A Mathematical Theory of the Topological Vertex

We have developed a mathematical theory of the topological vertex--a theory that was original proposed by M. Aganagic, A. Klemm, M. Marino, and C. Vafa in hep-th/0305132 on effectively computing Gromov-Witten invariants of smooth toric Calabi-Yau threefolds derived from duality between open string theory of smooth Calabi-Yau threefolds and Chern-Simons theory on three manifolds.Comment: 66 pages, 10 figures; notation simplified, references adde

Optimization Rotor Hole to Reduce Force in Cold Pressing Rotor into Crankshaft

Assembling rotor with crankshaft of a hermetic reciprocating compressor is, normally, heating of the rotor and then putting it into crankshaft. This assembly method allows larger magnitude of interference between rotor and crankshaft. Tolerance band of crankshaft could be relaxed and facilitate the process, however, the process requires heating equipment and higher energy consumption, obviously, this will increase the manufacturing cost of the compressor. In this situation, using cold pressing rotor into crankshaft can avoid the disadvantage mentioned above effectively, moreover, easily mount the rotor at the accurate location. Using of the original design of the rotor and crankshaft cold press will lead large force which may damage the crankshaft. This article presents an analysis about a geometric proposal for the rotor hole that guarantees to withstand sufficient torque, while cold press force is under the crankshaft yield strength

The Effects of Robots on the Long-Run Economic Growth

With the rapid development of artificial intelligence (AI) technology, the application of robots is widening and deepening. Due to the fact that robots are capable of machine learning and deep learning, we establish a theoretical model of the production process by considering the difference in learning ability between robots and labor forces, namely the difference in "learning by doing" ability. Based on this, the influence of robots on long-term economic growth is investigated. Our analytical results show that when the learning ability of robots is stronger than human capital, there will be no balanced growth path for the economy, and the economy will eventually show a sustained growth pattern, and the growth rate of capital per capita, output per capita and robot per capita will keep growing. However, more robots are not always better. There is an optimal robot investment ratio to maximize the long-term growth rate of output per capita. Managers should not only increase investments in robots. How to improve the learning ability of robots is also of great importance

2,3,4,6-Tetra-O-acetyl-1-O-(4-methoxy­cinnamo­yl)-β-d-glucopyran­ose

Mol­ecules of the title compound, C24H28O12, are linked by inter­molecular C—H⋯O hydrogen bonds. Bond lengths and angles are normal