The Terwilliger Algebra Associated with a Set of Vertices in a Distance-Regular Graph

Let Γ be a distance-regular graph of diameter D. Let X denote the vertex set of Γ and let Y be a nonempty subset of X. We define an algebra τ = τ(Y). This algebra is finite dimensional and semisimple. If Y consists of a single vertex then τ is the corresponding subconstituent algebra defined by P. Terwilliger. We investigate the irreducible τ-modules. We define endpoints and thin condition on irreducible τ-modules as a generalization of the case when Y consists of a single vertex. We determine when an irreducible module is thin. When the module is generated by the characteristic vector of Y, it is thin if and only if Y is a completely regular code of Γ. By considering a suitable subset Y, every irreducible τ(x)-module of endpoint i can be regarded as an irreducible τ(Y)-module of endpoint 0.This research was partially supported by the Grant-in-Aid for Scientific Research (No. 12640039), Japan Society of the Promotion of Science. A part of the research was done when the author was visiting the Ohio State University.     

Hall subgroups of -groups need not be -groups

In this paper, we shall give examples of -groups that have Hall subgroups that are not -groups.

     

A globally and superlinearly convergent primal-dual interior point trust region method for large scale constrained optimization

This paper proposes a primal-dual interior point method for solving large scale nonlinearly constrained optimization problems. To solve large scale problems, we use a trust region method that uses second derivatives of functions for minimizing the barrier-penalty function instead of line search strategies. Global convergence of the proposed method is proved under suitable assumptions. By carefully controlling parameters in the algorithm, superlinear convergence of the iteration is also proved. A nonmonotone strategy is adopted to avoid the Maratos effect as in the nonmonotone SQP method by Yamashita and Yabe. The method is implemented and tested with a variety of problems given by Hock and Schittkowskis book and by CUTE. The results of our numerical experiment show that the given method is efficient for solving large scale nonlinearly constrained optimization problems.Acknowledgement The authors would like to thank anonymous referees for their valuable comments to improve the paper.     

Equilibrium anionic polymerization of 4,7-dioxaoctanal and n-octanal

Equilibrium anionic polymerization of 4,7-dioxaoctanal (DOA) and n-octanal (OA) was carried out in tetrahydrofuran in the temperature range of ?90 to ?68°C, and thermodynamic parameters were evaluated as follows: ΔH_ss = ?4.0 ± 0.1 kcal/mole, ΔS_ss = ?18.4 ± 0.5 cal/mole-deg, and T_c,ss = ?56°C for the DOA system; ΔH_sc = ?3.4 ± 0.1 kcal/mole, ΔS_sc = ?15.7 ± 0.4 cal/mole-deg, and T_c,sc = ?59°C for the OA system. Comparison of these values with those in the cases of β-methoxypropionaldehyde and n-valeraldehyde made it clear that the aliphatic aldehyde having a longer alkyl group polymerizes with smaller changes of enthalpy and entropy and that the polar-substituted aldehydes have higher polymerizability than the corresponding unsubstituted aliphatic aldehydes in the temperature range studied. These effects of substituents are interpreted from the viewpoint of the intermolecular interactions of polar groups in monomers and their polymers.     

Environment potential in closing bonds case

A method of an electronic structure calculation of cluster is suggested. It consists of an “effective” potential with an electron to close the torn valence bonds which appear inevitably in a finite-size-cluster model. The method is applied to the C₅ cluster representing the diamond lattice and is shown to be effective to nullify the pseudo-surface effects.     

Stereoselective synthesis of (+)-cerulenin from d-glucose

(+)-Cerulenin $\text{1a}$ was synthesized stereoselectively from D-glucose.     

A proton-driven amino acid pump: lipophilic primary ammonium cation—crown ether complex as a new type of anion-transport carrier

A lipophilic primary ammonium cation—crown ether complex was shown to mediate effectively active and passive transport of amino acid derivatives via proton/amino acid anion cotransport as well as anion/amino acid anion countertransport. It may offer a new chemical analog to amino group-containing carrier proteins and a prototype for an anion separation membrane.     

Energy transfer in the doped poly(N-Vinylcabazole)films

The energy transfer process to guest molecule5 m poly(N-vinylcarbJZole) films WJS directly nir.isurcd In (lie film con- taining pciylencihc sandwich excimer site opcralcs as an cncrEy donor, while the evciple't si-itc composed ofthccaiba2olc- dirnettiyl IcrcphtliaJate pair is fornied by trapping tlie migrating monomer fluorescent state.