Acyclic Heaps of Pieces, I

Heaps of pieces were introduced by Viennot and have applications to algebraic combinatorics, theoretical computer science and statistical physics. In this paper, we show how certain combinatorial properties of heaps studied by Fan and by Stembridge are closely related to the properties of a certain linear map _E associated to a heap E. We examine the relationship between _E and _F when F is a subheap of E. This approach allows neat statements and proofs of results on certain associative algebras (generalized Temperley–Lieb algebras) that are otherwise tricky to prove. The key to the proof is to interpret the structure constants of the aforementioned algebras in terms of the maps .     

Frobenius splitting and geometry of G-Schubert varieties

Let X be an equivariant embedding of a connected reductive group G over an algebraically closed field k of positive characteristic. Let B denote a Borel subgroup of G. A G-Schubert variety in X is a subvariety of the form diag(G)⋅V, where V is a B×B-orbit closure in X. In the case where X is the wonderful compactification of a group of adjoint type, the G-Schubert varieties are the closures of Lusztig's G-stable pieces. We prove that X admits a Frobenius splitting which is compatible with all G-Schubert varieties. Moreover, when X is smooth, projective and toroidal, then any G-Schubert variety in X admits a stable Frobenius splitting along an ample divisors. Although this indicates that G-Schubert varieties have nice singularities we present an example of a nonnormal G-Schubert variety in the wonderful compactification of a group of type G₂. Finally we also extend the Frobenius splitting results to the more general class of R-Schubert varieties.     

On homotopy groups of quandle spaces and the quandle homotopy invariant of links

For a quandle X, the quandle space BX is defined, modifying the rack space of Fenn, Rourke and Sanderson (1995) [13], and the quandle homotopy invariant of links is defined in Z[π₂(BX)], modifying the rack homotopy invariant of Fenn, Rourke and Sanderson (1995) [13]. It is known that the cocycle invariants introduced in Carter et al. (2005) [3], Carter et al. (2003) [5], Carter et al. (2001) [6] can be derived from the quandle homotopy invariant.In this paper, we show that, for a finite quandle X, π₂(BX) is finitely generated, and that, for a connected finite quandle X, π₂(BX) is finite. It follows that the space spanned by cocycle invariants for a finite quandle is finitely generated. Further, we calculate π₂(BX) for some concrete quandles. From the calculation, all cocycle invariants for those quandles are concretely presented. Moreover, we show formulas of the quandle homotopy invariant for connected sum of knots and for the mirror image of links.     

陕西战国秦墓出土玻璃和汉紫六博棋子分析研究

利用超景深显微镜（OM）、激光拉曼光谱仪(Raman)、X射线荧光光谱仪(XRF)、扫描电子显微镜能谱(SEM-EDS)、色度仪等多种手段,对陕西战国秦墓出土的两种质地、颜色不同的六博棋子进行了综合分析检测。鉴定出蓝色样品为铅钡玻璃,紫色样品为中国紫制品,发现了中国紫在战国时期的新用途。并对比陕西出土的铅钡玻璃制品与两湖、四川地区出土的同时代的铅钡玻璃制品在成分组成上的差异,推测战国时期铅钡玻璃的制作工艺已成熟,可根据器物形制的需求进行不同的成分配比。同时,还发现当时的玻璃制作已有旧料重熔制作新器的现象。在确定中国紫成分的基础上,利用色度计进行色度测试,根据光谱数据,首次为人造硅酸铜钡颜料确定了特征光谱峰,使快速、无损的对人造硅酸铜钡颜料的鉴定识别成为可能。     

模板法制备α-MoO3纳米棒和纳米矩形片及光谱表征

以(NH4)6Mo7O24.4H2O为钼源,十六烷基三甲基溴化铵(CTAB)为模板剂,通过强酸性离子交换树脂(R-H)进行静态交换制备出前驱物,前驱物在600℃经不同时间焙烧,制备了α-MoO3纳米棒和纳米矩形小片。用FTIR,XRD,TEM和SEM等测试手段对样品的相态、结构和形貌进行了光谱表征,结果表明:前驱物经过600℃焙烧4和8h后,分别得到长度约1～1.6μm,直径约0.10～0.20μm,长径比为8的α-MoO3纳米棒和长度约0.14～0.18μm,宽度约60～80nm,厚度约28～32nm的纳米矩形小片。该法制备工艺简单,不用人为地调节pH、省去过多洗涤等过程,树脂可再生重复使用,副产品氯化铵可回收利用,无环境污染。     

Dissecting chemical markers for controlling “Paozhi” method of traditional Chinese medicine with untargeted metabolomics: Vinegar-baked Euphorbia kansui as a case study

The processing of Traditional Chinese Medicine requires the appropriate parameters, while the specific chemical markers are still absent to obtain the optimized processing. In this study, we used vinegar-baked Euphorbia kansui as a case to dissect the chemical markers for the baking process using untargeted metabolomics. The robust chemical markers were selected based on the three rules, correlation, significant difference, and controllability. All the differential features were categorized based on their mass defects. After the differential analysis, 310 differential compounds were screened out and could be mainly divided into six categories: diacylglycerols and triacylglycerols demonstrated increasing trends with the baking time in the discriminant model, while ingenane-type diterpenes, jatrophane-type diterpenes, fatty acid esters, and fatty acids had decreasing trends. It was unexpected to find that the diterpenes did not correlate with the baking time. Only very few compounds meet the three rules. They were validated with a high-performance liquid chromatography method. Finally, only 13-Hydroxy-9,11-octadecadienoic acid and its isomer 9-Hydroxy-10,12-octadecadienoic acid could be used further to differentiate the commercial vinegar-baked Euphorbia kansui. It would be of interest to evaluate whether these two compounds could be utilized as markers to control more processing methods in future studies.     

Postnikov pieces and -homotopy theory

We present a constructive method to compute the cellularization with respect to for any integer of a large class of -spaces, namely all those which have a finite number of non-trivial -homotopy groups (the pointed mapping space is a Postnikov piece). We prove in particular that the -cellularization of an -space having a finite number of -homotopy groups is a -torsion Postnikov piece. Along the way, we characterize the -cellular classifying spaces of nilpotent groups.

     

Active ferromagnetic shimming of the permanent magnet for magnetic resonance imaging scanner

This paper presents an approach of active ferromagnetic shimming for C-type permanent magnetic resonance imaging (MRI) magnet.It is designed to reduce inhomogeneity of magnetostatic field of C-type permanent magnet to meet the stringent requirement for MRI applications.An optimal configuration (locations and thicknesses) of active ferromagnetic pieces is generated through calculation according to the initial field map and the demanded final homogeneity specifications.This approach uses a minimisation technique which makes the sum of squared magnetic moment minimum to restrict the amount of the active ferromagnetic material used and the maximal thickness of pieces stacked at each hole location in the shimming boards.Simulation and experimental results verify that the method is valid and efficient.     

基于迭代拟合的集装箱角件边缘检测算法

噪声通常是影响集装箱角件图像中低层次语义信息提取精度的重要因素,传统的边缘检测算法通常通过改进滤波器和阈值来消除图像中的物理噪声和环境噪声,但是却无法去除边缘检测后的噪声,为解决这一问题,提出了一种基于迭代拟合的边缘检测算法。首先,对角件图像进行一系列预处理操作获取边缘点集,其次,使用拟合算法处理点集并且得到函数表达式,然后定义偏差值度量并计算,用于衡量目标点集到拟合或者检测结果的偏差,最后,去除定义下距离拟合结果最远的指定数量的点,如此迭代拟合直至评价函数收敛。实验结果与分析表明,该算法可以有效地去除边缘点集中的非真实边缘点,相比于传统的边缘检测算法更能去除特殊噪声,算法具有收敛速度快、准确率较高、灵活性好等特点。     

The existence of a kind of bundle map

By means of the theory of Postnikov resolution, a sufficient condition for the existence of a kind of bundle maps is obtained. Some applications of the result are given. Particularly, it is proven that the deleted products as well as configuration spaces of two simply connected manifolds with suitable dimension have the same homotopy type when the original manifolds are homotopically equivalent.