Site-Selective Supramolecular Complexation Activates Catalytic Ethane Oxidation by a Nitrido-Bridged Iron Porphyrinoid Dimer

Development of supramolecular methods to further activate a highly reactive intermediate is a fascinating strategy to create novel potent catalysts for activation of inert chemicals. Herein, a supramolecular approach to enhance the oxidizing ability of a high-valent oxo species of a nitrido-bridged iron porphyrinoid dimer that is a known potent molecular catalyst for light alkane oxidation is reported. For this purpose, a nitrido-bridged dinuclear iron complex of porphyrin-phthalocyanine heterodimer 3 ⁵⁺, which is connected through a fourfold rotaxane, was prepared. Heterodimer 3 ⁵⁺ catalyzed ethane oxidation in the presence of H₂O₂ at a relatively low temperature. The site-selective complexation of 3 ⁵⁺ with an additional anionic porphyrin (TPPS⁴⁻) through π–π stacking and electrostatic interactions afforded a stable 1:1 complex. It was demonstrated that the supramolecular post-synthetic modification of 3 ⁵⁺ enhances its catalytic activity efficiently. Moreover, supramolecular conjugates achieved higher catalytic ethane oxidation activity than nitrido-bridged iron phthalocyanine dimer, which is the most potent iron-oxo-based molecular catalyst for light-alkane oxidation reported so far. Electrochemical measurements proved that the electronic perturbation from TPPS⁴⁻ to 3 ⁵⁺ enhanced the catalytic activity.     

Polymerization of 1,3‐dienes with functional groups. III. Free‐radical polymerization of N,N‐diethyl‐2‐methylene‐3‐butenamide

Free‐radical homo‐ and copolymerization behavior of N,N‐diethyl‐2‐methylene‐3‐butenamide (DEA) was investigated. When the monomer was heated in bulk at 60 °C for 25 h without initiator, rubbery, solid gel was formed by the thermal polymerization. No such reaction was observed when the polymerization was carried out in 2 mol/L of benzene solution with with 1 mol % of azobisisobutyronitrile (AIBN) as an initiator. The polymerization rate (R_p) equation was R_p ∝ [DEA]^1.1[AIBN]^0.51, and the overall activation energy of polymerization was calculated 84.1 kJ/mol. The microstructure of the resulting polymer was exclusively a 1,4‐structure where both 1,4‐E and 1,4‐Z structures were included. From the product analysis of the telomerization with tert‐butylmercaptan as a telogen, the modes of monomer addition were estimated to be both 1,4‐ and 4,1‐addition. The copolymerizations of this monomer with styrene and/or chloroprene as comonomers were also carried out in benzene solution at 60 °C. In the copolymerization with styrene, the monomer reactivity ratios obtained were r₁ = 5.83 and r₂ = 0.05, and the Q and e values were Q = 8.4 and e = 0.33, respectively. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 999–1007, 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     

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.     

Reconstruction of the Point-Spread Function of the Human Eye Using a New Phase-Retrieval Algorithm

The double-pass method is thought to obtain the point spread function (PSF) in human eyes based on two techniques: the symmetric double-pass method using the same pupil size and the asymmetric double-pass method using a different pupil size. The symmetric double-pass method provides autocorrelation of the retinal PSF and, thus, the modulation transfer function. The asymmetric double-pass method provides low-frequency partial-phase information and the partial phase-retrieval algorithm is applied to obtain the complete-phase information, and to estimate the PSF. The partial phase-retrieval algorithm is based on the iteration method proposed by Fineup and Kowalczyk and requires a lengthy computation. In this study, we propose a new high-speed phase-retrieval algorithm based on the property that the real and imaginary parts of optical transfer functions (OTFs) continuously change in value.     

An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve

This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage pool’s cash flow is allocated by rule to the two bond classes such that PAC bondholders receive substantial prepayment protection, that protection being provided by the companion bondholders. The structure we propose provides greater protection to the PAC bondholders than current structures during periods of rising interest rates when this class of bondholders faces greater extension risk. We do so by allowing a portion of the cash flow from the collateral to be reserved to meet the PAC’s scheduled cash flow in subsequent periods. The greater protection is provided by the companion bondholders exposure to interest loss. To tackle this problem, we transform the problem of designing the optimal PAC-companion structure into a standard stochastic linear programming problem which can be solved efficiently. Moreover, we present an extended model by considering the quality of the companion bond and by relaxing the PAC bondholder shortfall constraint. Based on numerical experiments through Monte Carlo simulation, we show the utility of the proposed model.     

Application of novel SIMS technique for imaging the active sites of oxygen reduction at the SOFC cathode/electrolyte interfaces

The oxygen reduction active sites were visualized around the O₂/SOFC cathode/electrolyte triple phase boundaries (TPB) by the¹⁶O/¹⁸O exchange techniques and secondary ion mass spectrometry (SIMS) analysis. The higher¹⁸O concentration is observed on the cathode top surfaces (La_0.9Sr_0.1MnO₃-mesh, Au-mesh, and Ag-porous), which suggested the promotion of oxygen adsorption and oxygen surface exchange at the cathode. The oxygen diffusion through the bulk of cathode occurred at the La_0.9Sr_0.1MnO₃-mesh and the Ag-porous cathodes, not at the Au-mesh cathode. On the YSZ surfaces after removing the cathode, the active sites for oxygen incorporation were analyzed by SIMS. The active sites for oxygen incorporation were at the La_0.9Sr_0.1MnO₃/YSZ interface as well as the TPB. On the other hand, the active sites for oxygen incorporation are limited to the TPB in the case of the Au-mesh removed YSZ surface. From the SIMS analysis, the expansion of the active sites for oxygen incorporation is less than a few μm from the TPB lines. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.     

Primal-dual proximal point algorithm for linearly constrained convex programming problems

A primal-dual version of the proximal point algorithm is developed for linearly constrained convex programming problems. The algorithm is an iterative method to find a saddle point of the Lagrangian of the problem. At each iteration of the algorithm, we compute an approximate saddle point of the Lagrangian function augmented by quadratic proximal terms of both primal and dual variables. Specifically, we first minimize the function with respect to the primal variables and then approximately maximize the resulting function of the dual variables. The merit of this approach exists in the fact that the latter function is differentiable and the maximization of this function is subject to no constraints. We discuss convergence properties of the algorithm and report some numerical results for network flow problems with separable quadratic costs.