On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

Laser-induced periodic surface structures formed on the sidewalls of microholes trepanned by a femtosecond laser

Laser-induced periodic surface structures (LIPSSs) were observed on the sidewalls of 300-μm-diameter holes trepanned on cemented tungsten carbide using femtosecond laser pulses at a wavelength of 800 nm. For a circularly polarized beam, LIPSSs were formed at a period of 300 nm and oriented perpendicularly to the plane of incidence on the sidewalls. For a linearly polarized beam, LIPSS formation was dependent on the relative angle α between the polarization direction and the plane of incidence. For relative angles α from 0° to 70° and from 110° to 180°, LIPSS spacing was 300 nm. However, there were two types of LIPSSs coexisting from 70° to 110°. One had a spacing of 120 nm and the other had a spacing that varied from 500 to 760 nm. It was found that the orientation angle of LIPSSs measured between the LIPSS orientation and the plane of incidence had a nonlinear dependence on α. To understand this dependence, a model was proposed in which LIPSSs are assumed to align perpendicularly to the direction of the absorbed electric field lying in the tangent plane of the sidewall of a drilled hole. The calculated results from this model showed good agreement with the experimental results.     

Wavelength-Dependent Transient Characteristics Caused by Gain Saturation in Highly Nonlinear Fiber-Based Raman Amplifiers

We have investigated the transient characteristics of discrete Raman Amplifiers and found that the response time caused by gain saturation is dependent upon the wavelength, which corresponds to the effective length of the pump light.     

Modification of the surface state of rough substrates by two different varnishes and influence on the reflected light

Modification of the visual appearance when a rough surface is covered by a varnish is mostly attributed to the levelling of the substrate surface, which depends on the molecular weight of the varnish. The topography of varnished surfaces, however, has never been measured directly. Surfaces of varnishes applied over glass substrates of varying roughness were studied, therefore, using mechanical profilometry. Two different varnishes made with a low and a high molecular weight resin were studied. Both varnishes lower the r.m.s. roughness of the substrates and filter the high spatial frequencies. These results are amplified for the varnish containing the low molecular weight resin. The light reflected by the varnished samples is modelled from these topographical data. Its angular distribution, calculated from the probability density of slopes is presented, taking into account separately the air/varnish and the varnish/substrate interfaces. These analyses are presented in a back-scattering configuration. They show that varnishing significantly reduces the angular width of the reflected light and that this effect is magnified for the low molecular weight resin. Modelling furthermore shows that the influence of the roughness of the varnish/substrate interface is negligible in the total reflected light.     

On the Lp Space of Observables on Product MV Algebras

A weakly -distributive product MV algebra M is considered as a base of aquantum structure model. A state is a morphism from M to the unit interval, andan observable is a morphism from the system of all Borel sets to M. It is provedthat the subspace L ^p of the space of observables is a complete pseudometricspace. This result generalizes the previous result; the proof is new.     

Efficient approach to 1,2-diazepines via formal diazomethylene insertion into the C-C bond of cyclobutenones

Efficient monocyclic 1,2-diazepine formation via a tandem electrocyclization reaction of cyclobutenones with lithiodiazoacetate is demonstrated. The reaction proceeds through an oxy anion-accelerated 4π-ring opening of cyclobutene followed by an 8π-ring closure of the resultant oxy anion-substituted diazo-diene under mild conditions to furnish a 1,2-diazepine via formal diazomethylene insertion into the C-C bond of cyclobutenone.     

Stir bar sorptive extraction and thermal desorption-gas chromatography-mass spectrometry for trace analysis of triclosan in water sample

A simple and highly sensitive method called stir bar sorptive extraction (SBSE) and thermal desorption (TD)-gas chromatography-mass spectrometry (GC-MS), which is used for the determination of trace amounts of 5-chloro-2-(2,4-dichlorophenoxy)phenol (triclosan) in river water samples, is described. A stir bar coated with polydimethylsiloxane (PDMS) is added to a 10mL water sample and stirring is carried out for 120min at room temperature (25 degrees C) in a vial. Then, the PDMS stir bar is subjected to TD-GC-MS. The detection limit of triclosan is 5ngL(-1) (ppt). The method shows linearity over the calibration range (0.02-20mugL(-1)) and the correlation coefficient is higher than 0.997 for triclosan standard solution. The recovery of triclosan in river water samples ranges from 91.9 to 108.3% (RSD: 4.0-7.0%). This simple, accurate, sensitive, and selective analytical method may be used in the determination of trace amounts of triclosan in river water samples.     

Ruthenocene‐Type Complexes of N‐Fused Porphyrins

Ruthenocene‐type hybrid complexes with N‐fused porphyrinato ligands, [Ru(NFp)Cp] (NFp=N‐fused porphyrin, Cp=cyclopentadienyl), have been prepared and characterized by NMR and UV/Vis/NIR spectroscopy, cyclovoltammetry, and X‐ray crystallography. [Ru(NFp)Cp] is a common low‐spin ruthenium(II) complex and shows strong aromaticity. The Ru–Cp distance (1.833 Å) in [Ru(NFp)Cp] is comparable to that in [RuCp₂] (1.840 Å). DFT calculations on [Ru(NFp)Cp] showed the unequivocal contribution of the RuCp moiety as well as the NFp moiety to both the HOMO and LUMO, constructing a three‐dimensional d–π conjugated system. The HOMO–LUMO gaps of [Ru(NFp)Cp] are insensitive to the substituents on the NFp ligand, which is illustrated spectroscopically as well as theoretically. This is in sharp contrast to the ligand precursor, the N‐fused porphyrin, in which the HOMO–LUMO gap is affected by substituents in a similar manner to standard porphyrins and related macrocycles.