T 1 theorem for Besov spaces on nonhomogeneous spaces

Suppose μ is a Radon measure on ℝ ^d , which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀>0 such that for all x∈supp(μ) and r>0, μ(B(x, r))⪯C₀rⁿ, where 0<n⪯d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa’s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

Ternary univariate curvature-preserving subdivision

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original (in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.     

Synthesis and characterization of a polyfluorene containing carbazole and oxadiazole dipolar pendent groups and its application to electroluminescent devices

We have synthesized a blue‐light‐emitting polyfluorene (PF) derivative ( PF‐CBZ‐OXD ) that presents bulky hole‐transporting carbazole and electron‐transporting oxadiazole pendent groups functionalized at the C‐9 positions of alternating fluorene units. The results from photoluminescence and electrochemical measurements indicate that both the side chains and the PF main chain retain their own electronic characteristics in the copolymer. An electroluminescent device incorporating this polymer as the emitting layer was turned on at 4.5 V; it exhibited a stable blue emission with a maximum external quantum efficiency of 1.1%. Moreover, we doped PF‐CBZ‐OXD and its analogue PF‐TPA‐OXD with a red‐light‐emitting iridium phosphor for use as components of phosphorescent red‐light emitters to investigate the effect of the host's HOMO energy level on the degree of charge trapping and on the electrophosphorescent efficiency. We found that spectral overlap and individual energy level matching between the host and guest were both crucial features affecting the performance of the electroluminescence devices. Atomic force microscopy measurements indicated that the dipolar nature of PF‐CBZ‐OXD , in contrast to the general nonpolarity of polydialkylfluorenes, provided a stabilizing environment that allowed homogeneous dispersion of the polar iridium triplet dopant. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2925–2937, 2007     

Self-dual Chern–Simons Vortices on Bounded Domains

In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point.     

Transport properties of acetone aqueous solutions: molecular dynamics simulation and NMR studies

Two quantities η_rel and are applied to study the nonideal acetone–water association mixture. An all-atom acetone model and a TIP5P water model have been adopted for molecular dynamics simulation. We study the transport properties of the system comparing the 's of strong hydrogen bond and weak contact based on transport properties, MD simulations together with NMR experimental data and find good agreement of concentration dependence, which exhibits the cooperation effect.     

Composite Silica Particles Using a Mixture of Organosilane Monomers

Composite silica particles were synthesized by a two-step (acid-base) process in an aqueous solution with a mixture of organoalkoxysilane monomers. The two-step process separates the hydrolysis and condensation procedures to easily control condensation rate. In this study, the silane monomers used were phenyltrimethoxysilane (PTMS), vinyltrimethoxysilane (VTMS), methyltrimethoxysilane (MTMS), and tetraethyl-orthosilicate (TEOS). The physical properties of the resultant composite particles were investigated with the change in the molar ratio of monomers. The size of the particles increased with increasing the molar ratio of R_aSi(OR)₃/R_bSi(OR)₃ or R_aSi(OR)₃/TEOS (R_a: phenyl; R_b: vinyl, methyl).     

Synthesis and characterization of soluble polyimides containing trifluoromethyl groups in their backbone

A series of polyimides were synthesized from 2,2‐Bis(3,4‐dicarboxyphenyl)hexafluoropropane, 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane, and 4,4′‐oxydianiline by chemical imidization. The effects of the diamine ratios on the properties of the films were evaluated through the study of their thermal, electrical, and morphological properties. All the polymers exhibited better solubility in most of the organic solvents and hence were easily processable. Polyimides with more 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane exhibited better solubility and a low refractive index, which is highly desired for microelectronic applications. The dielectric constant and birefringence were strongly dependent on the fluorine content. With an increase in the fluorine substitution, both the dielectric constant and birefringence decreased. All the polymers exhibited high thermal stability (>400 °C). The absence of crystalline melting in differential scanning calorimetry and broad wide‐angle X‐ray diffraction patterns revealed the amorphous nature of the polymers, which was due to the presence of bulky CF₃ groups and hinged ether linkages of the diamine component. The residual stress values decreased with an increase in the 4,4′‐oxydianiline content, and the results were in agreement with the dielectric constant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4303–4312, 2004     

Influence of solvents on the formation of ultrathin uniform poly(vinyl pyrrolidone) nanofibers with electrospinning

Although there have been many reports on the preparation and applications of various polymer nanofibers with the electrospinning technique, the understanding of synthetic parameters in electrospinning remains limited. In this article, we investigate experimentally the influence of solvents on the morphology of the poly(vinyl pyrrolidone) (PVP) micro/nanofibers prepared by electrospinning PVP solution in different solvents, including ethanol, dichloromethane (MC) and N,N‐dimethylformamide (DMF). Using 4 wt % PVP solutions, the PVP fibers prepared from MC and DMF solvents had a shape like a bead‐on‐a‐string. In contrast, smooth PVP nanofibers were obtained with ethanol as a solvent although the size distribution of the fibers was somewhat broadened. In an effort to prepare PVP nanofibers with small diameters and narrow size distributions, we developed a strategy of using mixed solvents. The experimental results showed that when the ratio of DMF to ethanol was 50:50 (w/w), regular cylindrical PVP nanofibers with a diameter of 20 nm were successfully prepared. The formation of these thinnest nanofibers could be attributed to the combined effects of ethanol and DMF solvents that optimize the solution viscosity and charge density of the polymer jet. In addition, an interesting helical‐shaped fiber was obtained from 20 wt % PVP solution in a 50:50 (w/w) mixed ethanol/DMF solvent. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3721–3726, 2004     

Pr(0.5):ZBLAN的双频激发上转换发光的研究

报道了Pr(0.5):ZBLAN玻璃在双频双光束光源激发下的激发态上转换现象.发现上转换发射谱的荧光与常规荧光发射谱的荧光一致，还发现双频激发下的上转换激发谱有3个明显的谱峰，它们依此对应于788.5nm 1G4→3P2,850.5nm 1G4→1I6和805.0nm 3H6→1D2的激发态吸收跃迁，而大的850.5nm上转换激发谱峰是由大的1G4(Pr3+ )→1I6(Pr3+)跃迁的振子强度f=23.04×10-6所致.这说明起源于1G4能级的激发态吸收上转换尤其1G4(Pr3+)→1I6(Pr3+)