Solution of a diffusion equation of smoke molecules due to constant point source in gravitational field

From both the Langevin equation, including a gravitational term, the Fokker-Planck equation based on the dynamical behavior of Brownian particles, and equation of smoke molecular diffusion due to a constant point source is introduced and is solved by applying the Laplace transformation with the convolution theorem.The solution is expressed by the complementary error function with a mean pathway of smoke molecules affected by gravity and is proved to be reduced to conventional forms by a certain restriction neglecting gravity without any forced term.     

Facile synthesis and crosslinking reaction of trifunctional five‐membered cyclic carbonate and dithiocarbonate

The trifunctional five‐membered cyclic carbonate 2 and dithiocarbonate 3 were successfully synthesized by the reaction of trifunctional epoxide 1 with carbon dioxide and carbon disulfide, respectively. The crosslinking reactions of 2 with p‐xylylenediamine or hexamethylenediamine were carried out in dimethyl sulfoxide at 100 °C for 48 h to produce the corresponding crosslinked poly(hydroxyurethane)s quantitatively. The crosslinking reactions of 3 with both p‐xylylenediamine and hexamethylenediamine, followed by acetylation of thiol moiety, produced the corresponding crosslinked poly(thioester–thiourethane)s quantitatively. The obtained crosslinked poly(hydroxyurethane)s were thermally more stable than the analogous crosslinked poly(thioester–thiourethane)s, probably because of less thermal stability of thiourethane moiety than hydroxyurethane moiety. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5983–5989, 2004     

Highly resolved luminescence measurements for traces of 1,3-dibetanato europium(III) and terbium(III) complexes using a microscope laser Raman spectrometer toward the forensic discrimination.

The emission spectra of luminescent trivalent europium (Eu3+) and terbium (Tb3+) complexes were measured using a microscope laser Raman spectrometer with a doubled Nd:YAG laser (532 nm) and an Ar laser (488 nm). Excitation at 532 and 488 nm corresponded to wavelengths of the 7F1 --> 5D1 band of Eu3+ and the 7F6 --> 5D4 band of Tb3+, respectively. The Eu3+ and Tb3+ complexes were discriminated by high-resolution emission spectra more distinctly and sensitively than by fluorescence spectrometry, the usual analytical method.     

Synthesis and drug-release characteristics of the conjugates of mitomycin C with N-succinyl-chitosan and carboxymethyl-chitin.

By condensation of mitomycin C (MMC) with N-succinyl-chitosan (Suc-chitosan) and carboxymethyl-chitin (CM-chitin) using 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride, Suc-chitosan-MMC conjugate (Suc-chitosan-MMC) and CM-chitin-MMC conjugate (CM-chitin-MMC) were prepared, respectively. The reaction conditions for 45 min at pH 5 and for 2 h at pH 5 were selected as the most appropriate for the preparations of Suc-chitosan-MMC and CM-chitin-MMC, respectively. Suc-chitosan-MMC was obtained as a water-insoluble product, while CM-chitin-MMC was partially water-soluble. When the ratio of MMC to the polymer supports changed in the conjugation reaction, the conjugates with 33% (w/w) and 23% (w/w) MMC contents were obtained as those most highly drug-loaded for Suc-chitosan-MMC and CM-chitin-MMC, respectively. At pH 7.4 at 37 degrees C, Suc-chitosan-MMC regenerated MMC very slowly, while the release of MMC from CM-chitin-MMC was relatively fast. Each drug release followed very nearly pseudo-first order kinetics, in which the apparent drug release rate constants (k(apps)) of Suc-chitosan-MMC and CM-chitin-MMC were 3.9 x 10(-3) and 1.1 x 10(-1) (h-1), respectively.     

Extremal holomorphic diffusion processes

Extremal holomorphic diffusion processes are studied. We formulate a stochastic control problem for the extremal function of a set. We then characterize the extremal holomorphic diffusion processes as the optimal diffusion processes of the problem. By making use of SDE representation for the processes, we show that they move on an integral submanifold of the coefficients vector fields of the SDE passing through the starting point.     

Development of micromarkers with various photoluminescence colors as tracers for shadowing pursuits.

Micromarkers with five photoluminescence colors were developed as tracers for shadowing pursuits. The markers are colorless powders with particle diameters of several tens to several hundreds of micrometers, prepared using a cryogenic sample crusher. They were visualized using red, green, yellow, magenta or cyan photoluminescence under ultraviolet light at approximately 365 nm. The markers were composed of photoluminescent compounds dispersed in polyvinyl butyral. The photoluminescent compounds in the polyvinyl butyral were stable under ambient conditions for more than one year after application. The compounds with the red, green, yellow, magenta and cyan photoluminescence contained a europium (Eu(3+)) complex, a terbium (Tb(3+)) complex, a mixture of Tb(3+) and Eu(3+) complexes, a mixture of Eu(3+) complex and o-coumaric acid, and a mixture of Tb(3+) complex and 7-hydroxycoumarin along with a few drops of a sodium bicarbonate aqueous solution, respectively. Neodymium (Nd(3+)) and ytterbium (Yb(3+)) complexes with photoluminescence in the near-IR wavelength region can also be added to these visible photoluminescent compounds as secret markers for discrimination. The markers were non-destructively identified using a microscopic FT-IR spectrometer and a microscopic spectrometer equipped with a fluorescence detector.