Space-time analytic smoothing effect for the pseudo-conformally invariant Schrödinger equations

We study the global Cauchy problem for the mass critical nonlinear Schrödinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L ² critical level.     

Synthesis of nano-polycrystalline diamond from glassy carbon at pressures up to 25 GPa

ABSTRACT

Nano-polycrystalline diamond (NPD) with various grain sizes has been synthesized from glassy carbon at pressures 15–25?GPa and temperatures 1700–2300°C using multianvil apparatus. The minimum temperature for the synthesis of pure NPD, below which a small amount of compressed graphite was formed, significantly increased with pressure from ～1700°C at 15?GPa to ～1900°C at 25?GPa. The NPD having grain sizes less than ～50?nm was synthesized at temperatures below ～2000°C at 15?GPa and ～2300°C at 25?GPa, above which significant grain growth was observed. The grain size of NPD decreases with increasing pressure and decreasing temperature, and the pure NPD with grain sizes less than 10?nm is obtained in a limited temperature range around 1800–2000°C, depending on pressure. The pure NPD from glassy carbon is highly transparent and exhibits a granular nano-texture, whose grain size is tunable by selecting adequate pressure and temperature conditions.     

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002     

Tuning membership functions of kernel fuzzy classifiers by maximizing margins

We propose two methods for tuning membership functions of a kernel fuzzy classifier based on the idea of SVM (support vector machine) training. We assume that in a kernel fuzzy classifier a fuzzy rule is defined for each class in the feature space. In the first method, we tune the slopes of the membership functions at the same time so that the margin between classes is maximized under the constraints that the degree of membership to which a data sample belongs is the maximum among all the classes. This method is similar to a linear all-at-once SVM. We call this AAO tuning. In the second method, we tune the membership function of a class one at a time. Namely, for a class the slope of the associated membership function is tuned so that the margin between the class and the remaining classes is maximized under the constraints that the degrees of membership for the data belonging to the class are large and those for the remaining data are small. This method is similar to a linear one-against-all SVM. This is called OAA tuning. According to the computer experiment for fuzzy classifiers based on kernel discriminant analysis and those with ellipsoidal regions, usually both methods improve classification performance by tuning membership functions and classification performance by AAO tuning is slightly better than that by OAA tuning.     

噪音信号对夜间对流层臭氧探测准确度的影响

本文探讨在背景噪音影响下,差分吸收激光雷达测量臭氧的不确定性:背景噪音对臭氧浓度廓线的影响正比于背景噪音强度、强吸收波长和弱吸收波长的回波信号强度比,理论计算结果表明:合适的回波信号强度比可以使激光雷达背景信号对夜间臭氧探测浓度的影响变得非常小,可以忽略不计,实验结果表明:用波长对( 280 nm,283 nm)对大气臭氧进行观测时,适当调节两波长回波信号强度比为0.96时,背景信号对臭氧浓度探测的影响小到可以忽略的程度,模拟分析和实验观测结果相接近,证实了理论推算的合理性,在背景噪音强度未知的情况下,通过调整强吸收和弱吸收两波长的激光脉冲的能量,在示渡器上得到适合的回波信号强度比值,可以抑制背景噪音信号时臭氧探测结果的影响,确保夜间臭氧测量的准确性.     

Superionic Conduction in Co‐Vacant P2‐NaxCoO2 Created by Hydrogen Reductive Elimination

The layered P2‐Na_xMO₂ (M: transition metal) system has been widely recognized as electronic or mixed conductor. Here, we demonstrate that Co vacancies in P2‐Na_xCoO₂ created by hydrogen reductive elimination lead to an ionic conductivity of 0.045 S cm^?1 at 25 °C. Using in situ synchrotron X‐ray powder diffraction and Raman spectroscopy, the composition of the superionic conduction phase is evaluated to be Na_0.61(H₃O)_0.18Co_0.93O₂. Electromotive force measurements as well as molecular dynamics simulations indicate that the ion conducting species is proton rather than hydroxide ion. The fact that the Co‐stoichiometric compound Na_x(H₃O)_yCoO₂ does not exhibit any significant ionic conductivity proves that Co vacancies are essential for the occurrence of superionic conductivity.     

Lamellar thickening in nascent poly(acrylonitrile) upon annealing

No systematic study has been reported on the lamellar thickening in atactic poly(acrylonitrile) (PAN) upon annealing because PAN, in the form of solution‐cast films or their drawn products, generally shows no small‐angle X‐ray scattering (SAXS) maximum corresponding to the lamellar thickness. In this work, PAN crystals were precipitated during the thermal polymerization of acrylonitrile in solution. The nascent PAN film, obtained by the filtration of the crystal suspension, exhibited a clear SAXS maximum revealing the lamellar structure. The lamellar thickening upon annealing of the nascent PAN films was studied in the temperature range 100–180 °C, where the degradation was minimal, as confirmed by the absence of an IR absorption band at 1605 cm⁻¹ ascribed to the cyclized nitrile groups. Above 190 °C, the degradation of the samples was significant, and the SAXS became too broad to determine the scattering maximum. The long period was significantly affected by the annealing time (t_a) and the temperature (T_a). Depending on t_a, three stages were observed for the lamellar thickening behavior. The lamellar thickness stayed constant in stage I (t_a = 0.5–3 min, depending on T_a), rapidly increased in stage II (t_a = 0.5–8 min), and stayed at a constant value characteristic for each T_a at yet longer t_a's in stage III. The lamellar thickness characteristic for T_a increased rapidly with increasing T_a at 165 °C (or higher), which was 152 °C lower than the estimated melting temperature of PAN (T_m = 317 °C). A possible mechanism for such lamellar thickening in PAN far below the T_m is discussed on the basis of the enhanced chain mobility in the crystalline phase above the crystal/crystal reversible transition at 165–170 °C detected by differential scanning calorimetry and wide‐angle X‐ray diffraction. The structural changes associated with annealing are also discussed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2571–2579, 2000     

Presence of β-Turn Structure in Recombinant Spider Silk Dissolved in Formic Acid Revealed with NMR

Spider dragline silk is a biopolymer with excellent mechanical properties. The development of recombinant spider silk protein (RSP)-based materials with these properties is desirable. Formic acid (FA) is a spinning solvent for regenerated Bombyx mori silk fiber with excellent mechanical properties. To use FA as a spinning solvent for RSP with the sequence of major ampullate spider silk protein from Araneus diadematus, we determined the conformation of RSP in FA using solution NMR to determine the role of FA as a spinning solvent. We assigned ¹H, ¹³C, and ¹⁵N chemical shifts to 32-residue repetitive sequences, including polyAla and Gly-rich regions of RSP. Chemical shift evaluation revealed that RSP is in mainly random coil conformation with partially type II β-turn structure in the Gly-Pro-Gly-X motifs of the Gly-rich region in FA, which was confirmed by the ¹⁵N NOE data. In addition, formylation at the Ser OH groups occurred in FA. Furthermore, we evaluated the conformation of the as-cast film of RSP dissolved in FA using solid-state NMR and found that β-sheet structure was predominantly formed.     

Syntheses, characterization, and dioxygen reactivities of Cu(I) complexes with cis,cis-1,3,5-triaminocyclohexane derivatives: a Cu(III)2O2 intermediate exhibiting higher C-H activation

Six Cu(I) complexes with cis,cis-1,3,5-triaminocyclohexane derivatives (R3CY, R = Et, iBu, and Bn), [Cu(MeCN)(Et3CY)]SbF6 (1), [Cu(MeCN)(iBu3CY)]SbF6 (2), [Cu(MeCN)(Bn3CY)]SbF6 (3), [Cu(CO)(Et3CY)]SbF6 (4), [Cu(CO)(iBu3CY)]SbF6 (5), and [Cu(CO)(Bn3CY)]SbF6 (6), were prepared to probe the ability of copper complexes to effectively catalyze oxygenation reactions. The complexes were characterized by elemental analysis, electrochemical and X-ray structure analyses, electronic absorption spectroscopy, IR spectroscopy, 1H NMR spectroscopy, and ESI mass spectrometry. The crystal structures of 1-3 and 6 and the CO stretching vibrations (nuCO) of 4-6 demonstrate that the ability of R3CY to donate electron density to the Cu(I) atom is stronger than that of the previously reported ligands, 1,4,7-triazacyclononane (R3TACN) and 1,4,7-triazacyclodecane (R3TACD). Reactions of complexes 1-3 with dioxygen in THF or CH2Cl2 at -105 to -80 degrees C yield bis(mu-oxo)dicopper(III) complexes 7-9 as intermediates as confirmed by electronic absorption spectroscopy and resonance Raman spectroscopy. The Cu-O stretching vibrations, nu(Cu-O) for 7 (16O2: 553, 581 cm-1and 18O2: 547 cm-1) and 8 (16O2: 571 cm-1 and 18O2: 544 cm-1), are observed in a lower energy region than previously reported for bis(micro-oxo) complexes. The decomposition rates of complexes 7-9 in THF at -90 degrees C are 2.78 x 10-4 for 7, 8.04 x 10-4 for 8, and 3.80 x 10-4 s-1 for 9. The decomposition rates of 7 and 8 in CH2Cl2 were 5.62 x 10-4 and 1.62 x 10-3 s-1, respectively, and the thermal stabilities of 7-9 in CH2Cl2 are lower than the values measured for the complexes in THF. The decomposition reactions obeyed first-order kinetics, and the H/D isotope experiments for 8 and 9 indicate that the N-dealkylation reaction is the rate-determining step in the decomposition processes. On the other hand, the decomposition reaction of 7 in THF results in the oxidation of THF (acting as an exogenous substrate) to give 2-hydroxy tetrahydrofuran and gamma-butyrolactone as oxidation products. Detailed investigation of the N-dealkylation reaction for 8 by kinetic experiments using N-H/D at -90 degrees C showed a kinetic isotope effect of 1.25, indicating that a weak electrostatic interaction between the N-H hydrogen and mu-oxo oxygen contributes to the major effect on the rate-determining step of N-dealkylation. X-ray crystal structures of the bis(micro-hydroxo)dicopper(II) complexes, [Cu2(OH)2(Et3CY)2](CF3SO3)2 (10), [Cu2(OH)2(iBu3CY)2](CF3SO3)2 (11), and [Cu2(OH)2(Bn3CY)2](ClO4)2 (12), which have independently been prepared as the final products of bis(micro-oxo)dicopper(III) intermediates, suggest that an effective interaction between N-H and mu-oxo in the Cu(III)2(micro-O)2 core may enhance the oxidation ability of the metal-oxo species.     

Anthracene array-type porous coordination polymer with host-guest charge transfer interactions in excited states

Confinement of electron donor guests affords an efficient, photo-induced charge transfer (CT) with the anthracene moieties of a porous coordination polymer.