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Let r 1 , ... , r t be positive integers and let R 2 (r 1 , ... , r t) be the set of positive odd integers that can be represented as p + 2 k 1 r 1 + ⋯ + 2 k t r t , where p is a prime and k 1 , ... , k t are positive integers. It is easy to see that if r 1 − 1 + ⋯ + r t − 1 < 1 , then the set R 2 (r 1 , ... , r t) has asymptotic density zero. In this paper, we prove that if r 1 − 1 + ⋯ + r t − 1 ≥ 1 , then the set R 2 (r 1 , ... , r t) has a positive lower asymptotic density. Several conjectures and open problems are posed for further research. [ABSTRACT FROM AUTHOR]

It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch–Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology. [ABSTRACT FROM AUTHOR]

Abstract: Comparing with the studies on large estuarine systems, such as the Chesapeake Bay and the San Francisco Bay, the processes of stratification and transport in small and shallow estuaries are relatively less studied. The St. Lucie Estuary (SLE) is a riverine estuary located on the east coast of south Florida. It is small and shallow, with mean depth of 2.4m. To study the estuarine processes in the SLE, a hydrodynamic model was developed based on the Environmental Fluid Dynamics Code (EFDC) [Hamrick, J.M., 1992. A three-dimensional environmental fluid dynamics computer code: theoretical and computational aspects. The College of William and Mary, Virginia Institute of Marine Science, Special Report 317, 63 pp.]. The model was calibrated and verified using observational data obtained in 1999 and 2000, respectively. The model variables used for model data-comparisons are water elevation, velocity, temperature, and salinity. The model is then applied to study the hydrodynamic processes in the SLE. It is found that freshwater inflow plays a major role in the stratification and net flushing of the SLE. Stratification generally increases with freshwater inflow. But when the inflow is persistently large for a relatively long period, the estuary can suddenly change from very stratified to well mixed within a few tidal cycles and the stratification collapses. This finding suggests that large and persistent freshwater inflows do not always increase estuarine stratification. Instead, it may cause the stratification to collapse within a short period of time. In addition to gauged tributaries, ungauged lateral inflows can also be important to small and shallow estuaries like the SLE. Although small individually, the ungauged streams and surface runoffs can be a significant portion of the total inflow and affect salinity distribution significantly. Flushing time affects a wide range of hydrodynamic and water quality processes in the estuary. The model results indicate that commonly used formulas, such as the tidal prism formula and the Knudsen formula, may significantly underestimate the flushing time. [Copyright &y& Elsevier]

Hainan Province is in a tropical area of China and previously experienced serious P. falciparum and P. vivax malaria epidemics. After nearly 70 consecutive years of malaria prevention and control, malaria in Hainan has gradually been eliminated. To achieve the elimination of malaria, Hainan enacted six stages: investigative research and pilot prevention and control, large-scale antimalaria measures, adjustment of strategies for prevention and control, joint prevention and control measures, global funding of routine malaria control, and malaria elimination. Different strategies for malaria control were adopted at different stages. Malaria was most prevalent in the mountainous areas of central and southern Hainan, which contain a high-risk population (the forest goers) and two highly effective malaria vectors (An. dirus and An. minimus). Forest goers have been a high-risk population for malaria in Hainan since their identification in the 1990s. This paper summarizes malaria monitoring in forest goers and the response of forest goers to malaria control and elimination, distilling specific malaria control and elimination measures via case studies in Hainan Province. Two case studies in the malaria control stage demonstrated different measures for outbreaks and sporadic cases in forest goers. In view of the malaria outbreak in Sanya during the elimination stage, three-layered strategies (TLSs) were implemented to control outbreaks and improve control measures. Moreover, this paper also illustrates specific management measures to prevent malaria retransmission from sporadic imported malaria cases during the elimination phase. Hainan finally eliminated malaria in 2020. However, the risk of malaria retransmission is still high due to the prevalence of effective malaria vectors in Hainan, and forest goers are still a high-risk population for malaria retransmission. [ABSTRACT FROM AUTHOR]

Highlights: [•] Cholesterosis is a metabolic disease characterized by excessive lipid droplets. [•] Lipid droplet efflux is mediated by the ABCA1 transporter. [•] 22(R)-hydroxycholesterol can activate LXRα and up-regulate ABCA1. [•] Pioglitazone up-regulates ABCA1 in a PPARγ–LXRα–ABCA1-dependent manner. [•] 22(R)-hydroxycholesterol and pioglitazone synergistically decrease lipid droplets. [Copyright &y& Elsevier]