The index of Callias-type operators with Atiyah–Patodi–Singer boundary conditions

We compute the index of a Callias-type operator with APS boundary condition on a manifold with compact boundary in terms of combination of indexes of induced operators on a compact hypersurface. Our result generalizes the classical Callias-type index theorem to manifolds with compact boundary.     

基于单一量子级联激光器的大气多组分气体(CO、N2O、H2O)同时测量方法

针对海藻三维荧光光谱线性降维方法不理想、模型识别准确率低的问题,提出通过局部线性嵌入(LLE)算法进行降维、通过黄金正弦算法(Gold-SA)对支持向量机(SVM)进行优化来构建分类模型的方法。将LLE算法降维后的海藻三维荧光光谱数据作为SVM的输入,并与其他两种降维方法进行对比。结果显示：LLE算法的降维效果最好,识别准确率最高。为了进一步提高门类识别能力,采用Gold-SA对SVM进行优化并建立Gold-SA-SVM模型,再将其与其他4种分类模型进行对比。结果显示,Gold-SA-SVM模型在分类识别准确率、精准率、召回率和F1分数上都有明显提高,该方法可准确识别抑食金球藻、小球藻、细长聚球藻的门类,可为褐潮研究工作提供有效的参考。     

色胺酮衍生物无金属催化的高效合成及抗菌活性研究

以取代靛红酸酐为起始原料,二甲基亚砜（DMSO）为反应溶剂,在三乙烯二胺（DABCO）的作用下加热至80 ℃,与取代靛红经形式上的（4+2）环化反应以81%～94%的收率合成了一系列色胺酮衍生物,化合物结构经¹H NMR, ¹³C NMR和HR-MS（ESI-TOF）表征。该制备方法不仅避免了反应过程中金属的使用,而且后处理简单、无需柱层析,在减小对环境影响的同时提升了合成效率。在此基础上,通过最小抑菌浓度（MIC）试验初步揭示了化合物3g良好的体外抗菌活性（<4 μg·mL^-1）。     

Solubility and Mixing Thermodynamic Properties of Capecitabine in Five Acetic Acid Esters at Various Temperatures

Russian Journal of Physical Chemistry A - In pharmaceutical industry, capecitabine is often purified by crystallization from acetic esters. In this work, by using laser dynamic isothermal method,...     

Cobordism invariance of the index of Callias-type operators

We introduce a notion of cobordism of Callias-type operators overcomplete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application, we prove a gluing formula for Callias-type index. In particular, a usual index of an elliptic operator on a compact manifold can be computed as a sum of indexes of Callias-type operators on two noncompact but topologically simpler manifolds. As another application, we give a new proof of the relative index theorem for Callias-type operators, which also leads to a new proof of the Callias index theorem.