Finite-time blow-up for quasilinear degenerate Keller–Segel systems of parabolic–parabolic type

This paper deals with the quasilinear degenerate Keller–Segel systems of parabolic–parabolic type in a ball of ${\mathbb{R}}^N$ ($N\ge 2$). In the case of non-degenerate diffusion, Cie?lak–Stinner [3], [4] proved that if $q>m+\frac{2}{N}$, where m denotes the intensity of diffusion and q denotes the nonlinearity, then there exist initial data such that the corresponding solution blows up in finite time. As to the case of degenerate diffusion, it is known that a solution blows up if $q>m+\frac{2}{N}$ (see Ishida–Yokota [13]); however, whether the blow-up time is finite or infinite has been unknown. This paper gives an answer to the unsolved problem. Indeed, the finite-time blow-up of energy solutions is established when $q>m+\frac{2}{N}$.     

Photoinduced charge separation in titania nanotubes

The photocatalytic one-electron oxidation reaction of an aromatic compound during UV light irradiation of titania nanotubes and nanoparticles was investigated using time-resolved diffuse reflectance spectroscopy. Remarkably long-lived radical cations of the aromatic compound and trapped electrons were observed for the nanotubes when compared to those for nanoparticles. The influences of the morphology on the one-electron oxidation process of an aromatic compound adsorbed on the surface were discussed in terms of the charge recombination dynamics between the radical cation and electrons in TiO2.     

Halichonic acid,a new rearranged bisabolene-type sesquiterpene from a marine sponge Halichondria sp.

A new compound, halichonic acid (1), was isolated from a marine sponge Halichondria sp., together with (6R,7S)-7-amino-7,8-dihydro-α-bisabolene (2). The structure of 1 was elucidated by spectroscopic analysis and ECD spectrum calculation to be a rearranged bisabolene-type sesquiterpene having a 3-azabicyclo[3.3.1]nonene moiety. Compound 2 was cytotoxic against HeLa cells with an IC₅₀ value of 50?μM, whereas 1 did not show cytotoxicity even at 50?μM. It is possible that 1 is biosynthesized from farnesyl pyrophosphate and glycine, with rearrangement.     

Mean dimension and an embedding problem: An example

For any positive integer D, we construct a minimal dynamical system with mean dimension equal to D/2 that cannot be embedded into (([0, 1] ^D )^?, shift).     

Aerobic Toluene Oxidation Catalyzed by Subnano Metal Particles

Subnanocatalysts (SNCs) containing various noble metals (Cu, Ru, Rh, Pd, or Pt) with sizes of approximately 1 nm were synthesized using dendritic poly(phenylazomethine)s as a macromolecular template. These materials exhibit high catalytic performance during toluene oxidation without the use of harmful solvents or explosive oxidants, resulting in the formation of valuable organic products, including benzoic acid as the major product. In particular, Pt₁₉ SNC with a narrow particle size distribution exhibits extraordinary catalytic activity, with a turnover frequency of 3238 atom^?1 h^?1, which is 1700 times greater than that obtained by commercial Pt/C catalysts.     

Scalable Total Syntheses and Structure–Activity Relationships of Haouamines A,B, and Their Derivatives as Stable Formate Salts

Haouamines A, B, and their derivatives were synthesized via Suzuki–Miyaura coupling and three key cyclization reactions as follows: the newly developed palladium(0)-catalyzed arylative cyclization of phenylalanine-derived alkyne–aldehydes with 2-bromoarylboronic acid (an “anti-Wacker”-type cyclization); BF₃ ⋅ OEt₂-promoted Friedel–Crafts-type cyclization of symmetrical electron-rich aromatic rings adjacent to a tertiary allylic alcohol leading to the indeno-tetrahydropyridine skeleton; and (cyanomethyl)trimethylphosphonium iodide-mediated macrocyclization of amino alcohols to afford aza-paracyclophane precursors. The palladium-catalyzed reduction of mono- and di-triflate intermediates in the later stages enabled the alteration of both the position and number of hydroxyl groups on the C-ring. The instability of haouamine B was dramatically improved by salt formation with formic acid. An unambiguous evaluation of the cytotoxicity of the prepared haouamine derivative formates with and without hydroxyl groups at different positions on the C-ring indicated that the catechol structure in haouamine B produced weak cytotoxicity.     

Isolation of a new indoxyl alkaloid,Amoenamide B,from Aspergillus amoenus NRRL 35600: Biosynthetic implications and correction of the structure of Speramide B

A new prenylated indoxyl alkaloid, Amoenamide B (1), was isolated from Aspergillus amoenus NRRL 35600 along with Asperochramide A (2). Although many prenylated oxindole alkaloids, containing bicyclo[2.2.2]diazaoctane cores, have been isolated from the fungus of the genera Aspergillus and Penicillium to date, 1 is the fourth compound with the indoxyl unit containing the cores. During the structure elucidation of 1, we found that the planar structure matched to that of Speramide A (3), isolated from A. ochraceus KM007, but the reported structure of 3 was incorrect and turned out to be that of Taichunamide H (4), recently isolated from A. versicolor HDN11-84.     

Dissolution kinetics of K-alum crystals as judged from the measurements of surface undersaturations

The normal dissolution rates, the slopes and the average velocities of dissolution steps of etch pits on the (111) face of a K-alum crystal, originating from dislocations with Burgers vector 110, were measured in relation to the surface undersaturations. From the mutual relations, it was shown that the dissolution was controlled by both diffusion and surface kinetic processes, although the contribution of the latter process was smaller than in the case of growth. It was also demonstrated that the normal dissolution rate was always larger than the growth rate. This is attributed to the fact that the slopes of growth hillocks are invariably smaller than those of etch pits.     

Fine-tuning of boron complexes with cage-shaped ligand geometry: rational design of triphenolic ligand as a template for structure control

Boron complexes surrounded with organic cages were controlled precisely by a remote atom placed at the bottom of the cage. A replacement of the bottom tether atom (carbon or silicon) changed the characteristics (kinetic and thermodynamic factors) of boron complexes by geometric effects. A theoretical study shows that the bottom atoms also control eigenvalues of MO. This cage complex will provide a systematic template for fine-tuning of metal complexes to create various properties.