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.     

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.     

BS-RNA: An efficient mapping and annotation tool for RNA bisulfite sequencing data

Cytosine methylation is one of the most important RNA epigenetic modifications. With the development of experimental technology, scientists attach more importance to RNA cytosine methylation and find bisulfite sequencing is an effective experimental method for RNA cytosine methylation study. However, there are only a few tools can directly deal with RNA bisulfite sequencing data efficiently. Herein, we developed a specialized tool BS-RNA, which can analyze cytosine methylation of RNA based on bisulfite sequencing data and support both paired-end and single-end sequencing reads from directional bisulfite libraries. For paired-end reads, simply removing the biased positions from the 5′ end may result in “dovetailing” reads, where one or both reads seem to extend past the start of the mate read. BS-RNA could map “dovetailing” reads successfully. The annotation result of BS-RNA is exported in BED (.bed) format, including locations, sequence context types (CG/CHG/CHH, H = A, T, or C), reference sequencing depths, cytosine sequencing depths, and methylation levels of covered cytosine sites on both Watson and Crick strands. BS-RNA is an efficient, specialized and highly automated mapping and annotation tool for RNA bisulfite sequencing data. It performs better than the existing program in terms of accuracy and efficiency. BS-RNA is developed by Perl language and the source code of this tool is freely available from the website: http://bs-rna.big.ac.cn.     

基于步进啁啾光纤光栅的OCDMA频阈相位编码

本文提出了一种在步进啁啾光纤光栅实现OCDMA频阈相位编码的方案,该方案中引入了影射码,根据影射码在相应的子光栅之间加入相移以实现正确的编解码.该编解码器结构简单,数值模拟得到了好的相关输出.     

High Sensitive Microsensor Based on Organic‐Inorganic Composite for Two‐Dimensional Mapping of H2O2 by SECM

The present work describes the development of a selective, sensitive and stable sensing microsensor for scanning electrochemical microscopy (SECM) to measure H₂O₂ during electrochemical reduction of oxygen. The microsensor is based on graphene and Poly(3,4‐ethylenedioxythiophene) composite as support to iron (III) hexacyanoferrate (II) (PEDOT/graphene/Fe^III₄[Fe^II(CN)₆]₃ microsensor). The electrochemical properties of the PEDOT/graphene/Fe^III₄[Fe^II(CN)₆]₃ microsensor were investigated by cyclic voltammetry (CV) and scanning electrochemical microscopy (SECM). The PEDOT/graphene/Fe^III₄[Fe^II(CN)₆]₃ microsensor showed an excellent electrocatalytic activity toward hydrogen peroxide (H₂O₂) reduction with a diminution of the overpotential of about 500 mV in comparison to the process at a bare gold microelectrode. The microsensor presented excellent performance for two dimensional mapping of H₂O₂ by SECM in 0.1 mol L^?1 phosphate buffer solution (pH 7.0). Under optimized conditions, a linear response range from 1 up to 1000 µmol L^?1 was obtained with a sensitivity of 0.08 nA L µmol^?1 and limit of detection of 0.5 µmol L^?1.     

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.     

高光谱成像的土壤剖面水分含量反演及制图

传统土壤水分的获取方法仅可获得离散的土壤水分点位数据,难以获得剖面上精细且连续的水分含量分布图。研究了野外条件下利用近红外高光谱（882～1 709 nm）成像反演剖面土壤水分含量（SMC）,并实现精细制图的可行性。研究剖面位于江苏省东台市,我们利用近红外高光谱成像仪对剖面进行了5天原位连续观测,共采集了280个土样用于烘干法测定SMC。原始高光谱图像经数字量化值（DN）校正、黑白校正、拼接、几何校正、剪切和掩膜等一系列预处理后,提取各采样点的平均光谱反射率。提取光谱（Raw）经吸光度[LOG₁₀(1/R)],Savitzky-Golay平滑（SG）、一阶微分（FD）、二阶微分（SD）、多元散射校正（MSC）和标准正态变量（SNV）转换后,采用偏最小二乘回归（PLSR）和最小二乘支持向量机（LS-SVM）方法建立SMC预测模型,并对比分析不同光谱预处理方法与建模方法组合条件下SMC的预测精度。结果表明,光谱反射率随SMC增加逐渐降低,不同光谱预处理方法的预测精度有所差异,除MSC方法外,同一光谱预处理方法的LS-SVM模型预测精度均高于PLSR模型,并且基于LOG₁₀(1/R)光谱的LS-SVM模型对SMC预测精度最高,其建模集的决定系数（R2_c）和均方根误差（RMSE_c）分别为0.96和0.65%,预测集的决定系数（R2_p）、均方根误差（RMSE_p）和相对分析误差（RPD_p）分别为0.88,1.05%和2.88。利用最优模型进行剖面SMC的高空间分辨率精细制图,通过比较SMC反演图中提取的预测值与实测值关系发现预测精度较高（R2: 0.85～0.95, RMSE: 0.94%～1.02%）,且两者在剖面中的变化趋势基本一致,说明SMC反演图不仅能很好地反映出土壤水分在整个剖面中毫米级的含量分布信息,也可反映出同一位置处不同天数间的含量差异。因此,利用近红外高光谱成像结合优化的预测模型,能够实现土壤剖面SMC的定量预测及精细制图,有助于快速、有效监测田间剖面土壤水分状况。     

Efficient Spatial Modeling Using the SPDE Approach With Bivariate Splines

Gaussian fields (GFs) are frequently used in spatial statistics for their versatility. The associated computational cost can be a bottleneck, especially in realistic applications. It has been shown that computational efficiency can be gained by doing the computations using Gaussian Markov random fields (GMRFs) as the GFs can be seen as weak solutions to corresponding stochastic partial differential equations (SPDEs) using piecewise linear finite elements. We introduce a new class of representations of GFs with bivariate splines instead of finite elements. This allows an easier implementation of piecewise polynomial representations of various degrees. It leads to GMRFs that can be inferred efficiently and can be easily extended to nonstationary fields. The solutions approximated with higher order bivariate splines converge faster, hence the computational cost can be alleviated. Numerical simulations using both real and simulated data also demonstrate that our framework increases the flexibility and efficiency. Supplementary materials are available online.     

由格蕴涵代数诱导的伴随半群

给出由格蕴涵代数诱导出的伴随半群及有关概念 ,详细讨论伴随半群中的元素即格蕴涵代数的左映射的性质 ,得到它们的几个等价条件。最后讨论由格蕴涵代数诱导的两个双格半群与伴随半群之间的关系 ,并证明这些半群是幂等的当且仅当它们是由格 H蕴涵代数所诱导