Second order evolution equations with time-dependent subdifferentials

We study an abstract second order nonlinear evolution equation in a real Hilbert space. We consider time-dependent convex functions and their subdifferentials operating on the first derivative of the unknown function. Introducing appropriate assumptions on the convex functions and other data, we prove the existence and uniqueness of a strong solution, and give some applications of the abstract theorem to hyperbolic variational inequalities with time-dependent constraints.      

Cytotoxic activity of marine algae and a cytotoxic principle of the brown alga Sargassum tortile.

Partition fractions of hexane, CCl4 and CHCl3 from methanolic extracts of marine algae were each examined for cytotoxic activities against cultured P-388 lymphocytic leukemia cells. Cytotoxic activities were found for partition fractions of 21 species of seaweed. Bioactivity-guided fractionation of the CCl4 partition fraction from Sargassum tortile, exhibiting the most prominent activity, afforded dihydroxysargaquinone (1) and sargatriol (2) previously isolated from this alga. The former was evaluated as a cytotoxic principle, and the latter, showing moderate activity, was suggested to be an artifact derived from 1 during the isolation procedure.     

Analysis of Spectral Reflectance Using Normalization Method from Endoscopic Spectroscopy System

Objective assessment of gastrointestinal mucosal color is extremely important in the endoscopic diagnosis of digestive tract disease. In this paper, we propose a method to clarify the spectral characteristics of gastric and colon cancer. A large number of spectral reflectance data of mucous membrane are measured by the endoscopic spectroscopy system (ESS) in the National Cancer Center Hospital East, Kashiwa, Japan and the Department of Internal Medicine, Self-Defense Force Center Hospital, Tokyo, Japan. We assume that early cancer appears primarily in the spectral data of short wavelength, because it is usually present in a superficial cell where short wavelength light is scattered more strongly than long wavelength light. To identify the features in the short wavelength components, the spectral reflectance was divided by the reflectance of a long wavelength. We investigated the possibility of distinguishing early cancer from normal spectral data through statistical analysis, employing the projection axis as the mean difference between them. Early cancer and normal spectral data were projected on the projection axis, and the Student’s T-test was applied to evaluate the mean of the distribution between these data.     

Laser cleaning of glass

The pulse lasers, YAG-, CO₂-, and N₂-lasers, are examined for use in the cleaning of glass. Cleaning is found to be due to the evaporation and sputtering of stains on the glass by the heat energy of the laser light. Only the N₂ laser can be used for the cleaning of the exit surface of the glass (the opposite side to the laser). A laser with a high peak power of about 10⁶J/s and short-pulse duration below 100 ns is found to be necessary in practice.     

Structural and electrical properties of crystalline (1−x)Ta2O5−xTiO2 thin films fabricated by metalorganic decomposition

Polycrystalline (1−x)Ta₂O₅−xTiO₂ thin films were formed on Si by metalorganic decomposition (MOD) and annealed at various temperatures. As-deposited films were in the amorphous state and were completely transformed to crystalline after annealing above 600 °C. During crystallization, a thin interfacial SiO₂ layer was formed at the (1−x)Ta₂O₅−xTiO₂/Si interface. Thin films with 0.92Ta₂O₅–0.08TiO₂ composition exhibited superior insulating properties. The measured dielectric constant and dissipation factor at 1 MHz were 9 and 0.015, respectively, for films annealed at 900 °C. The interface trap density was 2.5×10¹¹ cm⁻² eV⁻¹, and flatband voltage was −0.38 V. A charge storage density of 22.8 fC/μm² was obtained at an applied electric field of 3 MV/cm. The leakage current density was lower than 4×10⁻⁹ A/cm² up to an applied electric field of 6 MV/cm.     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

Nonlinear degenerate parabolic equations with Neumann boundary condition

We study Neumann problem for a class of nonlinear degenerate parabolic PDE. A typical nonlinearity we have in mind is, for instance, β(u)=−1/u(u>0). We establish a necessary and sufficient condition on given data for existence of solution.     

Synthesis of the LMN-ring fragment of the Caribbean ciguatoxin C-CTX-1

Ciguatoxin C-CTX-1 was isolated as a principal causative toxin of ciguatera seafood poisoning in the Caribbean Sea, and is structurally classified as a ladder-shaped polycyclic ether. In this Letter, we report the synthesis of the tricyclic LMN-ring system of C-CTX-1. SmI₂-mediated reductive cyclization efficiently constructed the seven-membered M-ring with the axially oriented 1,3-dimethyl structure.