Sturm bounds for Siegel modular forms of degree 2 and odd weights

Mathematische Zeitschrift - We correct the proof of the theorem in the previous paper presented by Kikuta, which concerns Sturm bounds for Siegel modular forms of degree 2 and of even weights...     

Formal Total Synthesis of (−)‐Taxol through Pd‐Catalyzed Eight‐Membered Carbocyclic Ring Formation

A formal total synthesis of (?)‐taxol by a convergent approach utilizing Pd‐catalyzed intramolecular alkenylation is described. Formation of the eight‐membered carbocyclic ring has been a problem in the convergent total synthesis of taxol but it was solved by the Pd‐catalyzed intramolecular alkenylation of a methyl ketone affording the cyclized product in excellent yield (97 %), indicating the high efficiency of the Pd‐catalyzed intramolecular alkenylation. Rearrangement of the epoxy benzyl ether through a 1,5‐hydride shift, generating the C3 stereogenic center and subsequently forming the C1–C2 benzylidene, was discovered and utilized in the preparation of a substrate for the Pd‐catalyzed reaction.     

Balancedly splittable Hadamard matrices

Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are presented. As an application, commutative association schemes of 4, 5, and 6 classes are constructed.     

An Efficacious Synthetic Strategy for cis-Clerodane Diterpenoids

Clerodane diterpenoids are widely distributed in nature and constitute one of the largest and, yet, still rapidly growing family of secondary metabolites. Of the relatively few clerodanes tested for biological activity, many were found to possess interesting antifeedant and medicinal properties and are potentially useful as insecticidal, antitumour, antifungal, antibiotic, anti-peptic ulcer, and psychotropic agents. The structural complexity and biological activity associated with this class of natural products have attracted extensive effort towards their total synthesis. In most of the reported syntheses, the synthetic sequence is specific to the target molecule. We have recently developed a versatile synthetic approach which is applicable to the synthesis of a large number of target molecules with minor modifications. The key operation of this approach is the face-selective Diels-Alder reaction of dienone ester 1. The successful application of this approach has culminated in the total synthesis of several cisclerodane diterpenoids. We have since made considerable improvement on this general synthetic approach, in terms of the overall efficiency, making use of compounds 2 and 3 as dienophiles. This newly developed general synthetic approach towards clerodane diterpenoids will be presented.     

Raman studies of lattice and local vibrational modes of GaInNAs prepared by molecular beam epitaxy

Polarized Raman spectra have been studied on the lattice-matched Ga_0.94In_0.06N_0.025As_0.975 epitaxial layers grown on (100) GaAs by molecular beam epitaxy. Polarization dependence of TO and LO phonon modes has been examined. The N-related local vibrational mode (LVM) in GaInNAs has been studied with emphasis on the light polarization and the effect of the thermal annealing. The thermal annealing-induced change of the N-related LVM in GaInNAs is discussed in terms of the local atomic arrangement around N atoms.