Cluster transformations, the tetrahedron equation and three-dimensional gauge theories

We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three trivial cluster transformations with 8, 32 and 32 mutations. For each of these cluster transformations, a unitary operator representing a single braid move in a quantum mechanical system solves the tetrahedron equation. The solutions thus obtained are constructed from the noncompact quantum dilogarithm and can be identified with the partition functions of three-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories on a squashed three-sphere.Comment: 29 page

New Boundary Element Method For Analysis Of Surface Subsidence Due To Coal Mining

Rock and coal in coal bearing formation belong to layered sedimentary rocks. Their large-scale subsidence may occur because of coal mining. Thus, it is one of research highlights to develop an analytical tool suitable for these layered rocks. This paper presents a new Boundary Element Method(BEM) for analysis of the surface subsidence due to coal mining. The BEM uses the fundamental solution of layered materials,4-8 noded elements to discretize the boundaries, and effective numerical methods to calculate the singular integrals. An example with exact solutions is used to verify the numerical method. Finally, the numerical method is used to analyze in situ surface subsidence due to coal mining. The result shows that the proposed BEM can analyze the surface subsidence due to coal mining with high efficiency and good accuracy. 煤系地層為成層分布的沉積巖,煤層的開采會引起地表大規模的沉陷,發展適應此類介質的分析方法一直是本領域的研究熱點。本文發展了一種新型的邊界元方法來分析煤層開采引起的地表移動。該邊界元方法基于層狀材料基本解,采用4~8變結點單元離散邊界,并采用有效的數值方法計算各類奇異積分。然后,用有解析解的算例驗證建議數值方法。最后,采用新型邊界元方法分析煤層開采引起的地表移動。本文所建議的方法在分析煤層開采引起的地表沉陷時具有較高的計算精度和效率

The Clinical Efficacy of Yindanxinnaotong Soft Capsule in the Treatment of Stroke and Angina Pectoris: A Meta-Analysis

Objective. To systematically evaluate the clinical efficacy of Yindanxinnaotong (YD) soft capsule in adult patients with cardiovascular diseases (stroke and angina pectoris). Methods. We electronically searched databases including Medline, PubMed, Chinese National Knowledge Infrastructure (CNKI), Cqvip Database (VIP), and Wanfang Database for published articles of randomized controlled trials (RCTs) of YD capsule in treating stroke and angina pectoris. The meta-analysis was performed using RevMan 5.3 software. Results. 49 RCTs involving 6195 subjects with cardiovascular diseases (angina pectoris and stroke) were included. Compared with western conventional medicine (WCM) and/or other Chinese medicines, YD plus WCM therapeutic regimen could significantly improve the efficacy rate (RR = 1.21, 95% CI (1.17, 1.25), P<0.00001 for angina pectoris, RR = 1.24, 95% CI (1.18, 1.31), P<0.00001 for stroke), showing the clinical value. In addition, the therapeutic efficiency of WCM plus YD capsule regimen is better than that of WCM alone in improving CRP (MD = −2.07, 95% CI (−3.97, −0.17), P=0.03 <0.05) and TG (MD = −0.37, 95% CI (−0.52, −0.23), P<0.0001). Conclusion. YD is effective in the treatment of cardiovascular diseases (angina pectoris and stroke) in adults, and WCM plus YD therapeutic regimen can significantly improve the effective rate in the clinic