广义椭圆积分的广义凹凸性

函数的广义凹凸性是获取函数不等式的一种重要工具。利用广义凹凸函数(MN-凹凸函数)单调性之间的关系,揭示了由广义椭圆积分定义的若干重要函数的广义凹凸性。同时,利用这些结果可以获得广义椭圆积分的若干不等式。     

Isothermal crystallization of HDPE/octamethyl polyhedral oligomeric silsesquioxane nanocomposites: Role of POSS as a nanofiller

The isothermal crystallization of HDPE/POSS (polyhedral oligomeric silsesquioxane) nanocomposites (POSS content varying from 0.25 to 10 wt %) was studied using differential scanning calorimetry (DSC) technique. The Avrami model could successfully describe the isothermal crystallization behavior of the nanocomposites. The value of Avrami exponent (n) varies between 2 and 2.5 for all the compositions studied. For a given composition, the values vary with crystallization temperature and in general increased with POSS content up to 1 wt % POSS content and decreased thereafter. The presence of POSS was found to increase the rate of crystallization, which manifested itself in the increased value of the Avrami rate constant (K) and reduced value of crystallization half‐time (t_1/2). The rate of crystallization peaked at 1 wt % POSS content and was almost constant at higher POSS loadings. X‐ray diffraction studies revealed that POSS exists as nanocrystals in HDPE matrix while some POSS gets dispersed at molecular level too. It is observed that only the POSS dispersed at molecular level acts as a nucleating agent while the POSS nanocrystals do not affect the crystallization process. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

The time-dependent rural postman problem: polyhedral results

The Chinese postman problem is a famous and classical problem in graph theory. This paper introduces a new variant of this problem, namely, the time-dependent rural postman problem, which is motivated by applications, involving scheduling with time-dependent processing time. We present an arc-path formulation for the problem with a constraint set that is divided into two parts. The first part is linear and has a strong combinatorial structure, which defines the polytope of the arc-path alternation sequence (APAS), while the second part is nonlinear and is closely related to time-dependent travel time. First, we investigate the facial structure of the APAS polytope and present several facet inequalities. Second, considering the travel and service time functions as piecewise functions, we linearize the nonlinear inequalities and propose several strong, valid inequalities. Finally, we propose a cutting plane algorithm and report numerical results on several randomly generated instances.     

Minimal non-convex words

Using a combinatorial characterization of digital convexity based on words, one defines the language of convex words. The complement of this language forms an ideal whose minimal elements, with respect to the factorial ordering, appear to have a particular combinatorial structure very close to the Christoffel words. In this paper, those words are completely characterized as those of the form uw^kv where k≥1, w=u⋅v and u,v,w are Christoffel words. Also, by considering the most balanced among the unbalanced words, we obtain a second characterization for a special class of minimal non-convex words that are of the form u²v² corresponding to the case k=1 in the previous form.     

多胞约束LPV系统多面体不变集RMPC算法

针对一类输入和输出受约束且具有多胞结构的离散LPV 系统, 提出一种基于多面体不变集的鲁棒模型预测控制(RMPC) 算法. 选取一系列收敛于原点的离散状态点, 计算每个状态的反馈控制率, 构建相应的多面体不变集. 在每一个采样时刻, 确定包含当前状态的最小多面体不变集, 通过计算与相邻两个多面体不变集的位置关系, 执行连续的状态反馈控制率. 仿真结果表明, 相比椭圆不变集离线RMPC算法, 所提出算法扩大了系统的稳定区域, 取得了保守性较小的结果.

     

板形自动控制在热连轧中的应用

莱钢1500热连轧生产线的板形自动控制系统是国内自主研发的板形控制系统,它包括板预设定形、板形的PID调节、弯辊力的前馈控制、凸度仪的反馈控制、窜辊的闭环调节、平坦度的反馈控制、板形与板厚的解耦控制等多种控制于一体。主要介绍弯辊力前馈、凸度反馈和平坦度反馈3个模型在实际轧钢过程中的应用。     

Investigation of crystallisation and interfacial nature of polyhedral oligomeric silsesquioxane/polypropylene composites in the presence of β-nucleating agent

Polyhedral oligomeric silsesquioxane (POSS)/polypropylene (PP) composites in the presence of β-nucleating agent (β-NAs) were prepared by melt-blending, and the interfacial interaction and crystallisation behaviour were investigated. The experimental results indicated that strong hydrogen bonding interactions were generated between amino groups of β-NAs and silicon hydroxyl groups attached to POSS, allowing the absorption/anchoring of the former on the surface of latter. Compared to POSS, β-NAs exhibited higher nucleation effect on PP, as evidenced by an increment of the crystallisation temperature by 7°C in the presence of β-NAs. As a result, the absorbed β-NAs on the surface of POSS not only improved the interfacial interaction between POSS and polymer matrix using interfacial crystallisation but also promoted the formation of β-crystals with toughening effect, which is very important to prepare excellent-performance PP/POSS composite.     

Thermal and morphological properties of high‐density polyethylene/ethylene–vinyl acetate copolymer composites with polyhedral oligomeric silsesquioxane nanostructure

The demand for improved properties of common polymers keeps increasing, and several new approaches have been investigated. In the study reported here, composites with a polymer matrix comprising a blend of high‐density polyethylene with ethylene–vinyl acetate copolymer (EVA), and with polyhedral oligomeric silsesquioxane (POSS) as a nanostructure, were processed and characterized in terms of their thermal and morphological properties. For the preparation of the composites, the concentrations of the blend components (0, 50 and 100 wt%) and of the POSS (0, 1 and 5 wt%) were varied. X‐ray diffraction results indicated that the presence of EVA in the composites led to the appearance of crystalline domains at lower POSS concentrations. Transmission and scanning electron microscopy showed that samples with 1 wt% of POSS had a homogeneous distribution in the polymer matrix with average dimensions of ca 150 nm. However, the formation of aggregates occurred in samples with 5 wt% of POSS. Differential scanning calorimetry and thermogravimetic analyses indicated that the POSS did not affect the melt and degradation temperatures of the polymer matrix. POSS underwent aggregation at higher concentrations during the composite processing, indicating a solubility limit of around 1 wt%. The presence of EVA in the composite favors POSS aggregation due to an increase in the polarity of the polymer matrix. Copyright © 2009 Society of Chemical Industry     

Hybrid Organic-Inorganic Nanocomposites Based on Poly(ϵ-Caprolactone)/Polyhedral Oligomeric Silsesquioxane: Synthesis and In Vitro Evaluations

Hybrid poly(?-caprolactone) (PCL) containing nanocomposites and non-hybrid linear PCL diols were synthesized by anionic ring opening polymerization of ?-caprolactone on a POSS or ethylene glycol central blocks, respectively. Monolith scaffolds were then fabricated from the hybrid nanocomposites and non-hybrid linear PCL diols via non-solvent induced phase separation technique. The effects of inclusion of POSS nanocage in the polymer chain structure on specific surface area and pore size of the scaffolds was investigated by multipoint BET method. This perfect scrutiny will introduce an excellent nanoparticle pendent to the PCL chains to promote the in vitro properties of the implants potentially applicable in tissue engineering.     

Real Time Local Approximation of Deformations using Rotations

Additional realism can be achieved in computer generated images using smooth and increasingly complex deformations. Though significant effort has been spent on improving these deformations, no general method has been proposed yet to deal with rigid pieces connected to soft objects. This paper proposes a general framework to solve this problem. We will present several types of applications, such as flowing small objects in a deformation field, animating rigid features connected to some deformed object, or smoothly attached limbs to a deforming body. All the calculations presented here can be applied to any type of deformation, provided that the deformation at each point only depends on the point itself. Even though we can directly compute the result for some analytical deformation fields, we will show that a good sampling of the deformation in the area of interest is generally enough. One intermediate result consists of a practical method to find the best rotation that approximates a linear transformation. The proposed method is a superset of the Gram-Schmidt orthonormalization process, and is much easier to compute than global methods based on Taylor series.