Single- and multi-objective defensive location problems on a network

This paper considers a new optimal location problem, called defensive location problem (DLP). In the DLPs, a decision maker locates defensive facilities in order to prevent her/his enemies from reaching an important site, called a core; for example, “a government of a country locates self-defense bases in order to prevent her/his aggressors from reaching the capital of the country.” It is assumed that the region where the decision maker locates her/his defensive facilities is represented as a network and the core is a vertex in the network, and that the facility locater and her/his enemy are an upper and a lower level of decision maker, respectively. Then the DLPs are formulated as bilevel 0-1 programming problems to find Stackelberg solutions. In order to solve the DLPs efficiently, a solving algorithm for the DLPs based upon tabu search methods is proposed. The efficiency of the proposed solving methods is shown by applying to examples of the DLPs. Moreover, the DLPs are extended to multi-objective DLPs that the decision maker needs to defend several cores simultaneously. Such DLPs are formulated as multi-objective programming problems. In order to find a satisfying solution of the decision maker for the multi-objective DLP, an interactive fuzzy satisfying method is proposed, and the results of applying the method to examples of the multi-objective DLPs are shown.     

Accessing Improbable Foldamer Shapes with Strained Macrocycles

The alkylation of some secondary amide functions with a dimethoxybenzyl (DMB) group in oligomers of 8-amino-2-quinolinecarboxylic acid destabilizes the otherwise favored helical conformations, and allows for cyclization to take place. A cyclic hexamer and a cyclic heptamer were produced in this manner. After DMB removal, X-ray crystallography and NMR show that the macrocycles adopt strained conformations that would be improbable in noncyclic species. The high helix folding propensity of the main chain is partly expressed in these conformations, but it remains frustrated by macrocyclization. Despite being homomeric, the macrocycles possess inequivalent monomer units. Experimental and computational studies highlight specific fluxional pathways within these structures. Extensive simulated annealing molecular dynamics allow for the prediction of the conformations for larger macrocycles with up to sixteen monomers.     

A pair of diastereomeric 1:1 salts of (S)‐ and (R)‐2‐methylpiperazine with (2S,3S)‐tartaric acid

The structures of diastereomeric pairs consisting of (S)‐ and (R)‐2‐methylpiperazine with (2S,3S)‐tartaric acid are both 1:1 salts, namely (S)‐2‐methylpiperazinium (2S,3S)‐tartrate dihydrate, C₅H₁₄N₂²⁺·C₄H₄O₆²⁻·2H₂O, (I), and (R)‐2‐methylpiperazinium (2S,3S)‐tartrate dihydrate, C₅H₁₄N₂²⁺·C₄H₄O₆²⁻·2H₂O, (II), which reveal the formation of well defined ammonium carboxylate salts linked via strong intermolecular hydrogen bonds. Unlike the situation in the more soluble salt (II), the alternating columns of tartrate and ammonium ions of the less soluble salt (I) are packed neatly in a grid around the a axis, which incorporates water molecules at regular intervals. The increased efficiency of packing for (I) is evident in its lower `packing coefficient', and the hydrogen‐bond contribution is stronger in the more soluble salt (II).     

In situ x-ray diffraction measurements of the capillary fountain jet produced via ultrasonic atomization

In situ x-ray diffraction measurements were carried out for investigating the liquid structure in the ultrasonic fountain jet to consider the mechanism of the "ultrasonic ethanol separation" reported by Sato et al. [J. Chem. Phys. 114, 2382 (2001)]. For pure liquids (water and ethanol), it was found that the high frequency ultrasound does not affect the liquid structure microscopically. For the 20 mol % ethanol-water mixture, the estimated ethanol mole fraction in the ultrasonic fountain jet by using the position of the main maximum in the x-ray diffraction profile coincided with that in the reservoir. This result suggests that the ethanol separation is not caused by any distorted liquid structure under the ultrasound irradiation and occurs when or after the generation of the liquid droplet mist.     

Kinetic resolution displaying zeroth order dependence on substrate consumption: copper-catalyzed asymmetric alcoholysis of azlactones

Kinetic resolution of 4-alkyl-2-aryl-5-oxo-4,5-dihydrooxazole-4-carboxylic acid esters (azlactones 1) were achieved by copper-DTBM-SEGPHOS catalyzed alcoholysis reaction with good selectivity (12 examples). Variation of ee of unreacted substrates 1 and products 2 with conversion was found to follow the theoretical line of zeroth-order kinetic resolution, for which the selectivity profiles and graphical analysis were presented for the first time. The efficiency of resolution in zeroth-order reaction is higher than first-order reaction. For example, the reaction with 1a afforded (S)-1a (99% ee) and (R)-2a (74% ee) at 57% conversion, where the k(rel) values were calculated to be 6.7 as zeroth-order kinetic resolution and 37 as first-order kinetic resolution.     

Discrimination of enantiomeric excess of optically active trifluorolactate by distillation: Evidence for a multi-center hydrogen bonding network in the liquid state

The paper provides evidence for the existence of a multi-center hydrogen bonding network of trifluorolactate, the structure of which was elucidated by single crystal X-ray diffraction analysis, in the liquid state. We reported that the trifluorolactate experienced discrimination of its enantiomeric excess by distillation. X-ray crystallographic analyses of the single crystals of the trifluorolactates suggested that the phenomenon could be caused by a homo-chiral recognizing hydrogen bonding system. Low-angle X-ray diffraction measurement of the trifluorolactate in the liquid state showed a ca. 5 Å repeated, which indicates the existence of the hydrogen bonding network in the liquid state. Here, the chiral recognition could be caused by the electrostatic repulsion of the negative charges on trifluoromethyl groups.     

On the Gap between the First Eigenvalues of the Laplacian on Functions and p-Forms

We study the first positive eigenvalue ^(p) ₁(g) of the Laplacian on p-forms for a connected oriented closed Riemannianmanifold (M, g) of dimension m. We show that for 2 p m – 2 a connected oriented closed manifold M admits three metrics g _i (i = 1, 2, 3) such that ^(p) ₁(g ₁)> ⁽⁰⁾ ₁(g ₁),^(p) ₁(g ₂) < ⁽⁰⁾ ₁(g ₂) and^(p) ₁(g ₃)= ⁽⁰⁾ ₁(g ₃).Furthermore, if (M, g) admits a nontrivial parallel p-form,then ^(p) ₁ ⁽⁰⁾ ₁ always holds.     

Synthesis of thiophene/phenylene co‐oligomers. IV. 6‐ to 8‐ring molecules

We report the synthesis of various thiophene/phenylene co‐oligomers with a total number of thiophene and benzene (phenylene) rings of 6 to 8. These compounds include a phenyl‐capped sexithiophene, a thienyl‐capped quaterphenylene, as well as block and alternating co‐oligomers. The synthesis is based on either the Suzuki coupling reaction or the direct dimerization coupling. The latter method produces symmetric molecules with an even total ring number. These reaction schemes enabled us to obtain the target compounds in high quality. Although the resulting materials are difficult to dissolve in organic solvents and therefore difficult to identify by usual ¹H nmr spectroscopy, they have successfully been identified through Fourier‐transform ir spectroscopy. The specific group frequencies of ring‐stretching and out‐of‐plane deformation modes are characteristic of the substitution pattern of the individual thiophene and benzene rings.