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A one-dimensional Bose Hubbard model with unidirectional hopping is shown to be exactly solvable. Applying the algebraic Bethe ansatz method, we prove the integrability of the model and derive the Bethe ansatz equations. The exact eigenvalue spectrum can be obtained by solving these equations. The distribution of Bethe roots reveals the presence of a superfluid-Mott insulator transition at the ground state, and the critical point is determined. By adjusting the boundary parameter, we demonstrate the existence of non-Hermitian skin effect even in the presence of interaction, but it is completely suppressed for the Mott insulator state. Our result represents a new class of exactly solvable non-Hermitian many-body systems, which have no Hermitian correspondence and can be used as a benchmark for various numerical techniques developed for non-Hermitian many-body systems., 6+3 pages, 2+2 figures

The selection of optimal relay node ever remains a stern challenge for underwater routing. Due to a rigid and uncouth underwater environment, the acoustic channel faces inevitable masses that tarnish the transmission cycle. None of the protocols can cover all routing issues; therefore, designing underwater routing protocol demands a cognitive coverage that cannot be accomplished without meticulous research. An angle-based shrewd technique is being adopted to improve the data packet delivery, as well as revitalize the network lifespan. From source to destination, one complete cycle comprises three phases indeed; in the first phase, the eligibility of data packet belonging to the same transmission zone is litigated by Forwarder Hop Angle (FHA) and Counterpart Hop Angle (CHA). If FHA value is equal or greater than CHA, it presages that the generated packet belongs to the same transmission zone; otherwise, it portends that packet is maverick from other sectors. The second phase picks out the best relay node by computing a three-state link quality with prefix values using the Additive-Rise and Additive-Fall method. Finally, the third phase renders a decisive solution regarding exorbitant overhead fistula; a packet holding time is contemplated to prevent the packet loss probability. Simulation results using NS2 have been analyzed, regarding packet delivery ratio, packet error rate, communication overhead, and end-to-end delay. Comparing to HHVBF and GEDAR, USPF indeed has outperformed, leading into the evidence of applicability’s favor.