Manuals in orthogonal categories

The notion of a manual, introduced and investigated in detail by Foulis, Randall, and their followers, has turned out to be further reaching than its originators had envisaged. Its omnipresence is comparable with the notion of a sheaf, whose significance is well recognized by every pure and applied mathematician. The principal concern of this paper is to give an appropriate vehicle, as general as possible, by which the theory of manuals can be developed. The vehicle is called an orthogonal category, which is akin to the notion of a category with coproducts. Orthogonal categories provide also a new perspective on the notion of a sheaf over a complete Boolean algebra, deepening our comprehension of Boolean mathematics and paving the way to quantum mathematics.     

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     

Copolymers containing a spiro orthoester moiety that undergo no shrinkage during cationic crosslinking

A spiro orthoester with an exomethylene group (exoSOE) was radically copolymerized with acrylonitrile or vinyl acetate at several feed ratios to obtain the corresponding copolymers having spiro orthoester moieties in the side chain. The obtained copolymers could be crosslinked via the double ring‐opening polymerization of the spiro orthoester moieties in their side chain by a treatment with BF₃OEt₂. The volume changes upon the crosslinking of the copolymers were evaluated by density measurements with a micromeritics gas pycnometer. The copolymers experienced less than 1% volume expansion instead of volume shrinkage during typical cationic crosslinking, regardless of the copolymer compositions. Negligible shrinkage was observed during the thermal cationic crosslinking of a film cast from a nitrobenzene solution of the copolymers containing a benzylthiophenium salt as a thermally latent cationic initiator. The constantly low volume changes during the crosslinking of the copolymers from exoSOE probably depended on the almost zero volume change during the cationic polymerizations of spiro orthoester derivatives. This indicates that exoSOE is an effective monomer for crosslinkable polymers without volume changes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3666–3673, 2006     

Confinement by polynomial potentials

It is shown that the Dirac equation with attractive monomial vector potential cannot confine a particle. General polynomial type vector potential cannot confine a particle, either. This condition is not changed by a scalar potential smaller than the vector one.     

Diastereoselective synthesis of new psi[(E)-CH=CMe]- and psi[(Z)-CH=CMe]-type alkene dipeptide isosteres by organocopper reagents and application to conformationally restricted cyclic RGD peptidomimetics

Diastereoselective synthesis of new psi[(E)-CH=CMe]- and psi[(Z)-CH=CMe]-type alkene dipeptide isosteres corresponding to dipeptides having one N-methylamino acid, and application to bioactive peptides, are described. In a key reaction introducing the chiral alpha-alkyl group of the isosteres, organocopper-mediated alkylation of syn-beta-methylated gamma-mesyloxy-alpha,beta-enoate 26a afforded E- and Z-isomers of anti-S(N)2' products in a solvent-dependent manner. The resulting two isosteres, D-Phe-psi[(E)-CH=CMe]-L-Val 27a and D-Phe-psi[(Z)-CH=CMe]-L-Val 28b, which corresponded to trans- and cis-conformers of D-Phe-L-MeVal, respectively, were utilized in a structure-activity relationship study on cyclic RGD peptides 1 and 2, in company with a psi[(E)-CH=CH]-type alkene dipeptide isostere, D-Phe-psi[(E)-CH=CH]-L-Val. The cyclic isostere-containing pseudopeptides 3, 4, and 40 were synthesized and biological activity against integrin alpha(V)beta(3) and alpha(IIb)beta(3) receptors were also evaluated.     

Single molecular multianalyte sensor: jewel pendant ligand

[structure: see text] The jewel pendant ligand has multiple chromogenic units combined in a single molecule with the dyes linked to a semiselective binding site by three heteroatoms (O, N, S) having different HSAB characteristics, to indicate diverse response to individual transition metal ions. Using a single-molecular multianalyte sensor, multiple analytes could be determined with a minimal sensing system.     

Preparation and photolysis of polyamides having coumarin dimer component

The ring-opening polyaddition reaction of anti and syn head-to-head Coumarin dimers with diamines and the photocleavage behavior of the resulting polyamides were investigated. Anti head-to-head Coumarin dimer successfully reacted with aliphatic and aromatic diamines in an aprotic polar solvent to give corresponding high molecular weight polyamides. The polyamides showed good film forming ability and exhibited solubility behavior typical of polyelectrolytes. Furthermore, these polyamides were found to undergo exclusively asymmetric photocleavage on the cyclobutane rings in the polymer main chain to give a fumaramide unit with elimination of 2,2′-dihydroxystilbene. On the other hand, syn head-to-head Coumarin dimer gave only low molecular weight polyamides. These polymerization and photocleavage behaviors were elucidated in comparison with those of model reactions.