Companion stars of Type Ia supernovae and hypervelocity stars

{Context} Recent investigations of the white dwarf (WD) + He star channel of Type Ia supernovae (SNe Ia) imply that this channel can produce SNe Ia with short delay times. The companion stars in this channel would survive and be potentially identifiable. {Aims} In this Letter, we study the properties of the companion stars of this channel at the moment of SN explosion, which can be verified by future observations. {Methods} According to SN Ia production regions of the WD + He star channel and three formation channels of WD + He star systems, we performed a detailed binary population synthesis study to obtain the properties of the surviving companions. {Results} We obtained the distributions of many properties of the companion stars of this channel at the moment of SN explosion. We find that the surviving companion stars have a high spatial velocity (>400 km/s) after SN explosion, which could be an alternative origin for hypervelocity stars (HVSs), especially for HVSs such as US 708.Comment: 4 pages, 5 figures, accepted for publication in A&A Letter

A note on modular forms and generalized anomaly cancellation formulas

By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formula

Energy-Efficient Resource Allocation for Device-to-Device Underlay Communication

Device-to-device (D2D) communication underlaying cellular networks is expected to bring significant benefits for utilizing resources, improving user throughput and extending battery life of user equipments. However, the allocation of radio and power resources to D2D communication needs elaborate coordination, as D2D communication can cause interference to cellular communication. In this paper, we study joint channel and power allocation to improve the energy efficiency of user equipments. To solve the problem efficiently, we introduce an iterative combinatorial auction algorithm, where the D2D users are considered as bidders that compete for channel resources, and the cellular network is treated as the auctioneer. We also analyze important properties of D2D underlay communication, and present numerical simulations to verify the proposed algorithm.Comment: IEEE Transactions on Wireless Communication