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.     

Semi-local units modulo Gauss sums

For thep-th cyclotomic fieldk, Iwasawa proved thatp does not divide the class number of its maximal real subfield if and only if the odd part of the group of local units coincides with its subgroup generated by Jacobi sums related tok. We refine and give a quantitative version of this result for more general imaginary abelian fields. Our result is an analogy of the famous result on “semi-local units modulo cyclotomic units”. Partially supported by Grant-in-Aid for Scientific Research (C), Grant 09640054.     

PHOTORECEPTOR CELL TYPES IN THE RETINA OF VARIOUS VERTEBRATE SPECIES: IMMUNOCYTOCHEMISTRY WITH ANTIBODIES AGAINST RHODOPSIN AND IODOPSIN

Types of photoreceptor cells in the retinas of 36 species of vertebrates (5 classes, 14 orders) were investigated immunocytochemically with monoclonal antibodies against chicken iodopsin (Io-mAb) and antiserum against bovine rhodopsin (Rh-As). In mammals, Rh-As labeled the outer segments of some photoreceptor cells in striped squirrels (a diurnal mammal) and those of most photoreceptor cells in mice (a nocturnal mammal), while Io-mAb labeled any photoreceptor cells in either of them. In all species of birds studied, Io-mAb labeled the principal and accessory members of double cones and single cones with a red oil droplet. Rh-As labeled single cones with a yellow or clear oil droplet in addition to rods. In turtles, both Rh-As and Io-mAb labeled single cones with a red or clear oil droplet and the principal (with a yellow oil droplet) and accessory members of double cones. This suggests that the visual pigments in these cones of turtles have common epitopes with bovine rhodopsin and chicken iodopsin. In Japanese grass lizards, single cones with a yellow oil droplet and double cones were immunoreactive to both Rh-As and Io-mAb. In snakes, rods and cones could not be distinguished but both positively and negatively stained cells were observed by the use of each antibody. In geckos, however, all photoreceptor cells were immunonegative to Io-mAb. In all species studied in amphibians, Rh-As labeled rods but not cones. Neither rods nor cones reacted with Io-mAb. In fishes, almost all species studied had well developed cones, and some of these cones were labeled by Rh-As. However, Io-mAb labeled the outer segments of some cones only in loaches. Rh-As labeled photoreceptor cells in all species of fishes studied. Thus, Rh-As recognized the outer segments of rods in all species studied from fishes to mammals, whereas the epitope recognized by Io-mAb is conserved in some species of fishes, most species of reptiles and all species of birds studied.     

Determination of ppb levels of tryptophan derivatives by capillary electrophoresis with homogeneous liquid-liquid extraction and sweeping method

Tryptophan (Trp) derivatives were selectively separated from 24 kinds of amino acid mixture solutions. Capillary electrophoresis (CE) with UV detection using the described pretreatment system was able to separate and determine 4 kinds of Trp derivatives: 5-hydroxy L-tryptophan, 5-methyl L-tryptophan, 1-methyl L-tryptophan and L-tryptophan. The pretreatment system used a combination of a homogeneous liquid-liquid extraction and a sweeping method, the two are different kinds of powerful preconcentration/separation methods. Trp derivatives were thus separated by two different separation systems. First, these derivatives were selectively extracted at 57-100% by a homogeneous liquid-liquid extraction; secondly, they were respectively separated by micellar electrokinetic chromatography (MEKC) with a sweeping effect. The detection limits following complete separation of the Trp derivatives were 10(-8) mol l(-1) levels, respectively. The proposed method provided a more than 10-fold the improvement in sensitivity compared with fluorescence labeling/fluorophotometric analysis; the proposed method was also applied to the component analysis of nutritious medicine.     

Catalytic,asymmetric Mannich-type reactions of alpha-imino esters bearing readily removable substituents on nitrogen

[reaction: see text] Catalytic, enantioselective Mannich-type reactions of alpha-imino esters bearing readily removable substituents on nitrogen are described. Several N-carbamate-protected alpha-imino esters, which are readily prepared from 2-bromoglycine esters using a polymer-supported amine, reacted with silicon enolates to afford the desired adducts in high yields with high enantioselectivity using a copper(II)-diamine complex. Easy deprotection of the product amine and transformation to free alpha-amino acid derivatives have also been demonstrated.     

Efficient photochemical oxetane formation from 1-methyl-2,4,5-triphenylimidazole and benzophenones

In contrast to simple imidazoles, 1-methy1–2,4,5-triphenylimidazole ($\text{1}$) produced stable oxetane photoadducts $\text{3b}$ - $\text{e}$ with good efficiency upon irradiation in the presence of benzophenone derivatives $\text{2b}$ - $\text{e}$ in acetonitrile solution. Irradiation in the solid-phase was also studied. The oxetanes $\text{3b}$ - $\text{e}$ readily underwent cycloreversion by acid catalysis or by heating.     

Optically active 1,2-bis(1-arylhydroxymethyl) ferrocene: a new, efficient chiral ligand for scandium-catalyzed asymmetric Diels-Alder reaction

[reaction: see text] The Sc(OTf)3/FERRODIOL (2) complex was prepared at -78 degrees C in CH2Cl2 in the presence of 2,6-lutidine and MS 4A. The chiral scandium Lewis acid-catalyzed asymmetric Diels-Alder reaction of cyclopentadiene (3) with 3-acyloxazolidin-2-ones (4) effectively produced the adduct (5) in a high yield with good selectivity, i.e., endo/exo = 90:10 up to 91% ee (endo).     

Asymmetric induction copolymerization. Cationic copolymerization of l-menthyl vinyl ether with indene and acenaphthylene

l-Menthyl vinyl ether (l-MVE) was homopolymerized and copolymerized with the monomers indene (IN) and acenaphthylene (ANp) by BF₃OEt₂ as a catalyst. The chiral menthyl substituent was cloven from the homopolymers and copolymers using dry-hydrogen bromide gas. After the removal of optically active menthyl group, poly(vinyl alcohol) (PVA) from l-MVE homopolymer was optically inactive, and copolymers (VA-IN, VA-ANp) from l-MVE-IN and l-MVE-ANp copolymers were still optically active. Hence, in the case of l-MVE homopolymer, it was concluded that asymmetric induction in the polymer main chain can only produce pseudoasymmetry. In the case of l-MVE-IN and l-MVE-ANp copolymers, it was found that asymmetric induction proceeded in the copolymer main chain and was caused by the influence of chiral menthyl group.     

Asymmetric induction radical copolymerization of optically active l-menthyl vinyl ether with vinylene carbonate and indene

The copolymerizations of l-menthyl vinyl ether (l-MVE) with the monomers vinylene carbonate (VCA) and indene (IN) were carried out in benzene with azobisisobutyronitrile (AIBN) as an initiator to obtain optically active copolymers. The optically active l-menthyl residue from the copolymer main chain was removed using dry hydrogen bromide gas. After the ether cleavage reaction, the copolymers prepared (VA–VCA and VA–IN) were still optically active, and hence it was found that asymmetric induction had taken place in the copolymer main chain. The optical rotatory dispersion (ORD) and circular dichroism (CD) data of the original and ether-cloven copolymers were also determined.