analyses were conducted to simulate the effect of the MPP and adjoining cavity with and without partitioning on the sound field in the plenum. It was demonstrated that a MPP can be modeled as a transfer impedance and that partitioning the adjoining cavity enhances attenuation to acoustic modes that propagate transverse to the MPP.     

Balancing modular transfer lines with serial-parallel activation of spindle heads at stations

The paper deals with an as yet unexplored combinatorial optimization problem concerning balancing complex transfer lines in the machining/process environment. In contrast to similar problems for assembly lines, in transfer line balancing, tasks are grouped into blocks. All tasks of each block are executed simultaneously (in parallel) by one piece of equipment (spindle head). For the transfer lines considered in this paper, spindle heads at each station are activated in serial-parallel order. The set of all available spindle heads is known beforehand. Precedence, cycle time, compatibility, and parallelism constraints for the blocks and tasks are given. The line investment cost is estimated by the sum of block and station costs. The problem is to assign all tasks (using the available blocks) such that all constraints are respected and line investment cost is at a minimum. This paper focuses on solving the problem via a branch-and-bound algorithm. An approach for obtaining an efficient lower bound is offered, based on a reduction of the initial problem to a set partitioning problem. Computational experiments reveal that the proposed approach is efficient mathematically and can be used to solve practical transfer line design problems of a medium size.     

A partitioning algorithm for the network loading problem

This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The approach is an iterative method in which the integer programming solver is not used to produce the best integer point in the polyhedral relaxation of the set of feasible capacities. Rather, it selects an integer solution that is closest to the best known integer solution. Contrary to previous approaches, the method does not exploit the original mixed integer programming formulation of the problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be efficient for computing good upper bounds.     

On Borsuk's Problem in ℝ3

Mathematical Notes -     

Investigation of Symphytum cordatum alkaloids by liquid-liquid partitioning, thin-layer chromatography and liquid chromatography-ion-trap mass spectrometry

From the alkalised crude extract of Symphytum cordatum (L.) W.K. roots, pyrrolizidine alkaloids (PAs) were extracted as free tertiary bases and polar N-oxides in a merely one-step liquid-liquid partitioning (LLP) in separation funnel and subsequently pre-fractionated by preparative multiple-development (MD) thin-layer chromatography (TLC) on silica gel plates. In this way three alkaloid fractions of different polarities and retention on silica gel plates were obtained as: the most polar N-oxides of the highest retention, the tertiary bases of medium retention, and diesterified N-oxides of the lowest retention. The former fraction was reduced into free bases by sodium hydrosulfite and purified by LLP on Extrelut-NT3 cartridge. It was further analysed together with the two other fractions by high-performance liquid chromatography (HPLC)-ion-trap mass spectrometry with atmospheric pressure chemical ionization (APCI) interface on XTerra C₁₈ column using a gradient elution. Based on MSⁿ spectra, 18 various alkaloids have been tentatively determined for the first time in this plant as the following types of structure: echimidine-N-oxide (three diasteroisomers), 7-sarracinyl-9-viridiflorylretronecine (two diasteroisomers), echimidine (two diasteroisomers), lycopsamine (two diasteroisomers), dihydroechinatine-N-oxide, dihydroheliospathuline-N-oxide, lycopsamine-N-oxide (three diasteroisomers), 7-acetyllycopsamine-N-oxide, symphytine-N-oxide (two diasteroisomers) and 2″,3″-epoxyechiumine-N-oxide.