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The coexistence of reconfigurable intelligent surface (RIS) and dual-functional radar-communication base station (DFBS) in the same system has attracted increasing discussions. In this paper, we focus on a RIS-assisted target sensing and multi-user communications system. To improve the radar performance, we formulate a radar detection signal-to-noise ratio (SNR) maximization problem, by jointly considering the transmit beamforming and RIS phase vector design, while meeting predefined communication quality-of-service, transmit power budget, and phase-shift constraints. Since the variables are deeply coupled, we first utilize the penalty based method to decouple them. Then, we employ the block coordinate descent (BCD) method to split the problem into three sub-problems, and resort to semidefinite relaxation (SDR) and second order cone programming (SOCP) methods to solve subproblems. Finally, we …