ALGEBRAIC INDEPENDENCE OF CERTAIN NUMBERS OVER A FIELD OF FINITE TRANSCENDENCE TYPE

The transcendental degree of certain numbers concerned with the exponential funotion over a field of finite transcendence type is considered.     

金属板材冲压成型过程的有限单元法模拟

用有限单元法模拟了金属板材的冲压成型过程。在模拟过程中，应用了同时考虑了薄膜力和弯矩的板壳大变形理论，考虑了板材在塑性阶段各向异性的强化性质，考虑了模具和工件的接触和摩擦条件，分析了金属板在冲压过程中的屈曲现象，建立了增量形式的变分原理。弹塑性薄壳单元被引入，它的位移模式在变分的意义上满足单元边界上一阶导数连续的条件，并有足够的秩来适应单元的有限拉伸、转动和弯曲，计算中采用了罚函数方法，即在模具和工件的接触面上，模具的表面被假设为文克尔地基，采用了修正的库伦摩擦定律，迭代法被用来决定模具与工件的接触条件和金属板的塑性行为。本文最后提供了一个算例。     

Copolymer architecture effects on the morphology and surface performance of epoxy thermosets containing fluorinated block copolymers

The architecture effects on phases and surface enrichment behaviors of epoxy nanocomposites containing fluorinated block copolymers are investigated by the incorporation of two novel copolymers composed of poly (2, 2, 2‐trifluoroethyl methacrylate) (PTFEMA) and poly (ε‐caprolactone) (PCL), PCL‐b‐PTFEMA and PTFEMA‐b‐PCL‐b‐PTFEMA, with identical molecular weight and composition. These fluorinated copolymers in epoxy display distinguished self‐assembled structures, as evidenced by dynamic laser scattering and scanning electron microscopy measurements. Static contact angle detection suggests that the nanocomposites display an obvious improvement in surface water repellency and a reduction in surface free energy. The enhancement in surface hydrophobicity is attributed to the enrichment of PTFEMA blocks at the nanocomposite surface and to the formation of the specific surface morphology, as confirmed by atomic force microscopy. The different architectures of the two block copolymers give rise to differences in phase‐structures, and the ultimate surface performances of composites. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1037–1045     

Effect of the topology on the antibacterial activity of cationic polythioether synthesized by all-click chemistry

Cationic compounds often serve as antibacterial materials for a wide range of applications. However, the relationship of topology−antibacterial activity has been rarely revealed. Herein, three cationic polythioethers (CPTEs) with hyperbranched topologies are well designed and facilely synthesized via an all-click chemistry strategy (including thiol-ene and epoxy-amine additions). These as-prepared CPTEs were found to exhibited outstanding antibacterial activity against Escherichia coli and Staphylococcus aureus with minimum inhibitory concentrations against E. coli of 7.3, 14.6, and 14.6 μg ml⁻¹, and against S. aureus of 14.6, 29.2, and 29.2 μg ml⁻¹, respectively. The antibacterial activity is coincident with their degree of branching (DB, their DB values of 0.81, 0.48, and 0.27), which is mainly attributed to the inherent three-dimensional structure. The present strategy reveals the relationship of polymer topology and antibacterial activity, providing a novel possibility for designing and/or synthesis of high-efficiency antibacterial agents.     

Multi-dimensional hybrid flexible films promote uniform lithium deposition and mitigate volume change as lithium metal anodes

Lithium metal is the ultimate anode material for next-generation high-energy batteries.Yet,the practical application of lithium metal anodes is limited by the formation of Li dendrites and large volume changes.Herein,an effective multi-dimensional hybrid flexible film(MD-HFF)composed of iodine ion(0 dimension),CNTs(1 dimension)and graphene(2 dimensions)is designed for regulating Li deposition and mitigating volume changes.The multi-dimensional components serve separate roles:(1)iodine ion enhances the conductivity of the electrode and provides lithiophilic sites,(2)CNTs strengthen interlaminar conductance and mechanical strength,acting as a spring in the layered structure to alleviate volume changes during Li plating and stripping and(3)graphene provides mechanical flexibility and electrical conductivity.The resulting MD-HFF material supports stable Li plating/stripping and high Coulombic efficiency(99%)over 230 cycles at 1 mA cm^-2 with a deposition capacity of 1 mAh cm^-2.Theoretical calculations indicate that LiI contributes to the lateral growth of Li on the MD-HFF surface,thereby inhibiting the formation of Li dendrites.When paired with a typical NCM811 cathode,the assembled MD-HFF‖NCM811 cell exhibit improved capability and stable cycling performance.This research serves to guide material design in achieving Li anode materials that do not suffer from dendrite formation and volume changes.     

功能梯度矩形板的近似理论与解析解

提出了压电功能梯度矩形板在竖向载荷作用下的近似理论与解析解. 引入了板理论的Kirchhoff假设、Reissner-Mindlin假设和提出的补充假设, 并假设材料常数在板厚方向按指数规律变化. 推导了板在周边简支同时又接地情况下中性层法线转角的解和用Fourier级数表示的电势解. 该解在形式上比精确解简单得多, 进行数值计算时也相当方便与快捷. 计算结果与ANSYS软件用三维实体单元的有限元计算结果进行了比较, 证实了该方法即使在厚板情况下仍然具有很高的精度.      

Algebraic independence of values of certain Fourier series

The algebraic independence of values of certain Fourier series with algebraic coefficients and their derivatives at algebraic points is proved.     

A method for exact calculation of the discrepancy of low-dimensional finite point sets (II)

In the present paper a general formula for exact calculation of the discrepancy of an arbitrary finite point set of dimensiond2 is explicitly given only in terms of the components of the points.     

Criteria of algebraic independence of complex numbers over a field of finite transcendence type (II)

In the present paper we establish a criterion of algebraic independence of complex numbers ₁, ..., _n over a field of finite transcendence type using a sequence of nonzero polynomials in several variables with integral coefficients, which satisfy simultaneously certain upper and lower estimates in different orders of magnitude at the point ( ₁, ..., _q , ₁, ..., _n ), where { ₁, ..., _q } is a transcendence basis of over .The Project Supported by the National Natural Science Foundation of China     

On dense sequences of polynomials in several variables

In the present paper a form of generalization of Gelfond's lemma on dense sequences of polynomials is proposed. For a set of complex numbers ₁, ..., _s we define the coefficients_gk( ₁, ..., _s ) (0ks) and give the relations between them and the transcendental degrees or the transcendence types of the field © ( ₁, ..., _s ) or its subfields.This work was completed at the Dept. of Math., Univ. of Southern Mississippi, USA in 1987.