On critical exponents of Dowling matroids

The critical problem in matroid theory is the problem to determine the critical exponent of a given representable matroid over a finite field. In this paper, we study the critical exponents of a class of representable matroids over finite fields, called Dowling matroids. Then the critical problem for a Dowling matroid is corresponding to the classical problem in coding theory to determine the maximum dimension k such that there exists an \([n,k,d]_q\) code for given n, d and q. We give a necessary and sufficient condition on the critical exponents of Dowling matroids by using a coding theoretical approach.     

Mechanism and control of crack generation in glass substrates during crystallization of a-Si Films by flash lamp annealing

We investigate the impact of the materials of glass substrates on crack formation during flash lamp annealing (FLA) of 4.5 μm-thick precursor amorphous silicon (a-Si) films for the formation of polycrystalline Si (poly-Si) films. The use of soda lime glass substrates, with the largest thermal expansion coefficient (α) and the lowest glass transition temperature (T_g) in glass materials attempted in this study, results in the serious formation of cracks on and inside the glass substrates. Cracks are also seen on the surface of quartz glass substrates, which have much smaller α and higher T_g, after FLA. Furthermore, flash-lamp-crystallized (FLC) poly-Si films have linearly-connected low-crystallinity regions only when quartz glass substrates are used. These facts indicate that the expansion of Si films induces cracks in quartz glass substrates, while the expansion of the upper part of glass is the cause of the crack formation in glass substrates with large α. The generation of cracks is most significantly suppressed when we use alkali-free glass substrates, with a moderate α and a relatively high T_g, which will contribute to the realization of high-quality poly-Si films and high-performance solar cells.     

Study on solid structure of pentacene thin films using Raman imaging

We present a 532‐nm excited Raman imaging study of pentacene thin films (thickness, 2, 5, 10, 20, 50, 100, and 150 nm) prepared on an SiO₂ surface. The structure of the pentacene films has been investigated by images and histograms of the ratio (R) of intensity of the 1596‐cm⁻¹ band (b_3g) to that of the 1533‐cm⁻¹ band (a_g), which can be used as a marker of solid‐state phases: 1.54‐nm and 1.44‐nm phases. The Raman images showed that island‐like 1.44‐nm phase domains are grown on the 1.54‐nm phase layer from 50 nm, and all the surface of the 1.54‐nm phase layer is covered with the 1.44‐nm phase layer from 100 nm. The structural disorders have been discussed on the basis of the full width at half maximum of a band in the histogram of the R values for each film. Copyright © 2012 John Wiley & Sons, Ltd.     

Superconducting properties in Rh17S15 under magnetic field and pressure

We have studied superconducting properties by measuring the electrical resistivity and magnetization for a single crystal of Rh₁₇S₁₅ with a superconducting transition temperature T_c=5.4 K. The upper critical field H_c2(0) and the lower critical field H_c1(0) were obtained as 20.5 and 0.0033 T, respectively. Correspondingly, the coherence length and the penetration depth were estimated to be 40 and 4900 Å, respectively, indicating that Rh₁₇S₁₅ is a typical type-II superconductor with strong correlations of conduction electrons with a 4d-electron character of Rh atoms. The present electron correlations are formed to be enhanced with increasing pressure.     

Stereoselective Synthesis and Physicochemical Properties of Liquid‐Crystal Compounds Possessing a trans‐2,5‐Disubstituted Tetrahydropyran Ring with Negative Dielectric Anisotropy

Three stereoselective syntheses and the physicochemical properties of trans,trans‐5‐(4‐ethoxy‐2,3‐difluorophenyl)‐2‐(4‐propylcyclohexyl)tetrahydropyran, which is an important liquid‐crystal compound with a large negative dielectric anisotropy (Δε=?7.3), are described. The key step in the construction of the trans‐2,5‐disubstituted tetrahydropyran ring in the first approach involved a benzylic cation mediated intramolecular olefin cyclization of a 2‐allyloxy‐1‐arylethanol derivative. The second method included the Et₂Zn‐induced 1,2‐aryl shift of a bromohydrin obtained from a hetero‐Diels–Alder reaction, followed by stereoselective bromination. The third approach utilized the hetero‐Diels–Alder reaction of trans‐4‐propylcyclohexanecarboxaldehyde and a 2‐aryl‐3‐(trimethylsilyl)oxy‐1,3‐butadiene, followed by stereoselective protonation. From results obtained by using a quantum chemical calculation method, the reason why the target compound shows a large negative Δε value is discussed.