A hybrid-Trefftz element containing an elliptic hole

Much work on special elements that simplify geometrical modelling of structures containing holes, cracks and/ or inclusions has been reported extensively in the literature. This paper presents a hybrid-Trefftz element containing elliptic hole formulated using Hellinger–Reissner principle by employing trial functions based on the mapping technique and the Cauchy integral method. The element presented in this paper could be regarded as an improved formulation over Piltner [Special finite elements with holes and internal cracks, Int. J. Numer. Methods Eng. 21 (1985) 1471–1485] element because the chosen trail functions in this paper have provided relatively more stable solutions. The use of the element with other ordinary displacement-based finite elements has also yielded very accurate solutions even when very coarse meshes relative to the size of the elliptic hole have been used.     

Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

Computer-assisted optimization of reversed-phase HPLC isocratic separation of neutral compounds

An appropriate optimization strategy should be used to find a desired resolution or selectivity with a minimum number of experiments in a limited time, which could assure the baseline separation of all target compounds. It was usually realized by means of a specialized computer program. In this paper, mapping optimization method and overlapping resolution mapping were compared for the optimization of a reversed-phase high-performance liquid chromatography (HPLC) isocratic separation of neutral compounds. The calculated resolutions and separation time of 7 to 10 experiments are fitted by different equations, which were used to build a contour plot with a minimum effective resolution and maximum retention time as a function of a mobile phase composition. The balance between resolution and analysis time could be easily realized by the overlapping of the final overlapping resolution mapping and analysis time mapping. The validity of the two methods was confirmed by some typical experiments. The models are simple, visual, and common without theoretical arithmetic.     

Micro- and nano-mechanical characterization of polyamide 11 and its composites containing cellulose nanofibers

Nanocomposites from polyamide 11 and dried cellulose nanofibers (CNs), 16–30 nm in thickness and 50–400 nm in length, were prepared via direct melt mixing and their micro- and nano-mechanical properties were studied. (PF) QNM (Quantitative Nanomechanical Mapping) method was used to map nanomechanical properties at the surface of polyamide 11 and nanocomposites. This new AFM method emphasized both the increased modulus in nanocomposites as compared to the matrix and the microstructure on different levels in polyamide 11 and its nanocomposites. PF QNM showed that their crystalline structure consists of bundles of lamellar stacks, 200–350 nm in width and 20–40 nm wide lamellar stacks. Moreover, PF QNM study emphasized higher structural order in nanocomposites with 3 and 5 wt.% CNs and lower in the nanocomposite with 8 wt.% CNs as compared to the reference. These observations were verified and are consistent with both crystallinity values determined by DSC and micro-mechanical test results. The oriented bundles of lamellar stacks, observed by PF QNM, could be considered as the main blocks determining high mechanical properties for the studied nanomaterials.     

Nest代数上的在零点广义可导映射

设A为B（H）的子代数,　是A到B（H）的线性映射,我们说　在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有　（ST）=　（S）T+S　（T）-S　（I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_　 H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.     

透射式GaAs光电阴极的X射线衍射研究

本文介绍了高精度多晶多反射X射线衍射仪的一种新的应用.首次将其应用于研究高灵敏度第三代微光象增强器中由掺Zn的p型GaAs/GaAlAs、玻璃组成的光电阴极的材料特性；发展了用倒格子空间衍射图方法评价光电阴级组件晶体质量的方法.通过分析得知,衍射强度在倒格子空间沿。方向展宽主要起因于晶体中的嵌镶效应的增强.文中采用衍射动力学理论的计算方法并忽略初始条件,模拟后得到的曲线与衍射强度沿ω/θ方向的投影强度曲线符合的比较好.粘接良好的阴极样品表明,GaAs/GaAlAs晶格常数的变化基本上可以消除,但粘接引起的嵌镶效应的增强却不能完全消除.     

Stabilizing the monodromy of an open book decomposition

We prove that any mapping class on a compact oriented surface with non-empty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.      

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.     

On the combined use of scratch tests and CLA profilometry for the characterization of polyester powder coatings: Influence of scratch load and speed

The prediction of the mechanical properties of polyester powder coatings is of paramount importance, as they have to undergo a wide variety of forces and deformations during their service life. Determine the response of polymeric coatings to the actual loading conditions can be, however, very troublesome as their properties are function of the material physical state, rate-dependence and yield and break behaviour. Further, the characterization of soft, contaminated organic surfaces such as polymers can often cause severe problems with reliability and imaging accuracy due to instrumental artefacts.This is therefore the context in which this paper investigates the capability of multiple parameters scratch tests joined with non-contact CLA profilometry and FE-SEM to detect the scratch response of polyester powder coatings for protective and decorative outdoor applications. Scratch tests with blunt contact geometry were used to evaluate the response of polyester coatings baked at different time-temperature programs and, so, at different stages of their curing process. In particular, being such coatings highly non-linear in their response to mechanical stress or strain, the influence from scratch load and speed was carefully taken into account. Analytical evaluations of the experimental results led to good correlations between the extent of the deformed zone after scratch, scratch parameters and curing operational settings. This allows mapping the scratch response of the polyester topcoats to broad ranges of both scratch parameters and curing conditions.     

Mapping Class Groups of Nonorientable Surfaces

We obtain a finite set of generators for the mapping class group of a nonorientable surface with punctures. We then compute the first homology group of the mapping class group and certain subgroups of it. As an application we prove that the image of a homomorphism from the mapping class group of a nonorientable surface of genus at least nine to the group of real-analytic diffeomorphisms of the circle is either trivial or of order two.