On the maximum cocliques of the rank 3 graph of 211 : M24

In this article, we consider the maximum cocliques of the 2¹¹: M₂₄ ‐graph Λ. We show that the maximum cocliques of size 24 of Λ can be obtained from two Hadamard matrices of size 24, and that there are exactly two maximum cocliques up to equivalence. We verify that the two nonisomorphic designs with parameters 5‐(24,9,6) can be constructed from the maximum cocliques of Λ, and that these designs are isomorphic to the support designs of minimum weights of the ternary extended quadratic residue and Pless symmetry [24,12,9] codes. Further, we give a new construction of Λ from these 5‐(24,9,6) designs. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 323–332, 2009     

Study of excited nucleon states at EBAC: status and plans

We present an overview of a research program for the excited nucleon states in Excited Baryon Analysis Center (EBAC) at Jefferson Lab. Current status of our analysis of the meson production reactions based on the unitary dynamical coupled-channels model is summarized, and the N~* pole positions extracted from the constructed scattering amplitudes are presented. Our plans for future developments are also discussed.     

Construction of anomalously bent biphenyl structure using conformational properties of calix[4]amide

C_2v-symmetrical cyclic tetramers of aromatic amides were simply synthesized in moderate yield by condensation reaction of N,N′-dimethyl-1,3-phenylenediamine and isophthalic acid derivatives using dichlorotriphenylphosphorane. The calix[4]amides exist in 1,3-alternate structure with cis conformation of tertiary aromatic amides, which were shown to be a versatile scaffold leading to a bowl-shaped macrocyclic compound possessing a anomalously strained structure, a bent hinge angle between two aromatic ring planes of biphenyl moiety, via an intramolecular ligation reaction.     

Involutions and semiinvolutions

We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.     

Synthesis of unimolecular reversed micelle consisting of a poly(L‐lactide) shell and hyperbranched D‐mannan core

A novel biodegradable unimolecular reversed micelle consisting of a poly(L ‐lactide) (PLA) shell and a hyperbranched D ‐mannan (HBM) core, that is, a chestnut‐shaped polymer (PLA–HBM), was synthesized by the polymerization of L ‐lactide on HBM with 4‐(dimethylamino)pyridine (DMAP) as the catalyst. The obtained polymers were soluble in dimethyl sulfoxide, tetrahydrofuran, and chloroform but insoluble in H₂O. The molecular weights of the PLA chain on PLA–HBM tended to increase with increasing polymerization time. The number of PLA chains on PLA–HBM could be controlled by the ratio of DMAP to the sugar unit in HBM. The obtained copolymer, PLA–HBM, acted as a unimolecular reversed micelle with an encapsulation ability toward the hydrophilic molecule. In addition, the entrapped hydrophilic molecules were slowly released from the core of PLA–HBM, and the release rate was accelerated by the breaking of the PLA chains of the shell when proteinase K as a hydrolase of PLA was used. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 406–413, 2006     

Asymptotic expansion of the one-loop approximation of the Chern–Simons integral in an abstract Wiener space setting

In an abstract Wiener space setting, we construct a rigorous mathematical model of the one-loop approximation of the perturbative Chern–Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.