Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Phase Conjugation in Saturable Absorbing Dye Films by Degenerate Four-Wave Mixing and Holographic Processes Using Nanosecond Pulse and CW Lasers

We report on the simultaneous generation of phase-conjugate signals by degenerate four-wave mixing (DFWM) and holographic processes using a nanosecond pulse and a CW lasers in polyvinyl alcohol (PVA) films doped with four kinds of saturable absorbing dyes. For the pulse laser, of the four kinds of dye-doped PVA films, the erythrosine B-doped PVA and uranine doped-PVA films generate PC signals only by the DFWM process, while the other dye-doped PVA films generate PC signals simultaneously by not only the DFWM process but also the holographic process. Especially, the safranin T-doped PVA film generates strong PC signals by the holographic process. In contrast, all of the dye-doped PVA films generate the two types of PC signals for the CW laser. The fading of dye molecules is found to result in the generation of the holographic component of PC signals which governs the temporal behavior of the total PC signals.     

Plasma polymers from chloromethyltrimethylsilane and their modification with sodium azide

Plasma polymerization of chloromethyltrimethylsilane (CMTMS) was investigated by elemental analysis, infrared spectroscopy, and ESCA, and the modification of Cl substituents in the plasma polymers from CMTMS with sodium azide was discussed. CMTMS was plasma polymerized to yield filmy polymers. The polymer deposition rate was faster than that from tetramethylsilane containing no Cl atom. The plasma polymers from CMTMS were mainly composed of CH₃, CH₂, Si? CH₃, Si? O? Si, and Si? O? C groups with a small amount of C? Cl groups. The Cl substituents incorporated into the plasma polymers were capable of substitution reactions with azide groups to form azide polymers.     

Effect of annealing on structure and permeability of poly [(l-trimethylsilyl)-l-propyne]

The permeability of annealed poly (l-(trimethylsilyl)-l-propyne) was studied from the viewpoint of structural information obtained from x-ray diffraction and density. The sample cast from benzene solution had low density (0.82 g/cm³) and high permeability, whereas the annealed sample had a higher density (0.88 g/cm³) and permeability lower by two orders of magnitude. The smaller-angle x-ray diffraction peak for each sample, which was likely to reflect the distance between intermolecular chains, increased in intensity and shifted toward higher angle, corresponding to the change of the density with annealing. The logarithmic oxygen permeability was proportional to the density, namely the free volume fraction correlated with the diffusion coefficient and controlled by annealing and swelling by alcohols.     

Fast Optical Switching Using Oriented Cyanine Dye-Doped Nematic Liquid Crystal

A cyanine dye, 2-[7-（1,3-dihydro-1,3,3-trimethyl-2H-indol-2-ylidene）-1,3,5-heptatrienyl]-1,3,3-trimethyl-3H-indolium iodide （NK-125）, is doped in 4-cyano-4＇-pentylbiphenyl （5 CB）, and the mixture is sandwiched between two pieces of rubbed glass plates. The third-order nonlinear optical properties of the oriented NK-125-SCB layers are measured by the resonant femtosecond degenerate four-wave mixing （DFWM） technique at 760 nm. The third-order nonlinear optical susceptibility of one of the present samples is 5.5×10^-8 esu. The slow DFWM response of the NK-125-SCB layers due to a population grating is accelerated by the increasing laser power because of amplified spontaneous emission （ASE）. On the other hand, we do not observe a similar phenomenon for NK-125- polyethylene glycol （PEG-400）. Oriented NK-125 molecules in nematic liquid crystals must have very high ASE efficiency. Hence the population grating in a DFWM signal disappears within about 4 ps. It is expected that NK-125-SCB can be used as a material for very fast all-optical switching.     

Formation of Defect-Spinel Phase in CdSnO3

A spinel-type structure was found in cadmium stannate CdSnO₃ prepared by thermal decomposition of the hydroxostannate CdSn(OH)₆ at 550–800°C. Its occurrence depends strongly on the precipitation conditions of CdSn(OH)₆ from CdCl₂ and Na₂Sn(OH)₆ aqueous solutions. In the (Cd_1–xCa_x)SnO₃ system, the spinel phase appears in the composition range of 0.0 ≤ x ≤ 0.35. The experimental results suggest the presence of cation vacancies in the spinel octahedral sites.     

Major-to-ultratrace elements in bone-marrow fluid as determined by ICP-AES and ICP-MS.

The major-to-ultratrace elements in human bone-marrow fluid were determined by ICP-AES (inductively coupled plasma atomic emission spectrometry), and ICP-MS (inductively coupled plasma mass spectrometry). The bone-marrow fluid sample was centrifuged prior to acid digestion to exclude the bone piece from bone marrow, and then digested with nitric acid. As a result, 20 elements could be determined over the concentration range from 1610 microg g(-1) for Na to 0.00043 microg g(-1) for W. It was found that Fe, Zn and Sb were enriched by ca. 264-, 7- and 15-fold, respectively, in bone-marrow fluid, compared to those in human blood serum. Alkali metals (K, Rb, Cs), except for Na, were also significantly enriched in bone-marrow fluid. Furthermore, the concentrations of various elements, such as Fe, P, Al, Zn, Cu, Se, Zr, Sn, Ag and W, were significantly higher than those in open seawater.     

Formation of metallic NbSe2 nanotubes and nanofibers

We succeed in synthesizing NbSe₂ nanotubes along with nanofibers by chemical vapor transportation. They are stable crystalline systems and can be synthesized reproducibly in a nearly equilibrium reacting process. We have investigated these nanosize structures of NbSe₂ by transmission electron microscopy and electron diffraction. Both of the structures have a similar size of 100–200 nm in diameter. While nanotubes consist of rolled-up NbSe₂ layers, nanofibers are a pile of thin flat layers. We propose a mechanism of the formation of NbSe₂ nanotubes and nanofibers on the basis of deseleniditive transition from a NbSe₃ fiber-shaped crystal. We also measured electrical resistance of the nanofibers with conductive atomic force microscopy and demonstrated that the material show metallic behavior at room temperature.