Tree metrics and edge-disjoint S-paths

Given an undirected graph \(G=(V,E)\) with a terminal set \(S \subseteq V\) , a weight function on terminal pairs, and an edge-cost \(a: E \rightarrow \mathbf{Z}_+\) , the \(\mu \) -weighted minimum-cost edge-disjoint \(S\) -paths problem ( \(\mu \) -CEDP) is to maximize \(\sum \nolimits _{P \in \mathcal{P}} \mu (s_P,t_P) - a(P)\) over all edge-disjoint sets \(\mathcal{P}\) of \(S\) -paths, where \(s_P,t_P\) denote the ends of \(P\) and \(a(P)\) is the sum of edge-cost \(a(e)\) over edges \(e\) in \(P\) . Our main result is a complete characterization of terminal weights \(\mu \) for which \(\mu \) -CEDP is tractable and admits a combinatorial min–max theorem. We prove that if \(\mu \) is a tree metric, then \(\mu \) -CEDP is solvable in polynomial time and has a combinatorial min–max formula, which extends Mader’s edge-disjoint \(S\) -paths theorem and its minimum-cost generalization by Karzanov. Our min–max theorem includes the dual half-integrality, which was earlier conjectured by Karzanov for a special case. We also prove that \(\mu \) -EDP, which is \(\mu \) -CEDP with \(a = 0\) , is NP-hard if \(\mu \) is not a truncated tree metric, where a truncated tree metric is a weight function represented as pairwise distances between balls in a tree. On the other hand, \(\mu \) -CEDP for a truncated tree metric \(\mu \) reduces to \(\mu '\) -CEDP for a tree metric \(\mu '\) . Thus our result is best possible unless P = NP. As an application, we obtain a good approximation algorithm for \(\mu \) -EDP with “near” tree metric \(\mu \) by utilizing results from the theory of low-distortion embedding.     

Amphoteric poly(vinyl alcohol) gel as a force generator: Observation of microporous gel formation with cryo-SEM

Amphoteric PVA hydrogels were made from mixed aqueous solutions of poly(acrylic acid), poly(allylamine) hydrochloride and poly(vinyl alcohol) by repetitive freezing and thawing. The hydrogen bond induced gelation produced an elastic and tough microporous hydrogel which generated tension as high as 0.3MPa corresponding to the solvent exchange from water to acetone. In this paper we show the microscopic structure of hydrogels determined by means of cryo-SEM technique and X-ray analysis.     

Crystal structure and high-pressure properties of γ-Mo2N determined by neutron powder diffraction and X-ray diffraction

We prepared samples of cubic γ-MoN_x (x∼0.5) by high-pressure-high-temperature synthesis. N atom site occupancies within the defect rock salt structure were determined from time-of-flight neutron diffraction and powder X-ray diffraction data by Rietveld analysis. The results show that N atoms occupy only octahedral sites within the structure. The semi-metallic compound is a superconductor, with determined by SQUID magnetometry. The compressibility of the material was determined by synchrotron X-ray diffraction measurements at high pressure in the diamond anvil cell. The vibrational density of states was studied by Raman scattering spectroscopy.     

Surface design for precise control of spatial growth of a mesostructured inorganic/organic film on a large-scale area

A microfabrication technique is presented to fabricate a mesostructured inorganic/organic composite film, i.e., silica/cetyltrimethylammonium chloride (CTAC) film, with near-perfect site-selectivity on a large surface area based on a spatially regulated growth method. To precisely regulate the site-selective growth of this mesocomposite film at the solid/liquid interface, we designed a novel microtemplate consisting of a "dual-component" self-assembled monolayer (SAM) with alternating hydrophobic trifluorocarbon (CF3) and cationic amino (NH2) groups. First, (heptadecafluoro-1,1,2,2-tetrahydrodecyl)trimethoxysilane (FAS)-SAM was formed onto Si substrate covered with native oxide (SiO2/Si) from vapor phase. The substrate was then photolithographically micropatterned using 172 nm vacuum UV light. Finally, the micropatterned FAS-SAM was immersed in a solution of 1 vol % (aminoethylaminomethyl)phenethyltrimethoxysilane (AEAMPS) in absolute toluene. Due to these treatments, a dual-SAM microtemplate with CF3- and NH2-terminated surfaces was fabricated, as evidenced by lateral force microscopy, ellipsometry, and X-ray photoelectron spectroscopy. Using this template, the microfabrication of a mesocomposite film was demonstrated. As a control, the micropatterned hydrophobic FAS-SAM template (composed of CF3- and OH-terminated surfaces) was also treated under the same conditions. Optical microscopy and atomic force microscopy confirmed that the formation of the continuous mesocomposite film proceeded only on the FAS-SAM-covered regions, while the AEAMPS-SAM-covered regions remained free of deposits. This shielding effect also remained constant regardless of the pattern's geometry, i.e., the interval distance between the FAS-SAM-covered areas in the pattern. Through this approach, we were able to obtain well-defined 5-, 10-, and 20-mum wide mesocomposite microlines over the entire 10 x 10 mm2 area with high area-selectivity. On the other hand, when the SiO2 regions were not terminated with the cationic NH2 groups, cluster formation proceeded not only on the hydrophobic CF3 regions but also on the SiO2 regions, particularly with an increase in the pattern interval distance, resulting in lower final pattern resolution.     

Electric quadrupole model on the formation of molecular chirality dependent domain shapes of lipid monolayers at the air-water interface

Shapes and orientational deformation of a lipid monolayer domain have been analyzed taking into account the surface pressure, line tension, and electrostatic energy due to the spontaneous polarization and electric quadrupole density generated from the domain. The electrostatic energy due to the generation of spontaneous polarization and electric quadrupole density contributes to the formation of orientational deformation as the Frank elastic energy and spontaneous splay, respectively. Since the orientational configuration of the electric quadrupole density and in-plane spontaneous polarization is dependent on the molecular chirality, and the positive splay deformation of electric quadrupole density is induced by the spontaneous splay, the bending direction of in-plane spontaneous polarization depends on the chirality of constituent lipids. The electrostatic energy due to the in-plane spontaneous polarization is dependent on the orientational deformation of in-plane spontaneous polarization, and bends the domain shape towards the bending direction of the in-plane spontaneous polarization. It has been demonstrated that the chiral dependence of the domain shapes of lipid monolayers originated from the chiral dependence of orientational structure due to the electric quadrupole density.     

Energy Dissipation Processes of singlet‐excited 1‐Hydroxyfluorenone and its Hydrogen‐bonded Complex with N‐methylimidazole¶

Effects of solvent, pH and hydrogen bonding with N‐methylimidazole (MIm) on the photophysical properties of 1‐hydroxyfluorenone (1HOF) have been studied. Fluorescence lifetime, fluorescence quantum yield and triplet yield measurements demonstrated that intersystem crossing was the dominant process in apolar media and its rate constant significantly diminished with increasing solvent polarity. The acceleration of internal conversion in alcohols paralleled the strength of intermolecular hydrogen bonding. The faster energy dissipation from the singlet‐excited state in cyclohexane was attributed to intramolecular hydrogen bonding. The pK_a of 1HOF decreased from 10.06 to 5.0 on light absorption, and H₃O⁺ quenched the singletexcited molecules in a practically diffusion‐controlled reaction. On addition of MIm in toluene, dual fluorescence was observed, which was attributed to reversible formation of excited hydrogen‐bonded ion pair. Rate constants for the various deactivation pathways were derived from the combined analysis of the steady‐state and the time‐resolved fluorescence results.     

Synthesis of N-azolylindoles by copper-catalyzed C-H/N-H coupling-annulation sequence of o-alkynylanilines

A wide range of o-alkynylanilines undergo a copper-catalyzed direct C-H/N-H coupling with azoles followed by benzannulation to form the corresponding N-azolylindoles in good yields. The domino reaction proceeds effectively with molecular oxygen as the sole oxidant and provides a new dehydrogenative access to the titled compounds of interest in pharmaceutical and material sciences.     

Preparation, structure, and properties of tetranuclear vanadium(III) and (IV) complexes bridged by diphenyl phosphate or phosphate

Three novel tetranuclear vanadium(III) or (IV) complexes bridged by diphenyl phosphate or phosphate were prepared and their structures characterized by X-ray crystallography. The novel complexes are [{V(III)(2)(μ-hpnbpda)}(2){μ-(C(6)H(5)O)(2)PO(2)}(2)(μ-O)(2)]·6CH(3)OH (1), [{V(III)(2)(μ-tphpn)(μ-η(3)-HPO(4))}(2)(μ-η(4)-PO(4))](ClO(4))(3)·4.5H(2)O (2), and [{(V(IV)O)(2)(μ-tphpn)}(2)(μ-η(4)-PO(4))](ClO(4))(3)·H(2)O (3), where hpnbpda and tphpn are alkoxo-bridging dinucleating ligands. H(3)hpnbpda represents 2-hydroxypropane-1,3-diamino-N,N'-bis(2-pyridylmethyl)-N,N'-diacetic acid, and Htphpn represents N,N,N',N'-tetrakis(2-pyridylmethyl)-2-hydroxy-1,3-propanediamine. A dinuclear vanadium(IV) complex without a phosphate bridge, [(VO)(2)(μ-tphpn)(H(2)O)(2)](ClO(4))(3)·2H(2)O (4), was also prepared and structurally characterized for comparison. The vanadium(III) center in 1 adopts a hexacoordinate structure while that in 2 adopts a heptacoordinate structure. In 1, the two dinuclear vanadium(III) units bridged by the alkoxo group of hpnbpda are further linked by two diphenylphosphato and two oxo groups, resulting in a dimer-of-dimers. In 2, the two vanadium(III) units bridged by tphpn are further bridged by three phosphate ions with two different coordination modes. Complex 2 is oxidized in aerobic solution to yield complex 3, in which two of the three phosphate groups in 2 are substituted by oxo groups.     

Eu(III) emission band changes caused by peripheral C-H/O hydrogen bonding

We synthesized Eu(III) and Sm(III) complexes with tridentate phosphine oxide ligands, Eu(hfa)(3)(TPPM) and Sm(hfa)(3)(TPPM) (hfa: hexafluoroacetylacetonato, TPPM: tris(diphenylphosphinyl)methane), and we then examined their luminescent properties. In the complexes the Eu(III) and Sm(III) centres were fully surrounded by low-vibrational frequency ligands, which led to relatively high emission quantum yields (Φ(Eu) = 30%, Φ(Sm) = 4.7%). The X-ray single crystal structures of the Eu(hfa)(3)(TPPM) revealed nona-coordinated Eu(III) complexes and C-H/O hydrogen bonding formations between the acidic hydrogen atom of the TPPM ligand and oxygen atoms of solvent molecules. The C-H/O hydrogen bonding slightly affected the coordination structure around the Eu(III) ion. Despite the seemingly small effect on the structural change, because the emission band profile of the (5)D(0)→(7)F(2) transition is sensitive to changes in the coordination environment of the Eu(III) complex, we observed a red shift in the emission spectral line.