Resonance-enhanced multiphoton ionization mass spectrometry using a two-color laser beam generated by stimulated Raman scattering.

Two-color (1+1') resonance-enhanced multiphoton ionization/time-of-flight mass spectrometry (REMPI/TOF-MS) combined with supersonic jet (SSJ) spectrometry has been demonstrated. The methodology uses a two-color laser beam consisting of a Stokes beam generated by stimulated Raman scattering (SRS) and a fundamental beam for the excitation and subsequent ionization of p-dichlorobenzene. The MPI signal was found to be substantially increased when a two-color laser beam was employed. This approach greatly simplifies the analytical system and reduces the cost of the instrumentation required for two-color ionization. The potential advantage of applying this method for the analysis of polychlorinated dibenzo-p-dioxin (PCDD) and polychlorinated dibenzofuran (PCDF) emitted from an incinerator is discussed.     

Kinetic study of the crosslinking reaction of 1,2‐polybutadiene with dicumyl peroxide in the absence and presence of vinyl acetate

The crosslinking reaction of 1,2-polybutadiene (1,2-PB) with dicumyl peroxide (DCPO) in dioxane was kinetically studied by means of Fourier transform near-infrared spectroscopy (FTNIR). The crosslinking reaction was followed in situ by the monitoring of the disappearance of the pendant vinyl group of 1,2-PB with FTNIR. The initial disappearance rate (R₀) of the vinyl group was expressed by R₀ = k[DCPO]^0.8[vinyl group]^−0.2 (120 °C). The overall activation energy of the reaction was estimated to be 38.3 kcal/mol. The unusual rate equation was explained in terms of the polymerization of the pendant vinyl group as an allyl monomer involving degradative chain transfer to the monomer. The reaction mixture involved electron spin resonance (ESR)-observable polymer radicals, of which the concentration rapidly increased with time owing to a progress of crosslinking after an induction period of 200 min. The crosslinking reaction of 1,2-PB with DCPO was also examined in the presence of vinyl acetate (VAc), which was regarded as a copolymerization of the vinyl group with VAc. The vinyl group of 1,2-PB was found to show a reactivity much higher than 1-octene and 3-methyl-1-hexene as model compounds in the copolymerization with VAc. This unexpectedly high reactivity of the vinyl group suggested that an intramolecular polymerization process proceeds between the pendant vinyl groups located on the same polymer chain, possibly leading to the formation of block-like polymer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4437–4447, 2004     

On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

In this paper we focus on the problem of identifying the index sets P(x):=i|x_i>0, N(x):={i|F_i(x)>0 and C(x):=i|x_i=F_i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10     

Thermodynamic study of sodium-iron oxides: Part II. Ternary phase diagram of the Na-Fe-O system

Studies on ternary phase diagrams of the Na-Fe-O system have been carried out from the thermodynamic point of view. Thermodynamic data of main ternary Na-Fe oxides Na₄FeO₃(s), Na₃FeO₃(s), Na₅FeO₄(s) and Na₈Fe₂O₇(s) have been assessed. A user database has been created by reviewing literature data together with recent DSC and vapor pressure measurements by the present authors. New ternary phase diagrams of the Na-Fe-O system have been constructed from room temperature to 1000 K. Stable conditions of the ternary oxides at 800 K were presented in predominance diagram as functions of oxygen pressure and sodium pressure.     

A globally convergent Newton method for solving strongly monotone variational inequalities

Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.     

Multimode optical fiber demultiplexer-star coupler using a single gradient-index-rod lens and a multi-facet grating

An optical fiber multi-function device consisting of a single gradient-index-rod lens and a multi-facet blazed reflection grating is proposed to simultaneously realize functions of wavelength demultiplexing and optical signal distribution in a multimode optical fiber transmission system. We analyzed the demultiplexing characteristics and the tolerance of optical components using the ray trace method. This device can realize not only low loss optical signal distribution but also offers improved demultiplexing characteristics in comparison with the previously proposed demultiplexer-multiposition switch. The following characteristics are expected from the design using commercially available optical components: a working band of 0.64–0.88 μm, channel separation of 34–36 nm, 3 dB bandwidth of 27–28 nm, channel cross-talk of less than - 40 dB and minimum excess insertion loss of 0.9–2.1 dB.     

On equivalence of L p -norms related to Schrödinger type operators on Riemannian manifolds

In this paper, we study Schrödinger type operator on a Riemannian manifold. Under some assumptions on a potential function, we characterize the domain of the square root of the Schrödinger type operator on L ^p space. In the proof, the defective intertwining properties and the Littlewood-Paley inequalities play important roles.