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In this study, we constructed color singlet-singlet-type five-quark currents with isospins (I,I3)=(12,12)and (32,12)unambiguously to explore the D¯∑c,D¯∑c∗,D¯∗∑c, and D¯∗∑c∗pentaquark states via the quantum chromodynamics sum rules for the first time, where D¯,∑c,⋯, represent the color singlet clusters with the same quantum numbers as the corresponding physical mesons or baryons. The numerical results support assigning Pc(4312), Pc(4380), Pc(4440), and Pc(4457) as the D¯∑c, D¯∑c∗, D¯∗∑c, and D¯∗∑c∗pentaquark states, respectively, with the isospin I=12. The corresponding D¯∑c, D¯∑c∗, D¯∗∑c, and D¯∗∑c∗pentaquark states with the isospin I=32have slightly larger masses. The observations of the high pentaquark candidates in the J/ψ∆ invariant mass spectrum would shed light on the nature of the Pcstates and contribute in distinguishing the scenarios of the color antitriplet-antitriplet-antitriplet-type and color singlet-singlet-type pentaquark states.

The real-time and accurate analysis of water column height becomes the crucial step for measures of unloading flow is taken effectively to make sure gas well to work continuously and properly. Although the early researchers made a number of models used to calculate water column height, but they are the static calculation method and can not meet production requirements. This paper analyses the hydraulics of well-bore load-up for gas well, and present a computing method of transient water column height. This model based on node pressure analysis, and combined with pressure gradient formula of multiphase pipe flow and productivity equation of gas-water wells. Application of this technology allows real-time analysis to be used in production process, which is valuable in protection of gas reservoir and enhancement of ultimate recovery.