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11.
Kazuhiro Kurata Masataka Shibata Shigeru Sakamoto 《Applied Mathematics and Optimization》2004,50(3):259-278
Let $\Omega$ be a bounded domain in ${\bf R^n}$ with Lipschitz
boundary,
$\lambda >0,$ and $1\le p \le (n+2)/(n-2)$ if $n\ge 3$ and $1\le p< +\infty$
if $n=1,2$. Let $D$ be a measurable subset of $\Omega$ which belongs
to the class
$
{\cal C}_{\beta}=\{D\subset \Omega \quad | \quad |D|=\beta\}
$
for the prescribed $\beta\in (0, |\Omega|).$
For any $D\in{\cal C}_{\beta}$, it is well known that
there exists a unique
global minimizer $u\in H^1_0(\Omega)$, which we denote by
$u_D$, of the functional
\[\quad
J_{\Omega,D}(v)=\frac12\int_{\Omega}|\nabla v|^2\,
dx+\frac{\lambda}{p+1}\int_{\Omega}|v|^{p+1}\, dx
-\int_{\Omega}\chi_Dv\,dx
\]
on $H^1_0(\Omega)$.
We consider the optimization problem
$
E_{\beta,\Omega}=\inf_{D\in {\cal C}_{\beta}} J_D(u_D)
$
and say that
a subset $D^*\in {\cal C}_{\beta}$ which attains
$E_{\beta,\Omega}$
is an optimal configuration to this problem.
In this paper we show the existence, uniqueness
and non-uniqueness, and
symmetry-preserving and symmetry-breaking phenomena of the
optimal configuration $D^*$ to this
optimization problem in various settings. 相似文献
12.
Kazuhiro Yamamoto Haruhiko Ito Kouki Totsuka Tomohiro Sato 《Optics Communications》2006,265(2):692-695
We consider a new scheme of optically ionizing atoms with 10-nm-order spatial resolution. In this method, two-color near-field lights are generated on a narrow slit illuminated by two-color evanescent lights via total-internal reflection of two-wavelength light beams. In order to illustrate the feasibility, we first obtain the ionization cross section from two-step photionization of cold Rb atoms by two-color evanescent lights on a plane surface of a prism. Then, we numerically estimate the ionization efficiency as a function of the slit width using Bethe formula. The scheme is useful for detecting ground-state atoms under less perturbation by scattered light. 相似文献
13.
Yan Yin Otoo Yamada Shunsuke Hayashi Kazuhiro Tanaka Hidetoshi Kita Ken‐Ichi Okamoto 《Journal of polymer science. Part A, Polymer chemistry》2006,44(12):3751-3762
A series of branched/crosslinked sulfonated polyimide (B/C‐SPI) membranes were prepared and evaluated as proton‐conducting ionomers based on the new concept of in situ crosslinking from sulfonated polyimide (SPI) oligomers and triamine monomers. Chemical branching and crosslinking in SPI oligomers with 1,3,5‐tris(4‐aminophenoxy)benzene as a crosslinker gave the polymer membranes very good water stability and mechanical properties under an accelerated aging treatment in water at 130 °C, despite their high ion‐exchange capacity (2.2–2.6 mequiv g?1). The resulting polymer electrolytes displayed high proton conductivities of 0.2–0.3 S cm?1 at 120 °C in water and reasonably high conductivities of 0.02–0.03 S cm?1 at 50% relative humidity. In a single H2/O2 fuel‐cell system at 90 °C, they exhibited high fuel‐cell performances comparable to those of Nafion 112. The B/C‐SPI membranes also displayed good performances in a direct methanol fuel cell with methanol concentrations as high as 50 wt % that were superior to those of Nafion 112. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3751–3762, 2006 相似文献
14.
Hiroyuki Higuchi Kazuhiro Takatsu Tetsuo Otsubo Yoshiteru Sakata Soichi Misumi 《Tetrahedron letters》1982,23(6):671-672
A novel cage compound was obtained by irradiation of a quadruple-layered dithiacyclophane and showed thermally reverse reaction. 相似文献
15.
The title racemate-to-conglomerate transformation which occurs in the solid state on heating or contact with MeOH vapour has been studied by IR and DTA spectral measurements, microscopic observation, and by X-ray structural and X-ray powder diffraction analysis. 相似文献
16.
Kazuhiro Kobayashi Atsushi Takanohashi Kenichi Hashimoto Osamu Morikawa Hisatoshi Konishi 《Tetrahedron》2006,62(44):10379-10382
A facile synthetic method for 4,5-diaminopyrrolo[1,2-a]quinoline derivatives has been developed. Treatment of 2-(pyrrol-1-yl)benzaldehydes with secondary amine hydrochloride/NaI/TMSCl/Et3N in the presence of an isocyano compound leads to the formation of 4-alkyl(or aryl)amino-5-dialkylaminopyrrolo[1,2-a]quinolines. 相似文献
17.
Kazuhiro Endo Hideo Ihara Kazuhiro Watanabe Shun-Ichi Gonda 《Journal of solid state chemistry》1982,44(2):268-272
X-Ray photoelectron spectra of TiS3 with a one-dimensional structure were measured. TiS3 may be regarded as Ti4+(S2)2?S2? with pairs of S atoms (S2) and isolated S atoms. The spectra of the sulfur core-levels are assigned by comparison with those of TiS2, where all S atoms are largely separated. The binding energy of the S2 pairs is found to be 1.4 eV higher than that of the isolated S atoms, which is consistent with the larger negative charge of the isolated atoms. The structures of the valence band of TiS3 are discussed in terms of a molecular orbital scheme for the S2 pairs. 相似文献
18.
Soto-Chinchilla JJ Gámiz-Gracia L García-Campaña AM Imai K García-Ayuso LE 《Journal of chromatography. A》2005,1095(1-2):60-67
The determination of seven sulfonamides by means of HPLC with chemiluminescence detection is proposed for the first time. The analytes are derivatized with fluorescamine, separated and subsequently they participate in the post-column chemiluminescence (CL) peroxyoxalate system using imidazole as a catalyst. Among the different peroxyoxalates tested, bis[4-nitro-2-(3,6,9-trioxadecyloxycarbonyl)phenyl] oxalate provides higher sensitivities and stabilities, avoiding precipitation problems. A rigorous optimization of the significant variables by means of experimental designs has been developed in order to reconcile the chromatographic conditions with the CL reaction. The method provides detection limits in the low microgl(-1) range and has been satisfactorily applied to the analysis of spiked raw milk samples. 相似文献
19.
Itoh T Nagata K Yokoya M Miyazaki M Kameoka K Nakamura S Ohsawa A 《Chemical & pharmaceutical bulletin》2003,51(8):951-955
Chiral 1-substituted isoquinoline derivatives, which were obtained by the reaction using alanine derivatives as chiral auxiliaries, were transformed to (S)-2,3,9,10,11-pentamethoxyhomoprotoberberine (7) and a synthetic intermediate for O-methylkreysigine (9) in good yields and high stereoselectivity. The corresponding chiral allyl derivative of isoquinoline was transformed to a pyrrolidinoisoquinoline (16) in a highly enantioselective manner. 相似文献
20.
Kawasaki H Sasaki A Kawashima T Sasaki S Kakehashi R Yamashita I Fukada K Kato T Maeda H 《Langmuir : the ACS journal of surfaces and colloids》2005,21(13):5731-5737
Lyotropic phase behavior of the nonionic and the half-ionized oleyldimethylamine oxide (OlDMAO)/water systems was investigated using polarized light microscopy, small-angle X-ray diffraction, and differential scanning calorimetry. Nonionic OlDMAO formed isotropic micellar solution, nematic, hexagonal, cubic, and lamellar liquid crystalline phases as the surfactant concentration increased. In contrast, half-ionized OlDMAO (i.e., 1:1 mixture of the nonionic and the protonated species) had a greater tendency to form bilayer structures, and the phase diagram became quite similar to those of double-chained ionic surfactants rather than single-chained ones, despite the introduction of positive charges to the nonionic one. The preference of the bilayer structures in the half-ionized OlDMAO was interpreted in terms of the dimers stabilized by the hydrogen bond between the nonionic and protonated species. For alkyldimethylamine oxides with a saturated hydrocarbon chain (CnDMAO, chain length: n = 14, 16, and 18), the phase sequence of lyotropic liquid crystals was hardly affected by the protonation, but an elongation of the cylinders of the hexagonal phase was observed for the half-ionized C14DMAO. Consequently, it can be considered that the dominant bilayer formation of the half-ionized OlDMAO is attributed to the combined effect of the hydrogen-bonded dimer formation and the cis-double-bond configuration of the alkyl chain. 相似文献