Hamiltonicity of planar graphs with a forbidden minor

Tutte showed that -connected planar graphs are Hamiltonian, but it is well known that -connected planar graphs need not be Hamiltonian. We show that -minor-free -connected planar graphs are Hamiltonian. This does not extend to -minor-free -connected graphs in general, as shown by the Petersen graph, and does not extend to -minor-free -connected planar graphs, as we show by an infinite family of examples.     

Bulk-type all-solid-state batteries with mechanically prepared LiCoPO4 composite cathodes

Journal of Solid State Electrochemistry - All-solid-state Li batteries are suitable for the application of 5 V-class cathode materials that can provide high energy densities. However, it is hard to...     

Simultaneous measurement of surface shape and absolute optical thickness of a glass plate by wavelength tuning phase-shifting interferometry

The absolute optical thickness and the surface shape of a glass plate of 7-in. square and 3.1mm thick was simultaneously measured by three-surface interferometry using a wavelength tuning Fizeau interferometer. The wavelength of a tunable diode laser is scanned linearly from 632 to 642 nm, at which the initial and the final phases of the interference fringes for the surface shape and for the optical thickness were separated and measured by a tunable phase-shifting technique. The number of phase variations in the interference fringes during the scanning is counted by discrete Fourier analysis, in which systematic errors caused by a nonlinearity in the wavelength scanning is corrected by a correlation analysis between the observed and theoretical interference fringes. Experimental results demonstrate that the systematic errors in the measured value were 15 nm for the surface shape and 0.6 μm for the absolute optical thickness.     

Enhancement of artificial promoter activity by ultrasound-induced oxidative stress

We previously developed artificial promoters that were activated in response to X-ray irradiation. Sonication with 1.0 MHz ultrasound that causes intracellular oxidative stress was found to activate some of these promoters though to lesser degrees. The most sensitive one among these promoters showed intensity- and duration-dependent activations by sonication. In addition, its activation by sonication was attenuated when N-acetyl cysteine was present, suggesting the involvement of intracellular oxidative stress in the activation mechanism. Improved promoters for sensitivity to X-ray irradiation were also found more sensitive to sonication. The most improved one showed 6.0 fold enhancement after sonication with 1.0 MHz ultrasound at 1.0 W/cm² for 60 s. This enhancement was also attenuated with the presence of N-acetyl cysteine. When stably transfected HeLa cells with the most sensitive promoter were transplanted on to mice and sonicated, luciferase activity by the promoter increased to 1.35 fold in average though it was not statistically significant compared to control. Although gene regulation in vivo by sonication was not clear, this is the first report on artificially constructed promoters responsive to ultrasound.     

Observation/confirmation of hindered E2 strength in 18C/16C

We have measured the lifetime of the first excited 2⁺ state in ¹⁸C using an upgraded recoil shadow method to determine the electric quadrupole transition. The measured mean lifetime is 18.9±0.9 (stat)±4.4 (syst) ps, corresponding to B(E2;2₁ ⁺ $ \rightarrow$ 0⁺ _gs) = 4.3±0.2±1.0e ² fm^4, or about 1.5 Weisskopf units. The mean lifetime of the first 2⁺ state in ¹⁶C was remeasured to be 18.3±1.4±4.8 ps, about four times shorter than the value reported previously. The discrepancy is explained by incorporating the $ \gamma$ -ray angular distribution obtained in this work into the previous measurement. The observed transition strengths in ^{16, 18}C are hindered compared to the empirical values, indicating that the anomalous E2 strength observed in ¹⁶C persists in ¹⁸C .     

Two coordination modes of TCNE in the ruthenium amidinates: The first example providing experimental evidence for κ-N to η-C rearrangement

Reactions of Cp^∗Ru(κ²-N(R)C(R′)NR) (1a; R = ⁱPr, R′ = Me, 1b; R = ^tBu, R′ = Ph) with TCNE initially give dark green colored intermediary species, which are readily converted to brown colored “η²-C” coordination complexes, Cp^∗Ru(κ²-N(R)C(R′)NR)(η²-TCNE) (3a; R = ⁱPr, R′ = Me, 3b; R = ^tBu, R′ = Ph). These “η²-C” complexes are characterized by spectroscopy and crystallography. A stable ruthenium amidinate having a “κ¹-N”-coordinated TCNE, Cp^∗Ru(κ²-N(^tBu)C(Mes)N^tBu)(κ¹(N)-TCNE) (2c), is synthesized by treatment of Cp^∗Ru(κ²-N(^tBu)C(Mes)N^tBu) (1c) with TCNE, the structure of which is unequivocally confirmed by X-ray structure determination and the charge transfer nature is supported by ESR analysis. Close analogy in IR and UV-Vis spectroscopy of 2c with the dark green colored intermediary species formed from 1b suggests that this is “κ¹-N” ruthenium amidinate, which is rearranged to the “η²-C” complex 3b.     

Triply periodic minimal surfaces bounded by vertical symmetry planes

We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz–Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces. S. Fujimori was partially supported by JSPS Grant-in-Aid for Young Scientists (Start-up) 19840035. M. Weber’s material is based upon work for the NSF under Award No. DMS-0139476.     

Fixed-point property of random groups

In this paper, using the generalized version of the theory of combinatorial harmonic maps, we give a criterion for a finitely generated group Γ to have the fixed-point property for a certain class of Hadamard spaces, and prove a fixed-point theorem for random-group actions on the same class of Hadamard spaces. We also study the existence of an equivariant energy-minimizing map from a Γ-space to the limit space of a sequence of Hadamard spaces with the isometric actions of a finitely generated group Γ. As an application, we present the existence of a constant which may be regarded as a Kazhdan constant for isometric discrete-group actions on a family of Hadamard spaces.      

On a question of Gromov about the Wirtinger inequalities

We prove that Gromov’s \(\mathrm {Cycl}_4(0)\) condition implies \(\mathrm {Wir}_k\) inequalities for any \(k \ge 4\), which answers a question of Gromov (J Math Sci N Y 119(2):178–200, 2004).