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.     

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.     

Preparation of a cyclodextrin dimer linked with a bis(picolinyl)cystine moiety and its intra- and intermolecular inclusion behavior

A novel cyclodextrin (CD) dimer linked with a bis(picolinyl)cystine (Cys) moiety was prepared by the coupling of Boc-protected Cys with amino-modified CDs, followed by deprotection of the Boc groups and bispicolinylation. The dimer showed less affinity to an organic guest molecule compared to that of a native CD monomer. It was attributed to an intramolecular inclusion of the pyridine moiety into CD cavity. The dimer caused significant increase of its organic guest affinity by an addition of a copper ion. The included pyridine group may come out of a CD cavity to bind the copper ion and the two CDs included cooperatively and intermolecularly a guest molecule with high affinity.     

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.     

(Triisopropylsilyl)acetaldehyde acetal as a novel protective group for 1,2-diols

(Triisopropylsilyl)acetaldehyde dimethyl acetal (TIPS-ADMA) was synthesized from chlorotriisopropylsilane in three steps. Cyclic and acyclic 1,2-diols can be transformed to (triisopropylsilyl)ethylidene acetals (TIPS-AA). Removal of the acetal by LiBF₄ regenerates the starting diol in excellent yield even in the presence of an acetonide of 1,2-diol. The TIPS-AA group can survive under the deprotection conditions of the acetonide in acetic acid at 80 °C. Selective protection of 2,3- and 4,6-diols for O-methyl d-mannoside with TIPS-ADMA and selective deprotection of the acetals have been achieved.     

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.     

Electrochiroptical systems based on biphenyl-2,2′-diyl-type dicationic dyes: strong chiroptical signals through the transmission of point chirality to axial chirality

Huge CD amplitude (A = +538) was attained by diastereomeric preference (50% de) for the title dication with two bis[4-(R)-sec-butoxyphenyl]methylium units in benzene at 23 °C. Intramolecular π-π stacking is the origin for effective transmission of point chirality to axial chirality to attain the chiroptical enhancement of 400-times. Thanks to the strong CD signaling, chiroptical changes upon electrolysis could be readily detected, thus realizing a new class of electrochiroptical response systems. Chiroptical properties could also be modified by solvent polarity.