A Subspace of Hölder Space Consisting Only of Nonsmoothest Functions

In the first part of this paper, we give a complete answer to an old question of the geometric theory of Banach spaces; namely, we construct an infinite-dimensional closed subspace of Hölder space such that each function not identically zero is not smoother at each point than the nonsmoothest function in Hölder space. In the second part, using constructions from the first part, we show that the set of functions from Hölder space which are smoother on a set of positive measure than the nonsmoothest function is a set of first category in this space.     

Anisotropic elastic moduli and Poisson's ratios of a poly(ethylene terephthalate) film

Expressions for the directional dependence of Young's modulus and Poisson's ratio were derived for a general material under plane‐stress conditions. Experiments with a laser extensometer to measure the Young's modulus and Poisson's ratio directly by a tension test are described, and the results are compared with the theoretical expressions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 260–266, 2004     

Elastic shear modulus of biphasic gels

The effect on rheological properties on mixing one gel-forming and one nongelling polymer is investigated. It is found that on addition of a nongelling polymer to a constant amount of gel-forming polymer, the shear modulus of the resulting gel can either decrease or increase depending on the polymers. The results are interpreted within a simple qualitative model based on polymer incompatibility in combination with percolation theory and a uniform stress approximation.     

Porosity‐dependent Young's modulus of membranes from polyetherether ketone

The porosity‐dependent Young's modulus for PEEK membranes was determined and the data compared to several empirical and semiempirical equations often applied to porous systems. The Spriggs equation, Wang's approximation, Sudduth's equation, and the foam modulus‐density relationship were all tested against the data. The relatively wide range of porosities tested in these experiments shows the Spriggs equation to be inadequate to fitting the data, especially above 50% porosity where the Young's modulus decreases rapidly. Wang's approximation to second order fitted the data well, and the porosity‐modulus relations had non‐negative coefficients as required and consistent with the ceramic data obtained by others. The data also fitted Sudduth's equations, usually applied to sintered ceramics, but equivalently good fits were obtained with nonunique fitting parameters. The foam modulus‐density relationship fitted the data for foamlike membranes but fitted less well to nonfoam morphology membranes. Finally, the data were used to determine the range of porosities and hollow fiber dimensions necessary for microfiltration and composite membrane application. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1168–1174, 2003     

Generalized polynomial approximation providing the best reference

We pose the extremum problem of finding a polynomial approximation for a function of several variables so that this approximation by a fragment of the function provides the best reference. We obtain an upper bound for the modulus of informativity of polynomials and rational functions.Translated fromMatematickeskie Zametki, Vol. 60, No. 5, pp. 658–669, November, 1996.The author wishes to thank Yu. N. Subbotin for valuable discussions.This research was supported by the Russian Foundation for Basic Research under grant No. 93-011-196.     

Elastic modulus and atomic displacements of skeleton and side groups in stretching of a polymer chain

We propose a new method of calculating elastic modulus and atomic displacements of a stretched polymer chain. We use a stretched Cartesian coordinate system and a stretched B matrix defined by the Cartesian displacement components of the bonds to express the potential energy matrix F_x for stretching. The method is used to calculate elastic moduli of planar-zigzag-chain vinyl polymers and helical-chain isotactic polypropylene and the atomic displacements of their skeleton and side groups. The skeletal displacements of planar-zigzag-chain polymers are about ten times larger than those of the side groups and reverse displacements of the two adjacent skeletal units occur in the direction perpendicular to the stretching direction along the fiber axis. In the case of isotactic polypropylene, the methyl group has more effect than the torsional change around the C? C bond on the skeletal deformation. © 1993 John Wiley & Sons, Inc.     

3-D network model and its parameter calibration

A material model, whose framework is parallel spring-bundles oriented in 3-D space, is proposed. Based on a discussion of the discrete schemes and optimum discretization of the solid angles, a 3-D network cell consisted of one-dimensional components is developed with its geometrical and physical parameters calibrated. It is proved that the 3-D network model is able to exactly simulate materials with arbitrary Poisson ratio from 0 to 1/2, breaking through the limit that the previous models in the literature are only suitable for materials with Poisson ratio from 0 to 1/3. A simplified model is also proposed to realize high computation accuracy within low computation cost. Examples demonstrate that the 3-D network model has particular superiority in the simulation of short-fiber reinforced composites.     

左Bernstein逆插值算子的点态逼近性质

利用光滑模ω2φrλ(f,t)给出了左Bernste in逆插值算子的逼近等价定理.     

下卧软弱岩带变形模量取值研究

软弱岩带的变形模量对于工程建设意义重大,当前变形试验方法难以表征原位条件下软弱岩带的变形模量,导致取值偏于保守。本文基于弹性力学推导了下卧软弱岩带变形模量的解析解,建立了一种新的软弱岩带变形模量的取值方法。在现场试验成果的基础上,采用有限元反演,数值模拟成果与试验计算成果较为吻合,证明该计算方法合理可行,较常规方法直接在软弱岩带上开展的试验成果大幅提高。     

Flexural rigidity of honeycomb consisting of hexagonal cells

In this study,the flexural rigidity of a honeycomb consisting of regular hexagonal cells is investigated.It is found that the honeycomb bending can not be evaluated by using the equivalent elastic moduli obtained from the in-plane deformation because the moments acting on the inclined cell wall are different for in-plane deformation and bending deformation.Based on the fact that the inclined wall is twisted under the condition of the rotation angle in both connection edges being zero,a theoretical technique for calculating the flexural rigidity of honeycombs is proposed,and the validity of the present analysis is demonstrated by numerical results obtained by BFM.