The characteristic polynomial of a multiarrangement

Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using this polynomial we define the characteristic polynomial of a multiarrangement which generalizes the characteristic polynomial of an arrangement. The characteristic polynomial of an arrangement is a combinatorial invariant, but this generalized characteristic polynomial is not. However, when the multiarrangement is free, we are able to prove the factorization theorem for the characteristic polynomial. The main result is a formula that relates ‘global’ data to ‘local’ data of a multiarrangement given by the coefficients of the respective characteristic polynomials. This result gives a new necessary condition for a multiarrangement to be free. Consequently it provides a simple method to show that a given multiarrangement is not free.     

PTV investigation of phase interaction in dispersed liquid–liquid two-phase turbulent swirling flow

An investigation of dispersed liquid–liquid two-phase turbulent swirling flow in a horizontal pipe is conducted using a particle tracking velocimetry (PTV) technique and a shadow image technique (SIT). Silicone oil with a low specific gravity is used as immiscible droplets. A swirling motion is given to the main flow by an impeller installed in the pipe. Fluorescent tracer particles are applied to flow visualization. Red/green/blue components extracted from color images taken with a digital color CCD camera are used to simultaneously estimate the liquid and droplet velocity vectors. Under a relatively low swirl motion, a large number of droplets with low specific gravity tend to accumulate in the central region of the pipe. With increasing droplet volume fraction, the liquid turbulence intensity in the axial direction increases while that in the wall-normal direction decreases in the central region of the pipe. In addition, the turbulence modification in the present flow is strongly dependent on the droplet Reynolds number; however, the interaction of droplet-induced turbulences is significant due to vortex shedding, particularly at high droplet Reynolds numbers and higher droplet volume fraction.     

Influence of oxygen plasma treatment on boron carbon nitride film composition

Variations in the composition and bonds of boron carbon nitride (BCN) film caused due to an oxygen (O₂) plasma ashing process are investigated for a low dielectric constant (low-k) insulating film for next generation LSI devices. The O₂ plasma treatment is preformed for BCN samples with various C compositions. The etching rate of BCN films with an O₂ plasma decreases with increasing C composition. The reaction of O atoms is suppressed in the BCN film with a high C composition. B-N and B-C bonds with lower bond energies are easily broken by the O₂ plasma and replaced by the generation of B-O, N-O, and C-O bonds. The B-atom concentration for all samples is decreased significantly by the O₂ plasma treatment. Ion bombardment may play a more dominant role than the O-atom reaction in the etching of the BCN film. The existence of C-N bonds with a high bonding energy may suppress etching and incorporation of O atoms.     

Microscopic analysis of carbon phases induced by femtosecond laser irradiation on single-crystal SiC

Elemental analysis of femtosecond laser-induced modified region was carried out by transmission electron microscopy and Raman spectroscopy. The relative Raman intensities of a-SiC were higher in the peripheral region of laser irradiated spot where the fine ripple was formed. On the contrary, the relative Raman intensities of a-Si were higher in the central region where the coarse ripple was formed. This result suggests that the material migration has strongly occurred in the higher fluence region. On the other hand, the mapping of carbon atoms in the topmost amorphous layer of laser induced periodic structures did not show any significant segregation. In addition, Raman spectroscopic analysis showed that the domain size of carbon was very small (< 1 nm). From these facts, it was found that the carbon atoms were uniformly distributed in the topmost amorphous layer and were randomly connected without forming any observable fine particles.     

Chambers of 2-affine arrangements and freeness of 3-arrangements

We give a lower bound on the number of chambers divided by a family of lines in the real plane. Also, a sufficient condition for 3-arrangements to be free is given in terms of chambers. To prove them, we give the upper bound on differences of exponents for balanced 2-multiarrangements in terms of the cardinality of hyperplanes.     

Raman spectroscopic study of femtosecond laser-induced phase transformation associated with ripple formation on single-crystal SiC

Raman spectroscopy was performed to investigate microscopic structural changes associated with a ripple structure formation initiated by femtosecond laser irradiation on the surface of single-crystal silicon carbide. The amorphous phases of silicon carbide, silicon, and carbon were observed. The intensity ratio between amorphous silicon carbide and silicon changed discretely at the boundary between fine and coarse ripples. The physical processes responsible for the formation of the ripple structure are discussed.     

Novel freebase and zinc bilinone dimers with optically active peripheral groups. Synthesis and application to chiral nematic induction in a nematic mesophase

In order to investigate effective dopants to induce chiral nematic liquid crystalline phases, novel freebase (FbBL) and zinc bilinone (ZnBL) derivatives bearing optically active aliphatic groups ((S)-3,7-dimethyloctyls) at the peripheral positions were prepared. From the CD spectra, it was confirmed that M-helicity in the bilinone frameworks was modestly enriched for ZnBLs, whereas helicity was hardly induced for FbBLs except for the o-xylylene-spaced dimer. When N-(4-methoxybenzylidene)-4-butylaniline (MBBA) was doped with the bilinone derivatives, the chiral nematic phase was effectively induced, and the helical twisting powers (β_Ms) ranged from ?95 to ?159 μm^?1. The control experiment using (S)-3,7-dimethyl-1-phenyloctane (β_M = +14 μm^?1) clearly showed that the induced chiral helical frameworks of FbBL and ZnBL predominantly contribute to chiral nematic induction of MBBA.     

Design and concise synthesis of novel vitamin D analogues bearing a functionalized aromatic ring on the side chain

Five novel vitamin D analogues (2a, 2b, 3a, 3b and 4) bearing an aromatic side chain have been designed and synthesized in a convergent manner. The requisite CD-ring synthons (10a–c) were prepared from C22 aldehyde (5) using four- or five-step procedures. Using turbo-Grignard reagents allowed aromatic side chains with a polar functional moiety to be installed in a single step with excellent yields. A preliminary biological evaluation using bovine thymus vitamin D receptor (VDR) suggested that incorporating a carboxylic acid instead of the C25-hydroxy group had a positive effect on the VDR affinity compared with the corresponding esters.