Irregular Behavior of Solutions for Fisher’s Equation

This paper is concerned with the irregular behavior of solutions for Fisher’s equation when initial data do not decay in a regular way at the spatial infinity. In the one-dimensional case, we show the existence of a solution whose profile and average speed are not convergent. In the higher-dimensional case, we show the existence of expanding fronts with arbitrarily prescribed profiles. We also show the existence of irregularly expanding fronts whose profile varies in time. Proofs are based on some estimate of the difference of two distinct solutions and a comparison technique. Dedicated to Professor Pavol Brunovsky on his 70th birthday.     

Grow-up rate of solutions for a supercritical semilinear diffusion equation

We study solutions of the Cauchy problem for a supercritical semilinear parabolic equation which converge to a singular steady state from below as t→∞. We show that the grow-up rate of such solutions depends on the spatial decay rate of initial data.     

Reaction of poly(vinyl alcohol) with tetravalent ceric ion

Poly(vinyl alcohol) (PVAI) was oxidized by ceric ion, Ce(IV), in aqueous HNO₃ medium at different temperatures and found to be degraded as a result of selective cleavage of the 1,2-glycol unit existing in PVAl. The rate of oxidation increased with increasing temperature. The aldehyde groups formed at the ends of the degraded polymer upon oxidation were relatively stable at 0°C. With rise of temperature, the aldehyde groups reacted either with excess of Ce(IV) to carboxylic acids or with hydroxyl groups of PVAl molecules to give acetal linkage. When the acetalization predominated over the oxidation to carboxyl group, gelation of the reaction mixture was observed. Based on these results, a plausible mechanism of oxidation of PVAl with Ce(IV) and the subsequent reactions is discussed.     

First artificial receptors and chemosensors toward phosphorylated peptide in aqueous solution

The first fluorescent chemosensors toward a native phosphorylated peptide are successfully synthesized. Dinuclear zinc(II)-dipicolylamine-based anthracene (1, 2) can selectively recognize and sense phosphorylated species with an increase in the fluorescence intensity. We also demonstrated that these artificial receptors fluorometrically detect a phosphorylated peptide with high affinity (>107 M-1) in aqueous solution.     

High-speed counter-current chromatography of apple procyanidins

Apple procyanidins were separated by high-speed counter-current chromatography using a type-J multilayer coil planet centrifuge. Several two-phase solvent systems with a wide range of hydrophobicities from a non-polar hexane system to polar n-butanol systems were evaluated their performance in terms of the partition coefficient and the retention of the phase. The best separation of procyanidins B and C was achieved with a two-phase solvent system composed of n-butanol-methyl tert.-butyl ether-acetonitrile-0.1% trifluoroacetic acid (2:4:3:8) using the lower phase as a mobile at a flow-rate of 1.0 ml/min.     

FLAVIN-PHOTOSENSITIZED MONOMERIZATION OF DIMETHYLTHYMINE CYCLOBUTANE DIMER IN THE PRESENCE OF MAGNESIUM PERCHLORATE

We have investigated the photosensitized monomerization of the cis,syn -cyclobutane dimer of 1,3-di-methylthymine using riboflavin tetraacetate and a 5-deazaflavin derivative as photosensitizer. Although little monomerization of the dimer is induced by photoexcitation of the flavins in the absence of any additives, the flavins can function as an efficient photosensitizer in the presence of magnesium perchlorate. Mechanistic studies involving spectroscopic, quantum-yield and flash-photolysis measurements demonstrated that the photosensitized monomerization exclusively proceeds through electron transfer from the dimer to the triplet flavins complexed with Mg²⁺. The effects of magnesium perchlorate are compared with those on the chloranil-photosensitized monomerization and also with the effects of HClO₄ on the flavin-photosensitized reaction.     

A New Family of Indoaniline-Derived Calix[4]arenes: Synthesis and Optical Recognition Properties as a Chromogenic Receptor(1)

A new family of indoaniline-derived calix[4]arenes has been synthesized for the purpose of developing a new chromogenic receptor. A condensing reaction of calix[4]arene (1) with 4-(diethylamino)-2-methylaniline hydrochloride (2) in the presence of an oxidizing agent under alkaline conditions affords mono- (3), 1,2-bis- (4), 1,3-bis- (5), and tetrakisindoaniline-derived (6) calix[4]arenes after careful column chromatography. Compound 3 is crystallized from a CHCl(3)-MeOH solution, and the crystal structure was determined by X-ray analysis. The crystal is monoclinic, space group P2(1)/n, Z = 4, a = 19.507(6) ?, b = 18.591(6) ?, c = 8.524(2) ?, beta = 94.69(2) degrees. The final R value for 2406 reflections of F(o) > 3sigma(F(o)) is 0.085. A unique intramolecular hydrogen-bonding network involving the carbonyl oxygen of indoaniline for 3 implied that the quinone carbonyl group as an acceptor of the chromophore can easily be subjected to an electrostatic interaction in the lower rim. Indeed, 1,3-bis(indoaniline)-derived 2,4-bis((ethoxycarbonyl)methoxy)calix[4]arene 7, prepared by the reaction of 5 with ethyl bromoacetate in the presence of NaH, is capable of undergoing an efficient ion-dipole interaction between the binding cation and the two quinone carbonyl groups of the chromophores, so that a selective Ca(2+)-induced pronounced color change (wavelength change > 100 nm) occurs with an association constant on the order of 10(6) in 99% EtOH, making 7 of potential use as an optical sensor for Ca(2+) detection. The IR and NMR studies have indicated that Ca(2+) is encapsulated in the cavity made by the distally located OCH(2)CO(2) groups on the lower rim of the cone-shaped calix[4]arene segment. Interestingly, however, the shape of the cavity in which Ca(2+) has been encapsulated does not have a C(2) axis of symmetry, as inferred from the (1)H-(1)H COSY experiment. On the other hand, 1,2-bis(indoaniline)-derived analogue 8 shows no response with metal ions, which can be interpreted to mean the absence of a cavity for encapsulation on the lower rim.     

Efficient synthesis and hydrolysis of cyclic oxalate esters of glycols

Based on the mechanism postulated for the formation of the cyclic carbonates 3 in the reactions of glycols 1 with oxalyl chloride in the presence of triethylamine, we present here three efficient syntheses of the cyclic oxalates 2 of various glycols 1 by controlling the formation of 3: replacement of the base by pyridine markedly diminishes yields of 3 in all reactions, realizing dramatic reversals of the product ratios in the reactions with the (R*,R*)-compounds 1g-i,q,r and pinacol (1k); although considerable amounts of the oxalate polymers are formed in the reactions with some (R*,S*)-glycols, this drawback can be removed by the use of 2,4,6-collidine instead of pyridine; 1,1'-oxalyldiimidazole is useful for the synthesis of two selected cyclic oxalates 2e,f. The cyclic oxalates 2 other than trisubstituted and tetrasubstituted ones were found to be very reactive: kinetic studies on the hydrolysis of 1,4-dioxane-2,3-dione (2a) as well as its mono- and some selected 5,6-disubstituted derivatives 2 have revealed that they undergo hydrolysis 260-1500 times more rapidly than diethyl oxalate (12) in acetate buffer-acetonitrile (pH 5.69) at 25 degrees C. Although the cyclic oxalate 21 from cis-1,2-cyclopentanediol (11) was 1.5 times more reactive than 2a, it has been shown with other substrates that increasing number of the alkyl substituents decreases the rate of hydrolysis. On the contrary, the phenyl group was found to have somewhat accelerative effect.