Fragmentation of the metastable molecular ion of methyl lactate: The formation of oxygen-protonated methanol [CH3OH2]+ involving double hydrogen atom transfers

The spontaneous unimolecular dissociation reaction of methyl lactate (1) ionized by electron impact was investigated by a combination of mass-analyzed ion kinetic energy spectrometry and deuterium labeling. The metastable ions 1^+· decompose in a variety of ways: four fragment peaks are observed at m/z 89, 76, 61, and 45, which correspond to the losses of ?H₃, CO, CH₃?O, and ?OOCH₃, respectively. Double hydrogen atom transfer occurs in the third reaction. The source-generated m/z 61 ions decompose into oxygen-protonated methanols at m/z 33 ([CH₃OH ₂ ⁺ ]) by the loss of CO with double hydrogen atom migration. Both hydroxyl and methyne hydrogen atoms in 1 ^+· are present in the resultant protonated methanols.     

A descent method for submodular function minimization

We show a descent method for submodular function minimization based on an oracle for membership in base polyhedra. We assume that for any submodular function f: ?→R on a distributive lattice ?⊆2 ^V with ?,V∈? and f(?)=0 and for any vector x∈R ^V where V is a finite nonempty set, the membership oracle answers whether x belongs to the base polyhedron associated with f and that if the answer is NO, it also gives us a set Z∈? such that x(Z)>f(Z). Given a submodular function f, by invoking the membership oracle O(|V|²) times, the descent method finds a sequence of subsets Z ₁,Z ₂,···,Z _k of V such that f(Z ₁)>f(Z ₂)>···>f(Z _k )=min{f(Y) | Y∈?}, where k is O(|V|²). The method furnishes an alternative framework for submodular function minimization if combined with possible efficient membership algorithms. Received: September 9, 2001 / Accepted: October 15, 2001?Published online December 6, 2001     

Inter-collisional cutting of multi-walled carbon nanotubes by high-speed agitation

High-speed agitation by a mixing blade has efficiently achieved the cutting of a large diameter (100-150 nm) of multi-walled carbon nanotubes. The cutting process is caused by an inter-collision of the nanotubes with high transfer energy. The collision-induced cutting allows for the shortening of the nanotubes without serious damage of the original graphitic layers due to the cutting effect being limited to the collision points. Furthermore, the operation under ambient atmosphere introduces oxygen-containing functional groups to the cut nanotubes. The estimated length distribution has indicated that high-speed agitation achieves a large cutting effect during a short duration of several minutes.     

Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimization

Bisubmodular functions are a natural “directed”, or “signed”, extension of submodular functions with several applications. Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function minimization (SFM) to bisubmodular function minimization (BSFM). However, they were able to extend only the weakly polynomial version of IFF to BSFM. Here we investigate the difficulty that prevented them from also extending the strongly polynomial version of IFF to BSFM, and we show a way around the difficulty. This new method gives a somewhat simpler strongly polynomial SFM algorithm, as well as the first combinatorial strongly polynomial algorithm for BSFM. This further leads to extending Iwata’s fully combinatorial version of IFF to BSFM. The research of S. T. McCormick was supported by an NSERC Operating Grant. The research of S. Fujishige was supported by a Grant-in-Aid of the Ministry of Education, Culture, Science and Technology of Japan.     

A note on Faigle and Kern’s dual greedy polyhedra

U. Faigle and W. Kern have recently extended the work of their earlier paper and of M. Queyranne, F. Spieksma and F. Tardella and have shown that a dual greedy algorithm works for a system of linear inequalities with {:0,1}-coefficients defined in terms of antichains of an underlying poset and a submodular function on the set of ideals of the poset under some additional condition on the submodular function.?In this note we show that Faigle and Kern’s dual greedy polyhedra belong to a class of submodular flow polyhedra, i.e., Faigle and Kern’s problem is a special case of the submodular flow problem that can easily be solved by their greedy algorithm. Received: February 1999 / Accepted: December 1999?Published online February 23, 2000     

Optimization over the polyhedron determined by a submodular function on a co-intersecting family

A greedy algorithm solves the problem of maximizing a linear objective function over the polyhedron (called the submodular polyhedron) determined by a submodular function on a distributive lattice or a ring family. We generalize the problem by considering a submodular function on a co-intersecting family and give an algorithm for solving it. Here, simple-minded greedy augmentations do not work any more and some complicated augmentations with multiple exchanges are required. We can find an optimal solution by at most 1/2n(n – 1) augmentations, wheren is the number of the variables and we assume a certain oracle for computing multiple exchange capacities.