Existence of positive solutions to a coupled system of fractional differential equations

We consider the following system of fractional differential equations where is the Riemann‐Liouville fractional derivative of order α,f,g : [0,1] × [0, ∞ ) × [0, ∞ ) → [0, ∞ ). Sufficient conditions are provided for the existence of positive solutions to the considered problem. Copyright © 2014 John Wiley & Sons, Ltd.     

Density functional study of α-graphyne derivatives: Energetic stability,atomic and electronic structure

The energetic stability, atomic and electronic structures of α-graphyne and its derivatives (α-GYs) with extended carbon chains were investigated by density functional (DF) calculations in this work. The studied α-GYs consist of hexagon carbon rings sharing their edges with carbon atoms N=1–10. The structure and energy analyses show that α-GYs with even-numbered carbon chains have alternating single and triple C–C bonds (polyyne), energetically more stable than those with odd-numbered carbon chains possessing continuous double C–C bonds (polycumulene). The calculated electronic structures indicate that α-GYs can be either metallic (odd N) or semiconductive (even N) depending on the parity of number of atoms on hexagon edges despite the edge length. The semiconducting α-graphyne derivatives are found to possess Dirac cones (DC) with small direct band gaps 2–40 meV and large electron velocities 0.554×10⁶–0.671×10⁶ m/s, 70–80% of that of graphene. Our DF studies suggest that introducing sp carbon atoms into the hexagon edges of graphene opens up an avenue to switch between metallic and DC electronic structures via tuning the parity of the number of hexagon edge atoms.     

Ethylene propylene diene monomer rubber‐based heat shielding materials for solid rocket motor: Impact of Kevlar fiber reinforcement on the thermal and mechanical properties

This work scrutinizes the utilization of ethylene propylene diene monomer rubber matrix (EPDM) with an embodiment of aramid fiber for the heat shielding applications in solid rocket motor (SRM). Aramid fibers are aromatic poly‐paraphenylene terephthalamide, here deployed are Kevlar fibers (KF). However, the literature that encompasses the thermal and mechanical behavior with the fiber loading is reported nowhere else. The effect of fiber addition on the surface morphology and density was thoroughly studied, and it revealed that the EHSMs were of lower density to act as an efficient payload for the SRM. In this regard, the thermal conductivity, heat capacity, thermal diffusivity, fire behavior, and mechanical properties of the EPDM/KF‐based EHSMs were explored. The results revealed that the EHSMs are thermally insulating and thermally stable material with balanced mechanical properties that can engender the thermal and mechanical strains of the rocket motor. Furthermore, other analytical techniques such as scanning electron microscopy and energy dispersive X‐ray spectroscopy have been exploited to monitor the performance of the char residues of the EHSM to delineate its performance in the fire atmosphere.     

Stereoisomeric Tris-BINOL-Menthol Bulky Monophosphites: Synthesis,Characterisation and Application in Rhodium-Catalysed Hydroformylation

Four stereoisomeric monoether derivatives, based on axially chiral (R)- or (S)-BINOL bearing a chiral (+)- or (−)-neomenthyloxy group were synthesised and fully characterised by NMR spectroscopy and X-ray crystallography. The respective tris-monophosphites were thereof prepared and fully characterised. The coordination ability of the new bulky phosphites with Rh(CO)₂(acac), was attested by ³¹P NMR, which presented a doublet in the range of δ = 120 ppm, with a ¹J(¹⁰³Rh-³¹P) coupling constant of 290 Hz. The new tris-binaphthyl phosphite ligands were further characterised by DFT computational methods, which allowed us to calculate an electronic (CEP) parameter of 2083.2 cm⁻¹ and an extremely large cone angle of 345°, decreasing to 265° upon coordination with a metal atom. Furthermore, the monophosphites were applied as ligands in rhodium-catalysed hydroformylation of styrene, leading to complete conversions in 4 h, 100% chemoselectivity for aldehydes and up to 98% iso-regioselectivity. The Rh(I)/phosphite catalytic system was also highly active and selective in the hydroformylation of disubstituted olefins, including (E)-prop-1-en-1-ylbenzene and prop-1-en-2-ylbenzene.     

A review of mobility metrics for next generation vehicle mobility models

In the United States, the NATO Reference Mobility Model (NRMM) has been used for evaluating military ground vehicle mobility and the Vehicle Cone Index (VCI) has been selected as a mobility metric. VCI represents the minimum soil strength required for a vehicle to consistently make a specific number of passes, usually one or fifty passes. In the United Kingdom, the Mean Maximum Pressure (MMP) has been adopted as a metric for assessing military vehicle cross-country mobility. MMP is the mean value of the maxima occurring under all the wheel stations of a vehicle. Both VCI and MMP are empirically based. This paper presents a review of the basis upon which VCI and MMP were developed, as well as their applications to evaluating vehicle mobility in practice. With the progress in terramechanics and in modelling and simulation techniques in recent years, there is a growing desire to develop physics-based mobility metrics for next generation vehicle mobility models. Based on the review, criteria for selecting physics-based mobility metrics are proposed. Following these criteria, metrics for characterizing military vehicle traction limits and traversability on a given operating area are recommended.     

倒锥微孔阵列的激光微加工技术研究进展

激光微加工技术凭借其加工效率高、加工材料广泛、无物理损伤以及操控性强等优点在高精度机械部件的加工上有较好的应用前景,易加工出尺寸微小、数量庞大、高品质的倒锥微孔阵列.首先对激光加工微孔的工作原理和特点进行了介绍,综述了激光在加工微孔阵列、倒锥微孔以及倒锥微孔阵列的研究现状,详细介绍了准分子激光、飞秒激光、纳秒激光在加工...     

弹塑性摩擦接触问题形状设计灵敏度分析

提出了一种计算二维有限变形弹塑性摩擦接触问题形状设计灵敏度的算法. 采用主动集策略和mortar方法处理接触边线上的约束条件. 在mortar接触边线的切线和法线方向上采用相同的名义罚函数,提出基于名义罚函数的移动摩擦锥算法来正则化接触约束条件,发展了一种新的二维多体有限变形摩擦接触算法. 在此基础上, 通过将离散形式的摩擦接触问题控制方程对形状设计变量微分,得到了该路径相关问题的直接微分法解析设计灵敏度计算格式, 其节点位移灵敏度方程在每个增量步不用迭代、直接求解. 与国际上现有的二维多体有限变形摩擦接触问题的解析设计灵敏度算法相比,本算法不需分解为法向和切向推导,表达式较简洁,便于编程实现. 数值算例验证了算法的精度和有效性.      

An explicit counter-example for the shephard problem of convex bodies in ℝ n

Comparing the volume of the projection body of a double cone and that of the projection body of a ball, we give an explicit counter-example for the Shephard problem of convex bodies in Rⁿ (n ≥ 3) and an affirmative answer to the question of Zhang.     

一类凹与凸算子的推广

运用锥的性质以及单调迭代技巧给出了一类广义凹算子与凸算子正不动点的存在唯一性,并讨论了算子特征值方程的性质.作为应用,利用所获结果研究了一类积分方程正解的存在唯一性.