Harmonic 2-forms and positively curved 4-manifolds

Science China Mathematics - We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality, then it is definite. We also discuss...     

Si内标-X射线衍射法定量测定铁矿中Fe3O4、Fe2O3和SiO2

铁矿物相的准确定量对矿物价值评价及选冶工艺研究有重要作用,现有化学法流程复杂效率低,X射线衍射全谱拟合法可溯源性差,结果准确性难以评价和验证。本研究建立了以Si为内标,以Cu靶X射线为辐射光源,步进扫描方式获得衍射谱图,以待测相含量为横坐标,待测相与内标相峰面积比值为纵坐标建立校准曲线,以曲线对铁矿中Fe3O4、Fe2O3和SiO2物相进行定量的方法。试验对制样条件、扫描参数、内标物选择、积分方式、重叠峰校正等进行了优化选择,结果表明,试样全部通过45 μm标准筛,Si内标比例为10%,步进长度0.01°,步进时间30S,选择对Fe3O4（311）、Fe2O3（104）、SiO2（011）和Si（111）的衍射峰进行积分强度计算,可获得最优结果。在选定工作条件下,Fe3O4在1.07～100%范围内线性相关系数(R2)为0.9953,相对标准偏差(RSD)1.1%～13.2% (n=6),加标回收率99.7 %~114.8 %,检出限(LOD)4.29%;Fe2O3在1.51～100%范围内线性相关系数(R2)为0.9991,相对标准偏差(RSD)2.8%～10.6% (n=6),加标回收率87.1%~112.2%,检出限(LOD)2.56%;SiO2在0.79～29.72 %范围内线性相关系数(R2)为0.9957,相对标准偏差(RSD)3.2%～10.3% (n=6),加标回收率86.6%~98.9%,检出限(LOD)0.68%。方法易溯源、准确性易评价和验证,适合开展标准化检测和应用。     

Chloroacetate‐Promoted Selective Oxidation of Heterobenzylic Methylenes under Copper Catalysis

The efficient selective oxidation and functionalization of C? H bonds with molecular oxygen and a copper catalyst to prepare the corresponding ketones was achieved with ethyl chloroacetate as a promoter. In this transformation, various substituted N‐heterocyclic compounds were well tolerated. Preliminary mechanistic investigations indicated that organic radical species were involved in the overall process. The N‐heterocyclic compounds and ethyl chloroacetate work synergistically to activate C? H bonds in the methylene group, which results in the easy generation of free radical intermediates, thus leading to the corresponding ketones in good yields.     

煤矿顶板离层回归分析与稳定性评价

以光纤Bragg光栅位移传感器对淮北朱仙庄煤矿顶板离层监测为实际数据依据,选择最佳的典型函数模型对顶板离层进行非线性回归分析,得出能够反映位移发展趋势的回归曲线。监测结果与回归拟合数据表明:非线性回归分析预测方法不仅可以反映煤矿顶板离层实时变化过程,还能根据其变化趋势进行巷道稳定性判断。     

GROWTH OF MEROMORPHIC SOLUTIONS OF SOME ALGEBRAIC DIFFERENTIAL EQUATIONS

In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases.     

一道全国大学生数学竞赛决赛题的推广

解答一道全国大学生数学竞赛非数学类决赛试题,该试题涉及微分方程,定积分及一元函数求极限.针对以积分形式表示的函数求极限问题,将定义在[0,1]区间上特定的被积函数分别推广到单调连续函数、连续函数及[-1,1]区间上的连续函数这三种形式.利用夹逼准则、连续函数的定义及反常积分一致收敛的性质可证推广命题成立.     

Analysis of 2-D thin structures by the meshless regular hybrid boundary node method

Thin structures are generally solved by the Finite Element Method (FEM), using plate or shell finite elements which have many limitations in applications, such as numerical locking, edge effects, length scaling and the envergence problem. Recently, by proposing a new approach to treating the nearly-singular integrals, Liu et al. developed a BEM to successfully solve thin structures with the thickness-to-length ratios in the micro- or nano-scales. On the other hand, the meshless Regular Hybrid Boundary Node Method (RHBNM), which is proposed by the current authors and based on a modified functional and the Moving Least-Square (MLS) approximation, has very promising applications for engineering problems owing to its meshless nature and dimension-reduction advantage, and not involving any singular or nearly-singular integrals. Test examples show that the RHBNM can also be applied readily to thin structures with high accuracy without any modification.     

加注稀土元素铒改善轴承表面性能的研究

在Ｍｏ＾＋＋Ｎ＾＋注入模式的基础上，应用电子能谱、卢瑟福背散射谱、扫描电子显微镜和ＭＨＫ－５００型摩擦磨损试验机等研究了加注稀土元素铒正离子Ｅｒ＾＋对轴承表面摩擦学性能和耐蚀性能的影响。结果表明，在合理配置Ｍｏ＾＋、Ｎ＾＋、Ｅｒ＾＋之能量和剂量的情况下，加注Ｅｒ＾＋既能更好地改善轴承的表面性能，又能使重离子的强韧化效果提高２－４倍以上，表明ＭＯ＾＋＋Ｎ＾＋＋Ｅｒ＾＋注入模式是一种具有良好应用前景的     

超载下桩锚支护基坑安全系数的计算分析

假设桩锚支护下基坑土体塑性变形破坏机构以及满足边界条件的合理机 动场，而不是传统方法中那样将土体离散为许多相对运动的刚性块. 运用土塑性力学中 极限分析法的上限定理从能量功率角度探讨了超载下桩锚支护基坑竖直边坡安全系数的计算 方法. 并以一工程为例，用FLAC数值分析软件的模拟结果对该方法进行了验证.