Selective Propargylation of Carbonyl Compounds and Imines with Barium Reagents

A Barbier‐type regioselective propargylation of aldehydes and ketones with (3‐bromobut‐1‐ynyl)trimethylsilane has been achieved using reactive barium as a low‐valent metal in THF. Especially in the case of ketones, the corresponding homopropargylic alcohols form almost exclusively. In the reaction of α,β‐unsaturated carbonyl compounds, only 1,2‐adducts have been observed. This method is also applicable to propargylation of imines, and the corresponding homopropargylic amines are obtained regiospecifically in good yields with diastereomeric ratios of up to 87:13.     

Rhodium-catalyzed addition of arylstannanes to carbon-heteroatom double bond

The addition of arylstannanes to the carbon-heteroatom double bond in the presence of a catalytic amount of a cationic rhodium complex ([Rh(cod)(MeCN)₂]BF₄) was examined. The reactions of aldehydes, α-dicarbonyl compounds, and N-substituted aldimines with the arylstannanes gave corresponding alcohols, α-hydroxy carbonyl compounds, and amines, respectively. An arylrhodium complex generated by the transmetalation with the arylstannane was probably the active catalytic species.     

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.     

Novel dinucleoside phosphotriester unit conjugated with an intercalative moiety in a stereospecific manner enhances thermal stability of an alternate-stranded triple helix

A novel phosphoramidite synthon of a dinucleoside phosphotriester unit bearing an intercalative moiety at its internucleotide linkage in a stereospecific manner was prepared and successfully incorporated into the middle portion of α-β chimeric oligoDNA. One of the resulting stereoisomeric chimera DNAs strongly enhances the thermal stability of an alternate-stranded triplex formed between the chimera and a double-stranded DNA.     

Rhodium-catalyzed carbonylation of 2-alkynylbenzylamine: a new route to the synthesis of benzazepinones

Rhodium-catalyzed carbonylation of 2-alkynylbenzylamines under water-gas shift reaction conditions gives a seven-membered heterocyclic product, 2,4-disubstituted-1,4-dihydrobenz[c]azepin-3-ones, in a good yield.     

Carbonyl allylations by 3-halopropenes or 2-propenyl mesylate with tin(IV) chloride and tetrabutylammonium iodide

2-Propenyl tin species, prepared from 3-halopropenes or 2-propenyl mesylate with tin(IV) chloride and tetrabutylammonium iodide in dichloromethane, causes nucleophilic addition to aldehydes to produce the corresponding homoallylic alcohols.     

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.