A local structure theorem on 5‐connected graphs

An edge of a 5‐connected graph is said to be contractible if the contraction of the edge results in a 5‐connected graph. Let x be a vertex of a 5‐connected graph. We prove that if there are no contractible edges whose distance from x is two or less, then either there are two triangles with x in common each of which has a distinct degree five vertex other than x, or there is a specified structure called a K₄^?‐configuration with center x. As a corollary, we show that if a 5‐connected graph on n vertices has no contractible edges, then it has 2n/5 vertices of degree 5. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 99–129, 2009     

Classification Performance of a Low Pressure Differential Mobility Analyzer for Nanometer-sized Particles

Size distribution measurements and classification tests by a low pressure differential mobility analyzer (LPDMA) for nanometer-sized silver particles and cesium iodide particles under low pressure conditions (123–300 Torr) were performed using a transmission electron microscope (TEM) and the tandem DMA technique. When the ratio of the sheath gas flow rate and the aerosol gas flow rate was set at 5 : 1, the targeted sizes calculated from the classification voltage applied to the LPDMA at 160 Torr are found to be in good correlation with the count mean Feret diameter obtained from the TEM observation of the particles collected after a classification ranging from 6 to 25 nm, although the targeted sizes set by the LPDMA were approximately 15% greater than the count mean Feret diameter measured by the TEM after classification. The geometric standard deviations of DMA-classified particles measured by TEM and those obtained from the tandem DMA method ranged from 1.08 to 1.17 and from 1.05 to 1.13, respectively. They were slightly greater than the ideal geometric standard deviations (1.05) of the particles classified with the LPDMA, which was calculated by neglecting the broadening effects due to Brownian diffusion. We experimentally demonstrated the validity of our LPDMA system for size measurements and classification of the nanometer-sized particles under low pressure conditions.     

Structure of ultrahigh-molecular-weight polyethylene in the solid state as studied by variable-temperature 13C CP/MAS NMR spectroscopy

In order to obtain some insight into the structure of an ultrahigh-molecular-weight polyethylene sample, ¹³C CP/MAS NMR experiments have been carried out at temperatures from 23 to ?108°C. The peak for the crystalline component moves upfield with a decrease in temperature, which is contrary to what was reported previously for a melt-crystallized polyethylene sample. On the basis of x-ray diffraction results and quantum-chemical calculations, it is suggested that the methylene carbons are in the distorted orthorhombic form at low temperatures.     

Solvent dependence of the ultrafast ground state recovery dynamics of phenol blue

We have studied femtosecond ground state recovery dynamics of phenol blue (PB) by pump-probe spectroscopy with a time resolution of 33 fs. Multiexponential decay with time constants extending from 300 fs to 10 ps were observed. Some low frequency intramolecular quantum beats were also observed. Solvent dependence of these decays and beats are discussed.     

Appearance of pseudo-band-gaps in a disordered quantum wire array

The density of states and the conductivity are calculated in lateral superlattices with disorder in the period within a self-consistent Born approximation. Although the potential loses its periodicity on average due to disorder, it leads to an opening up of a pseudo-band-gap and modifies the conductivity perpendicular to the superlattice even qualitatively, when the energy reaches the zone boundary.     

Nonlinear response in evaluating the subjective diffuseness of sound fields

Tests were conducted to determine which horizontal reflection angles are most effective in stimulating subjective diffuseness for a listener in a room. Paired comparison tests were carried out where subjects were asked to judge in which of two sound fields they perceived more diffuseness. Results show that the most effective horizontal angle depends on the frequency of the one-third-octave-band noise, as is indicated by the interaural cross correlation. The remarkable finding in this investigation is that the scale value of subjective diffuseness may be formulated in terms of the 3/2 power of the magnitude of interaural cross correlation (IACC) and that the scale value does not vary with the frequency of the bandpass noise source.     

Extreme point axioms for closure spaces

A pair (X,τ) of a finite set X and a closure operator τ:2^X→2^X is called a closure space. The class of closure spaces includes matroids as well as antimatroids. Associated with a closure space (X,τ), the extreme point operator ex:2^X→2^X is defined as ex(A)={p|p∈A,p∉τ(A-{p})}. We give characterizations of extreme point operators of closure spaces, matroids and antimatroids, respectively.     

Assembly of a Benzo-Fused Bridged Ketone Scaffold from 1,5,10-Enediynes through One-Pot Ruthenium-Catalyzed Cyclization/Iodine-Mediated Oxidative Ring Expansion

In the presence of a cationic Ru catalyst, 1,6-diynes bearing a terminal styryl moiety underwent [2+2+2] cyclization to produce dehydrobiphenylenes fused with a five-membered ring. Although the cycloadducts were unstable toward purification, their one-pot iodine-mediated ring expansion successfully afforded unprecedented bridged ketone products containing a benzo-fused bicyclo[3.2.1] framework.     

The axial methionine ligand may control the redox reorganizations in the active site of blue copper proteins

Structural and energetic reorganizations in redox reaction of type 1 copper proteins are studied by density functional and ab initio molecular orbital calculations. Model complexes of the active site with varying number of ligands, from Cu(SCH(3))(0/+) to Cu(SCH(3))(Im)(2)(S(CH(3))(2))(0/+), where Im denotes imidazole, are investigated. Following the findings of structural instability in Cu(I)(SCH(3))(Im)(2) and its stabilization by the addition of the axial methionine (Met) ligand model, the structure and energetics are examined as functions of the Cu-S(Met) distance in the range of 2.1-3.3 A?. The reorganization energies in both redox states exhibit a minimum at the Cu-S(Met) distance of ～2.4?A?, whereas the ionization potential increases monotonically. The changes of reorganization energies correlate well with one of the Cu-N(His) distances rather than the Cu-S(Cys) distance. The estimated Arrhenius factor for oxidation of plastocyanin by P700(+) (in photosystem I) changes by an order of magnitude when the Cu-S(Met) distance fluctuates between 2.4 and 3.0 A?, whereas the factor for reduction of plastocyanin by cytochrome f is nearly constant. Together with the data from our previous classical molecular dynamics simulation of solvated protein, we argue that the electron transfer rate is affected, and thus may be controlled, by the fluctuation of a weakly bound axial Met ligand. We also present the assessment of various exchange-correlation functionals, including those with the long-range correction, against the CCSD(T) reference and on the basis of a perturbative adiabatic connection model. For Cu(SCH(3)) and Cu(SCH(3))(Im), simple correlations have been found between the reorganization energies and the amount of Hartree-Fock exchange.