New light on Hensel''s lemma

The historical development of Hensel's lemma is briefly discussed (Section 1). Using Newton polygons, a simple proof of a general Hensel's lemma for separable polynomials over Henselian fields is given (Section 3). For polynomials over algebraically closed, valued fields, best possible results on continuity of roots (Section 4) and continuity of factors (Section 6) are demonstrated. Using this and a general Krasner's lemma (Section 7), we give a short proof of a general Hensel's lemma and show that it is, in a certain sense, best possible (Section 8). All valuations here are non-Archimedean and of arbitrary rank. The article is practically self-contained.     

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.     

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.     

Lipschitz Continuity and Interpolation Properties of Some Classes of Increasing Functions

We study local Lipschitz continuity and interpolation properties of some classes of increasing functions defined on the cone Rⁿ ₊₊ of n-vectors with positive coordinates. We also study the so-called self-conjugate increasing positively homogeneous functions.     

关于K-拟可加模糊积分的几点注记

在K-拟可加模糊积分定义及积分转换定理的基础上，证明这种模糊积分恰好构成K-拟可加模糊测度，并依据积分转换定理讨论这种K-拟可加模糊积分的一些补充性质。     

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.