On the behavior of solutions for a semilinear parabolic equation with supercritical nonlinearity

This paper is concerned with a Cauchy problem where and is a nonnegative radially symmetric function in with compact support. Denote the solution of (P) by . Let if and $p^{\ast} = 1+6/(N-10) N \geq 11 p_{\ast} < p < p^{\ast} \lambda_{\varphi} > 0 $ such that: (i) If $ \lambda < \lambda_{\varphi} u_{\lambda} $ exists globally in time in the classical sense and converges to zero locally uniformly in as . (ii) If , then $ u_{\lambda} $ blows upincompletely in finite time. (iii) If , then blows upcompletely in finite time. Received: 20 December 1999; in final form: 26 May 2000 / Published online: 4 May 2001     

Photochemistry of naphthalimide photoacid generators

The photophysical properties of a series of 1,8-naphthalimide photoacid generators were studied by steady state fluorescence and phosphorescence spectroscopy. Emission and excitation anisotropies, triplet quantum yields in polar and nonpolar solvent and photoacid generation were evaluated. The singlet excited state exhibits a low polarity and is strongly deactivated by an efficient intersystem crossing process. In protic solvent, a homolytic singlet cleavage of the N-O bond occurs and leads to the acid production. The existence of a triplet state close to the singlet state was clearly evidenced. The presence of close singlet excited states is supported by fluorescence anisotropy and picosecond laser spectroscopy experiments. Results of DFT calculations well confirm the experimental contentions and yield important information about the cleavage process involved in such compounds.     

Magnetic field effect on fluorescence in a mixture of N-ethylcarbazole and dimethyl terephthalate in a polymer film in the presence of electric fields

Magnetic field effects on the fluorescence spectrum and on the electrofluorescence spectrum (plots of the electric field-induced change in fluorescence intensity as a function of wavelength) have been examined in electron donor and acceptor pairs of N-ethylcarbazole (ECZ) and dimethyl terephthalate (DMTP) in polymer films at different ratios of donor/acceptor concentration. In the mixture having a high concentration of ECZ, electric field-induced quenching of the exciplex fluorescence originating from the photoinduced electron transfer becomes less efficient in the presence of a magnetic field. In the mixture having a low concentration of ECZ, on the other hand, no magnetic field effect was observed in the electrofluorescence spectrum, indicating that the hole carrier plays an important role in synergy effects of magnetic and electric field effects on exciplex fluorescence. In the absence of the applied electric field, the magnetic field does not affect either exciplex fluorescence with a peak at 450 nm or LE fluorescence emitted from the locally excited state of ECZ but enhances the broad emission with a peak at approximately 380 nm, probably assigned to the fluorescence of another type of exciplex between ECZ and DMTP. Thus, two kinds of magnetic field effects on fluorescence have been observed in a mixture of ECZ and DMTP in a polymer film.     

Bi2/3Ce1/3Rh2O5: A new mixed-valent Rh oxide with hitherto unknown structure

The new compound Bi_2/3Ce_1/3Rh₂O₅ has been discovered. It is currently the only known compound in the Bi-Ce-Rh-O system, and it crystallizes in a previously unknown structure type. The structure was established from single crystal X-ray diffraction data. Interatomic distances indicate the oxidation states as Bi_2/3³⁺Ce_1/3⁴⁺Rh₂^3.33+O₅. The structure indicates no ordering between Rh³⁺ and Rh⁴⁺. The lack of charge ordering is consistent with the metallic properties determined from electrical conductivity, Seebeck coefficient, and magnetic susceptibility measurements.     

The 17-propionate function of (bacterio)chlorophylls: biological implication of their long esterifying chains in photosynthetic systems

Molecular structures of (bacterio)chlorophylls [= (B)Chls] in photosynthetic apparatus are surveyed, and a diversity of the ester groups of the 17-propionate substituent is particularly focused on in this review. In oxygenic photosynthetic species including green plants and algae, the ester of Chl molecules is limited to a phytyl group. Geranylgeranyl and farnesyl groups in addition to phytyl are observed in (B)Chl molecules inside photosynthetic proteins of anoxygenic bacteria. In main light-harvesting antennas of green bacteria (chlorosomes), a greater variety of ester groups including long straight chains are used in the composite BChl molecules. This diversity is ascribable to the fact that chlorosomal BChls self-aggregate to form a core part of chlorosomes without any specific interaction of oligopeptides. Biological significance of the long chains is discussed in photosynthetic apparatus, especially in chlorosomes.     

Synthesis and charge/discharge properties of polyacetylenes carrying 2,2,6,6-tetramethyl-1-piperidinoxy radicals

The 2,2,6,6-tetramethyl-1-piperidinoxy (TEMPO)-containing acetylenic monomers HC[triple bond]CC(6)H(3)-p,m-(CONH-4-TEMPO)(2) (1), HC[triple bond]CC(6)H(3)-p,m-(COO-4-TEMPO)(2) (2), (S,S,S,S)-HC[triple bond]CC(6)H(3)-p,m-[CO-NHCH{COO-(4-TEMPO)}CH(2)COO-(4-TEMPO)](2) (3), (S,S)-HC[triple bond]CC(6)H(4)CO-NHCH{COO-(4-TEMPO)}CH(2)COO-(4-TEMPO) (4), HC[triple bond]CC(6)H(4)-p-OCO-4-TEMPO (5), HC[triple bond]CCH(2)C(CH(3))(CH(2)OCO-4-TEMPO)(2) (6), HC[triple bond]CCH(2)NHCO-4-TEMPO (7), and HC[triple bond]CCH(2)OCO-4-TEMPO (8) were polymerized to afford novel polymers containing the TEMPO radical at high densities. Monomers 1, 3-6, and 8 provided polymers with average molecular weights of 10 000-136 500 in 62-99 % yield in the presence of a rhodium catalyst, whereas monomers 2 and 7 gave insoluble polymers in 100 % yield. The formed polymers were thermally stable up to approximately 274 degrees C according to thermogravimetric analysis (TGA). All the TEMPO-containing polymers demonstrated reversible charge/discharge processes, whose discharge capacities were 21.3-108 A h kg(-1). In particular, the capacity of poly(1)-, poly(4)-, and poly(5)-based cells reached 108, 96.3, and 89.3 A h kg(-1), respectively, which practically coincided with their theoretical values.     

BF2 complexes of beta-tetraethyl-substituted dipyrrolyldiketones as anion receptors: potential building subunits for oligomeric systems

Synthesis and anion binding properties of BF2 complexes of beta-tetraethyl-substituted dipyrrolyldiketones, with and without electron-withdrawing ethoxycarbonyl moieties at pyrrole alpha-positions, are reported. The substituents at pyrrole rings of these acyclic anion receptors are found to play a key role to control not only the polarization of binding sites (NH and CH) but also the relative stabilities of the preorganized conformations and the degrees of sterical repulsion, both of which notably affect the affinities for anions.     

Undulating layers in a new rhodate network: structure of Bi(1.4)CuORh5O10

A new rhodate, Bi(1.4)CuRh(5)O(11), with an hitherto unknown channel structure containing undulating layers of RhO(6) octahedra sharing corners and edges has been discovered and its structure refined from single crystal X-ray diffraction data. The channels contain Bi(3+), Cu(2+), and some O strongly bound to Cu. The Cu coordination is distorted square planar. Mixed Rh(3+)/Rh(4+) valency leads to significant electrical conductivity.     

Frequency Dependence of ESR in Pristine Trans-Polyacetylene: Spin Lattice Relaxation Time T1

We have measured ESR T in pristine trans-polyacety-lene at frequencies 5～450 MHz and at temperatures 4.2～300 K. This experiment provided a new evidence of one dimensionally moving neutral solitons.     

Effect of Pressure on Antiferromagnetic Transition in Alkali-Electro-Sodalite

Abstract

Pressure (0–19 kbar) and temperature (4–300 K) dependent EPR study of Sodium-Electro-Sodalite (SES) is presented. SES, which consists of a bcc sub-lattice of F-centers supported by a zeolite-like framework, is known to be a Mott insulator at room temperature. On cooling, SES undergoes an AF transition at 48±2 K providing the first example of an s-electron antiferromagnet. We find that the width of the EPR resonance above T _N is influenced not only by a strong exchange interaction, but also by a fast spin-lattice relaxation. Also, with increasing pressure, T _N decreases linearly and extrapolates to 0 K at about 65 kbar. The reason for this seemingly unexpected behavior is briefly discussed.