Activation behavior and dielectric relaxation in polyvinyl alcohol and multiwall carbon nanotube composite films

The dc and ac electrical transport property of Polyvinyl Alcohol-Multiwall Carbon Nanotubes (PVA-MWNT) composites has been investigated within a temperature range and in the frequency range 20Hz-1MHz. The temperature variation of dc conductivity gives the presence of two different activation energies. The dielectric properties of the samples have been explained in terms of electric modulus vector.The dielectric relaxation has been explained in terms of interfacial polarization occurring in between the insulating PVA matrix and MWNT conductive filler. The variation of the relaxation time with temperature also indicates the presence of two different activation energies.     

Determination of Young's modulus of epoxy coated polyethylene micro-cantilever using phase-shift shadow moiré method

Young′s moduli of various epoxy coated polyethylene terephthalate (PET) micro-cantilevers were determined from the deflection results obtained using the phase-shift shadow moiré (PSSM) method. The filler materials for epoxy coatings were aluminum and graphite powders that were mixed with epoxy at various percentages. Young′s moduli were calculated from theory based on the deflection results. The PET micro-cantilever coated with aluminum-epoxy coating showed increasing value of Young′s modulus when the ratios of the aluminum-epoxy were increased. The graphite-epoxy coating on the PET micro-cantilever also showed the same trend. The experimental results also show that Young′s modulus of the graphite-epoxy coating is higher than aluminum-epoxy coating in comparison at the same mixing ratio.     

Mechanical characteristics of Fe-based coating obtained by nanoindentation

In this study, clad layers of iron-based alloy with a nature of self-fluxing were melted on low carbon steel by plasma cladding process. Nanoindentation with atomic force microscopy (AFM) has been used to investigate the mechanical properties of the coating. Hardness and elastic modulus at ultra-low loads were first determined using the method proposed by Giannakopoulos and Suresh (G&S method). The true contact area and mechanical properties were then determined using atomic force microscopy (AFM) combined with the Oliver and Pharr method (new proposed method) as the correction group. The mechanical properties calculated by the two methods showed the same distribution while had deviation in specific values. The effect of surface roughness to the calculated mechanical properties was investigated. Both hardness and elastic modulus were found to exhibit certain surface roughness dependence. When root mean square (RMS) roughness ranged from 2.2 nm to 4.4 nm, hardness calculated by both the methods increased obviously and reached maximums around 4.1 nm. Elastic modulus calculated by G&S method at different RMS showed the same distribution with that of hardness, while reduced elastic modulus obtained by AFM was insensitive to the range of RMS.     

Multiscale modeling of the effect of carbon nanotube orientation on the shear deformation properties of reinforced polymer-based composites

A combination of molecular dynamics (MD), continuum elasticity and FEM is used to predict the effect of CNT orientation on the shear modulus of SWCNT-polymer nanocomposites. We first develop a transverse-isotropic elastic model of SWCNTs based on the continuum elasticity and MD to compute the transverse-isotropic elastic constants of SWCNTs. These constants are then used in an FEM-based simulation to investigate the effect of SWCNT alignment on the shear modulus of nanocomposites. Furthermore, shear stress distributions along the nanotube axis and over its cross-sectional area are investigated to study the effect of CNT orientation on the shear load transfer.     

APPROXIMATION BY WALSH-KACZMARZ-FEJ ′ER MEANS ON THE HARDY SPACE

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.     

一类推广的Bernstein-Kantorovich算子的点态逼近

讨论Bernstein-Kantorovich算子的一种推广形式的逼近性质,运用插项的方法证明了逼近正定理,并证明了逆定理,得到了逼近等价定理.完善了算子在逼近性质方面的结果.     

Dunkl’s theory and best approximation by entire functions of exponential type in L 2-metric with power weight

In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,κ(Rd) by a subspace E2κ(σ)(SE2κ(σ)), which is a subspace of entire functions of exponential type(spherical exponential type) at most σ. Here L2,κ(Rd) denotes the space of all d-variate functions f endowed with the L2-norm with the weight v2κ(x) =ξ∈R, which is defined by a positive+|(ξ, x)|κ(ξ)subsystem R+ of a finite root system RRdand a function κ(ξ) : R → R+ invariant under the reflection group G(R) generated by R. In the case G(R) = Zd2, we get some exact results. Moreover,the deviation of best approximation by the subspace E2κ(σ)(SE2κ(σ)) of some class of the smooth functions in the space L2,κ(Rd) is obtained.     

Regularity of the inverse of a homeomorphism with finite inner distortion

Let f:Ω→ f(Ω) R~n be a W~(1,1)-homeomorphism with L~1-integrable inner distortion.We show that finiteness of min{lip_f(x),k_f/(x)},for every x ∈Ω\E,implies that f~(-1) ∈ W~(1,n)and has finite distortion,provided that the exceptional set E has cr-finite H~1-measure.Moreover,/ has finite distortion,differentiable a.e.and the Jacobian J_f 0 a.e.     

二元三次样条空间S31,2(Δmn(2)) 的样条拟插值

本文首先利用由两组具有局部最小支集的样条所组成的基函数,构造非均匀2 型三角剖分上二元三次样条空间S₃^1,2(Δ_mn⁽²⁾)的若干样条拟插值算子. 这些变差缩减算子由样条函数B_ij¹支集上5 个网格点或中心和样条函数B_ij²支集上5 个网格点处函数值定义. 这些样条拟插值算子具有较好的逼近性,甚至算子V_mn（f） 能保持近最优的三次多项式性. 然后利用连续模,分析样条拟插值算子V_mn（f）一致逼近于充分光滑的实函数. 最后推导误差估计.     

Pressure–volume–temperature behavior of two polycyanurate networks

The pressure–volume–temperature (PVT) behavior was studied for two polycyanurate networks having different crosslink densities using a pressurizable dilatometer. The samples were studied at temperatures ranging from 60 to 180 °C and at pressures up to 170 MPa to yield PVT data in both rubbery and glassy states. The Tait equation is found to well describe the isobaric temperature scan and isothermal pressure scan data. The thermal expansion coefficients, instantaneous bulk moduli, and thermal pressure coefficients are extracted from the data and their dependence on crosslink density is examined. The time‐dependent viscoelastic bulk modulus (K(t)) is also calculated in the vicinity of the α‐relaxation from previously published pressure relaxation experimental data, and the strength and shape of the dispersion are found to be independent of crosslink density. The limiting bulk moduli depend strongly on temperature with those of the more loosely crosslinked sample being lower at a given temperature and pressure, although at T_g(P), the limiting moduli of the more loosely crosslinked sample are slightly higher than those of the more highly crosslinked sample. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010