Mathematical background for a method on quotient signal decomposition

The blind source separation problem is discussed in this article. Focusing on the assumption of independency of the sources in the time-frequency domain, we present a mathematical formulation for the estimation problem of the number of sources. The proposed method uses the quotient of complex valued time-frequency information of only two observed signals to detect the number of sources. No fewer number of observed signals than the detected number of sources is needed to separate sources. The assumption on sources is quite general independence in the time-frequency plane, which is different from that of independent component analysis. We propose algorithms with feedback and give numerical simulations to show the method works well even for noisy case.     

Closure, stability and iterated line graphs with a 2-factor

We consider 2-factors with a bounded number of components in the n-times iterated line graph Lⁿ(G). We first give a characterization of graph G such that Lⁿ(G) has a 2-factor containing at most k components, based on the existence of a certain type of subgraph in G. This generalizes the main result of [L. Xiong, Z. Liu, Hamiltonian iterated line graphs, Discrete Math. 256 (2002) 407-422]. We use this result to show that the minimum number of components of 2-factors in the iterated line graphs Lⁿ(G) is stable under the closure operation on a claw-free graph G. This extends results in [Z. Ryjá?ek, On a closure concept in claw-free graphs, J. Combin. Theory Ser. B 70 (1997) 217-224; Z. Ryjá?ek, A. Saito, R.H. Schelp, Closure, 2-factors and cycle coverings in claw-free graphs, J. Graph Theory 32 (1999) 109-117; L. Xiong, Z. Ryjá?ek, H.J. Broersma, On stability of the hamiltonian index under contractions and closures, J. Graph Theory 49 (2005) 104-115].     

Size-selected copper oxide nanoparticles synthesized by laser ablation

Size-tuned copper oxide nanoparticles with sizes of 9, 12, and 15 nm were fabricated by laser ablation and on-line size selection using a differential mobility analyzer at a gas pressure of 666 Pa. The dependence of the particle properties on the in situ annealing temperatures and selection sizes was investigated. The crystalline phases of the nanoparticles fabricated at temperatures below 973 K were assigned to monoclinic cupric oxide (CuO) which converted into cubic cuprous oxide (Cu₂O) when the annealing temperature was above 1,173 K. This indicates that the crystalline phases can be easily controlled by changing the annealing temperature. TEM images confirmed that well-crystallized and well-dispersed CuO and Cu₂O nanoparticles with narrow size distributions were obtained using this method. This fabrication process is useful and promising for the future investigation of the intrinsic size-dependent properties of CuO and Cu₂O.     

On a conjecture of ōshima

The set of homotopy classes of self maps of a compact, connected Lie group G is a group by the pointwise multiplication which we denote by H(G), and it is known to be nilpotent. ōshima [H. ōshima, Self homotopy group of the exceptional Lie group G₂, J. Math. Kyoto Univ. 40 (1) (2000) 177-184] conjectured: if G is simple, then H(G) is nilpotent of class ?rankG. We show this is true for PU(p) which is the first high rank example.     

Solvation dynamics of coumarin 153 in alcohols confined in silica nanochannels

Solvation dynamics in alcohols confined in silica nanochannels was examined by time-resolved fluorescence spectroscopy using coumarin 153 (C153) as a fluorescent probe. Surfactant-templated mesoporous silica was fabricated inside the pores of an anodic alumina membrane. The surfactant was removed by calcination to give mesoporous silica (Cal-NAM) containing one-dimensional (1D) silica nanochannels (diameter, 3.1 nm) whose inner surface was covered with silanol groups. By treating Cal-NAM with trimethylchlorosilane, trimethylsilyl (TMS) groups were formed on the inner surface of the silica nanochannels (TMS-NAM). Fluorescence dynamic Stokes shifts of C153 were measured in alcohols (ethanol, butanol, hexanol, and decanol) confined in the silica nanochannels of Cal- and TMS-NAMs, and the time-dependent fluorescence decay profiles could be best fitted by a biexponential function. The estimated solvent relaxation times were much larger than those observed in bulk alcohols for both Cal- and TMS-NAMs when ethanol or butanol was used as a solvent, indicating that the mobility of these alcohol molecules was restricted within the silica nanochannels. However, hexanol or decanol in Cal- and TMS-NAMs did not cause a remarkable increase in the solvent relaxation time in contrast to ethanol or butanol. Therefore, it was concluded that a relatively rigid assembly of alcohols (an alcohol chain) was formed within the silica nanochannels by hydrogen bonding interaction and van der Waals force between the surface functional groups of the silica nanochannels and alcohol molecules and by the successive interaction between alcohol molecules when alcohol with a short alkyl chain (ethanol or butanol) was used as a solvent.     

Synthesis of novel pentafluorosulfanylfurans. Two retro-Diels-Alder approaches

The first examples of furan substituted with an SF5 group are reported. 3-pentafluorosulfanylfurans were prepared from their respective 2-pentafluorosulfanyl-5-cyano-7-oxabicyclo[2.2.1]hept-2-ene precursors via retro-Diels-Alder reactions. Also, a tandem cycloaddition/retrocycloaddition reaction between 4-phenyloxazole and 1-pentafluorosulfanylhex-1-yne was used to prepare 3-pentafluorosulfanyl-4-butylfuran. [reaction: see text].     

Polymerization of allyl esters of unsaturated acids. VII. Copolymerization of methyl allyl maleate and fumarate with styrene

Radical copolymerizations of methyl allyl maleate (MAM) and methyl allyl fumarate (MAF) with styrene (St) are carried out in bulk using AIBN as an initiator at 60°C, and their copolymerization behaviors are compared in detail. The different rate features are observed with each other; thus in the MAF-St copolymerization the rate was quite enhanced and, also, the maximum rate was found at the molar ratio of 1:1 in the monomer feed, whereas no maximum phenomenon of the rate was apparent for the MAM—St copolymerization. The copolymerizability of MAF with St was quite high, whereas that of MAM was very poor. The cyclization of MAM or MAF was hindered by the highly reactive St monomer. These results are discussed in terms of the formation of the charge—transfer complex between MAF and St and, furthermore, the cyclocopolymerization kinetics involving the 17 elementary reactions as the propagation reactions.     

Synthesis of chiral oxime ethers based on regio- and enantioselective allylic substitution catalyzed by iridium-pybox complex

The oxygen atom of oximes acts as a reactive nucleophile in the iridium-catalyzed allylic substitution of unsymmetrical substrates to give the branched oxime ethers. Among several chiral ligands evaluated, the iridium complex of pybox ligand having phenyl group catalyzed the allylic substitution of phosphates with high activity to form the branched oxime ethers with good enantioselectivities.     

Studies on the biosynthesis of terrecyclic acid A II confirmation of the cyclization mechanism and hydrogen shifts using [2-2H3]acetate and [213C2H3]acetate

Feeding experiments with [2-³H₃]acetate and [2-¹³C²H₃]acetate in $\text{Aspergillus terreus}$ Thom No. 14 indicated that the hydrogen at C-2 in terrecyclic acid A is incorporated without migration from the precursor acetic acid; the results favour our group's earlier speculation for the cyclization to the tricyclic skeleton in the biosynthetic scheme.