Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Heat-generating property of a local plasmon resonator under illumination

We have investigated the heat generation from gold nanoparticles resulting from their local plasma resonance. We have demonstrated the self-assembly of Au nanoparticle arrays/dielectric layer/Ag mirror sandwiches, i.e., a local plasmon resonator, using a dynamic oblique deposition technique. The thicknesses of the Au and dielectric layers were changed combinatorially on a single substrate. As a result, local plasmon resonator chips were successfully fabricated. Because of strong interference, their optical absorption can be controlled between 0.0% and 97% in the near-IR region, depending on the thickness of the dielectric layer. We evaluated the heat generation from Au nanoparticles by measuring the temperature of water with which a cell prepared on a chip is filled under laser illumination. The change in the water temperature is proportional to the optical absorption of the local plasmon resonator chips. This suggests that the photothermal conversion efficiency can be controlled by interference. These features make the application of the local plasmon resonator to nanoheaters, which can spatiotemporally control heat generation, suitable.     

Almost Complex Structures Which Are Compatible with Kähler or Symplectic Structures

In this note we prove that half of all homotopy classes of almost complex structures on M is not compatible with any symplectic structure for a certain class of oriented compact 4-manifolds M. In particular, half of all homotopy classes of almost complex structures on an oriented 4-manifold is not compatible to any Kähler structure.     

Variations on the theme of slacks-based measure of efficiency in DEA

In DEA, there are typically two schemes for measuring efficiency of DMUs; radial and non-radial. Radial models assume proportional change of inputs/outputs and usually remaining slacks are not directly accounted for inefficiency. On the other hand, non-radial models deal with slacks of each input/output individually and independently, and integrate them into an efficiency measure, called slacks-based measure (SBM). In this paper, we point out shortcomings of the SBM and propose four variants of the SBM model. The original SBM model evaluates efficiency of DMUs referring to the furthest frontier point within a range. This results in the hardest score for the objective DMU and the projection may go to a remote point on the efficient frontier which may be inappropriate as the reference. In an effort to overcome this shortcoming, we first investigate frontier (facet) structure of the production possibility set. Then we propose Variation I that evaluates each DMU by the nearest point on the same frontier as the SBM found. However, there exist other potential facets for evaluating DMUs. Therefore we propose Variation II that evaluates each DMU from all facets. We then employ clustering methods to classify DMUs into several groups, and apply Variation II within each cluster. This Variation III gives more reasonable efficiency scores with less effort. Lastly we propose a random search method (Variation IV) for reducing the burden of enumeration of facets. The results are approximate but practical in usage.     

Ultrasonic butt welding of aluminum,aluminum alloy and stainless steel plate specimens

Welding characteristics of aluminum, aluminum alloy and stainless steel plate specimens of 6.0 mm thickness by a 15 kHz ultrasonic butt welding system were studied. There are no detailed welding condition data of these specimens although the joining of these materials are required due to anticorrosive and high strength characteristics for not only large specimens but small electronic parts especially. These specimens of 6.0 mm thickness were welded end to end using a 15 kHz ultrasonic butt welding equipment with a vibration source using eight bolt-clamped Langevin type PZT transducers and a 50 kW static induction thyristor power amplifier. The stainless steel plate specimens electrolytically polished were joined with welding strength almost equal to the material strength under rather large vibration amplitude of 25 microm (peak-to-zero value), static pressure 70 MPa and welding time of 1.0-3.0 s. The hardness of stainless steel specimen adjacent to a welding surface increased about 20% by ultrasonic vibration.     

Molecular structure and puckering potential of gas-phase 1-pyrroline as determined by microwave and infrared spectroscopy

The microwave spectrum of 1-pyrroline has been measured from 8 to 48 GHz. The transitions have been assigned to those of the ground state and the four lowest excited states of the ring-puckering vibration of monomer, which is a five-membered ring molecule with one CN double bond. The trimer, which exists in the liquid phase, has not been detected in the gas phase. The geometrical structure of the monomer has been estimated by an ab initio calculation and the trimer by a molecular mechanics calculation. The former is consistent with the experimental rotational constants. A gas-phase infrared spectrum has also been measured, and the ring-puckering potential has been determined by an analysis of the combination bands of the ring-puckering mode and the ring-stretching modes. The potential is described using a puckering coordinate, z, as V(z) = az² + bz⁴, where $\text{a = ?3.358(16) × 10}{}^4\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^{\mathrm{?2}}$ and $\text{b = 1.345(9) × 10}{}^6\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^{\mathrm{?4}}$; these values are intermediate of the corresponding values for cyclopentene and 1-pyrazoline. The nuclear quadrupole coupling constants, χ_aa = ?4.39(10), χ_bb = 1.04(10), and χ_cc = 3.35(10) MHz, have been determined by an analysis of well-resolved hyperfine splittings. These constants have been reproduced by an ab initio calculation with a 4-31G(N¹) basis set.     

Efficient Rabin-type Digital Signature Scheme

Rabin's cryptosystem was proved to be as hard as factorization. However, Rabin's digital signature schemes is probabilistic. This paper shows two efficient Rabin type digital signature schemes, a basic scheme and an improved scheme. Both schemes run much faster than Rabin's scheme. They are deterministic and the size of a signature is much smaller than that of a signature in Rabin's scheme. Furthermore, it is proved that, by applying the technique of Bellare and Rogaway, the proposed scheme is secure against chosen plaintext attack. More precisely, breaking the proposed digital signature scheme by chosen plaintext attack is as hard as factoring N.     

Irreducible Representations of Wreath Products of Association Schemes

The wreath product of finite association schemes is a natural generalization of the notion of the wreath product of finite permutation groups. We determine all irreducible representations (the Jacobson radical) of a wreath product of two finite association schemes over an algebraically closed field in terms of the irreducible representations (Jacobson radicals) of the two factors involved.