Structure-activity study of intact porcine motilin

Biologically important sites on intact porcine motilin (pMTL) were explored using its partial peptides. The partial peptides were synthesized using Fmoc (9-fluorenylmethyloxycarbonyl) solid phase methodology, and tested for the binding activity to motilin receptor and the smooth muscle contractile activity. The results were as follows: important residues for the contractile activity were found to be Phe1, Ile4, and Tyr7, and an open space existed beyond the N-terminus between motilin and its receptor. On the model of interaction between motilin and motilin receptor evolved from these results, the three points of interaction, due to Phe1, Ile4, and Tyr7, and the presence of an open space were expected. The motilin agonist and antagonist, designed on this model, will help the inquiry into motilin associated diseases.     

Rapid time-decay and net force to the obstacles by the Stokes flow in exterior domains

Consider the nonstationary Stokes equations in exterior domains with the compact boundary . We show first that the solution decays like for all as . This decay rate is optimal in the sense that for some as occurs if and only if the net force exerted by the fluid on is zero. Received: 15 June 2000 / Published online: 18 June 2001     

A removable isolated singularity theorem for the stationary Navier-Stokes equations

We show that an isolated singularity at the origin 0 of a smooth solution (u,p) of the stationary Navier-Stokes equations is removable if the velocity u satisfies u∈Lⁿ or |u(x)|=o(|x|^-1) as x→0. Here n?3 denotes the dimension. As a byproduct of the proof, we also obtain a new interior regularity theorem.     

Viscoelastic properties of bis(phenyl)fluorene‐based cardo polymers with different chemical structure

Viscoelastic properties of urethane and ester conjugation cardo polymers that contain fluorene group, 9,9‐bis(4‐(2‐hydroxyethoxy)phenyl)fluorene (BPEF), were investigated. As for the urethane‐type cardo polymers containing BPEF in the main chain, it had a high glass‐transition temperature (T_g), which was observed as the α dispersion on viscoelastic measurement, and its temperature depended on the chemical structure of the spacing unit, such as toluene diisocyanate (TDI), 4,4′‐methylene diphenyl diisocyanate (MDI), methylene dicycloexyl diisocyanate (CMDI), and hexamethylene diisocyanate (HDI). Moreover, the T_g of urethane‐type cardo copolymers with various cardo contents increased with an increase of cardo content. Owing to the increase of T_g of cardo polymers, another molecular motion can be measured at the temperature between the α and β dispersion that was assigned to the molecular motion of urethane conjugation unit around 200 K, and it was referred to as the α_sub dispersion. The peak temperature of the α_sub dispersion was influenced by the chemical structure of the spacing unit, but it did not change for the cardo polymer containing the same spacing unit. Consequently, it was deduced that the α_sub dispersion was originated in the subsegmental molecular motions of the cardo polymers. Ester‐type cardo polymer had higher T_g in comparison with noncardo polymer that consisted of dimethyl groups (BPEP) instead of BPEF as well. The α_sub dispersion was also measured at the temperature between the α and β dispersion, which was assigned to the molecular motion of ester conjugation unit, around 220 K. For ester cardo polymer, the γ dispersion was measured in a low‐temperature region around 140 K, and it was due to a small unit motion in the ester‐type cardo polymers, such as ethoxyl unit, ? C₂H₄O? . Moreover, the intensity of the γ dispersion of noncardo polymer was higher than that of cardo polymer, which means the molecular motion was much restricted by the cardo structure of BPEF. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2259–2268, 2005     

The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in and the gradient flow to the harmonic map to the sphere are discussed. Namely the Serrin-Ohyama type regularity criteria are improved in the terms of the Besov spaces. Received: 21 September 2000; in final form: 16 Feburary 2001 / Published online: 18 January 2002