On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

On the Shintani zeta function for the space of binary quadratic forms

Partially supported by NSF Grant DMS-8803085, DMS-8610730     

Constructive and Destructive Two-Pulse Excitation Investigated with a White-Light Michelson Interferometer

Linear propagation of two pulses through methanol solution of aluminum phthalocyanine chloride is investigated using a modified white-light Michelson interferometer. The observed coherence time of the white light is 6 fs, and the separation between the two-excitation pulses is set to about 10 fs. The excitation is dependent on the phase-relation between the two pulses. We have observed an enhancement of the excitation when the two pulses are in-phase and strong suppression of the excitation when the two pulses are out of phase by π.     

Spacer effect of appended moieties for molecular recognition in doubly-sodium anthranilate modified γ-cyclodextrin

-Cyclodextrin with two sodium anthranilate moieties (1) has been prepared as a sensor for detecting organic compounds including terpenoids and steroids. Compound1 shows a pure monomer fluorescence whose intensity is increased or decreased upon addition of the guest species examined. In this system, the sodium anthranilate moieties act either as a spacer, which enables the cyclodextrin to form a 1:1 host-guest complex by narrowing the -cyclodextrin cavity, or as a hydrophobic cap.1 recognizes steroids with much higher sensitivity than terpenoids, in which the appended moieties act as a hydrophobic cap for terpenoids and a spacer for steroids, respectively.     

Syntheses and thermal reactions of 2-alkyl(or aryl)-1-benzoyl-3,4-dihydro-2-thianaphthalenes

1-Benzoyl-2-methy1-3,4-dihydro-2-thianaphthalene ($\text{4a}$) underwent novel intermolecular 1,4-rearrangement in refluxing toluene to give an enol ether $\text{5a}$, while rearrangement of 2-phenyl derivative $\text{4e}$ proceeded intramolecularly in refluxing xylene to afford a 1,4-rearranged enol ether $\text{5b}$. On the other hand, ylides $\text{4a–e}$ were refluxed in alcohols to afford some ring-opened products $\text{10–12}$.     

Resolution of lymphocyte subpopulations derived from rat spleen by polyamine-graft-PHEMA copolymer

The retention behavior of lymphocyte subpopulations, B cell, T cell and null cell, derived from rat spleen to polyamine-graft-poly(2-hydroxyethyl methacrylate) copolymer (HA) surface was investigated, focusing on the conformational transition of the polyamine side chain as well as the protonation of amino groups in the polyamine grafts. Furthermore, the availability of HA was discussed as a column adsorbent for separation of lymphocyte subpopulations derived from spleen. The conformational transition of polyamine grafts significantly influenced the mode of retention of lymphocyte subpopulations. When polyamine grafts existed in an aggregated conformation (protonatin degree α < 0.5), the retention of lymphocyte subpopulations was decreased in the order B cell> null cell> T cell. On the other hand, when polyamine existed in an extended conformation into the aqueous interior from the matrix interface (α > 0.5), T cell retention became greater than null cell retention, resulting in a decreased B cell> T cell> null cell order. These results indicate that the differential retention of spleen lymphocyte subpopulations is attributed to their differential responses to the change in matrix interface accompanied by the protonation of amino groups. Furthermore, spleen lymphocytes were compared with lymph node lymphocytes in terms of resolution efficacy by an HA copolymer column.     

Cation binding properties of crown ether-modified polyethylenimines

Crown ether-modified polyethylenimines (PEI-CR) were prepared to elucidate their cation binding efficiency and selectivity by liquid-liquid and solid-liquid extraction methods. With alkali metal cations it was found that polyethylenimines containing benzo-15-crown-5 moieties (Ia and Ib) extracted all cations examined more efficiently than their monomeric analogs, especially in the cases of K⁺ and Rb⁺ cations. The solid-liquid extraction revealed clearly that the polymers complexed with K⁺ and Rb⁺ cations according to a 1:2 cation-to-crown stoichiometry. The high selectivities of the polymers for K⁺ and Rb⁺ were interpreted in terms of the favourable conformation of the polymer chain for the formation of intramolecular 1:2 complexes. On the contrary, these polymers bound alkali earth cations less effectively with low selectivities.     

Novel polycationic biocides: Synthesis and antibacterial activity of polymeric phosphonium salts

Various polymeric phosphonium salts and the corresponding low-molecular-weight model compounds were prepared and their antibacterial activities against Staphylococcus aureus and Escherichia coli were explored by the viable cell counting method in sterile distilled water. Antibacterial activity of the polymers was found to be higher than that of the corresponding model compounds, particularly against S. aureus. Furthermore, the polymeric phosphonium salt exhibited a higher activity by 2 orders of magnitude than the polymeric quaternary ammonium salt with the same structure except the cationic part. Compounds with the longest alkyl chain (octyl) studied were found to exhibit particularly high activity, and this finding may be ascribed to the contribution of the increased hydrophobicity of the compounds to the cidal activity. © 1993 John Wiley & Sons, Inc.     

α-Carboxylation reaction of carbonyl compounds with bromomagnesium ureide-carbon dioxide adducts

Bromomagnesium ureide-carbon dioxide adducts, models of the carboxylated biotin complex, undergo caboxylation of a variety of carbonyl compounds in good yield.     

A novel measurement method of Donnan potential at an interface between a charged membrane and mixed salt solution

We developed a novel measurement method of the Donnan potential difference at a charged membrane/salt solution interface. The method can measure the potential under the condition that the membrane charge density is much lower than the KCl concentration of the salt bridge. This method is very useful for obtaining the effective charge density of each layer of a bipolar membrane. The present experiments in a system of a negatively charged poly(vinyl alcohol) membrane and a single salt solution of KCl, NaCl, LiCl, CaCl₂ and LaC₃ revealed that the membrane effective charged density has the same value for all the ions. The experiments in mixed KCl and CaCl₂ solution revealed that the potential in the system is governed mainly by the concentration of the counterion having the highest valence in the system.