The deformation characters and load status of the blank＇s potential fracture zone are analyzed at the moment when blank is approaching to punch comer in drawing process of cone shape part. Based on tension instabilit...The deformation characters and load status of the blank＇s potential fracture zone are analyzed at the moment when blank is approaching to punch comer in drawing process of cone shape part. Based on tension instability theory, the formula for calculating fracture limit load of cone shape part in drawing process is derived. Also, the formula is analyzed and verified by experiment.展开更多
Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under t...Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.展开更多
基金This project is supported by Doctoral Education Foundation of Ministry ofEducation of China (No.96021602).
文摘The deformation characters and load status of the blank＇s potential fracture zone are analyzed at the moment when blank is approaching to punch comer in drawing process of cone shape part. Based on tension instability theory, the formula for calculating fracture limit load of cone shape part in drawing process is derived. Also, the formula is analyzed and verified by experiment.
基金Supported by the National Natural Science Foundation of China(No.10671176)
文摘Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.
