The dominance of prolate over oblate ground-state deformations has been a well-known empirical fact. With the state-of-the-art deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) and taking Te, Xe, and Ba isotopes with neutron number $82⩽N⩽126$ as examples, a self-consistent and microscopic study of the prolate-shape dominance is given. According to the calculated potential-energy curves, most of these isotopes have both prolate and oblate minima and prefer prolate in the ground state, while the small amount of oblate ground-state shapes mainly appear after the major shell is half filled. It is also found that the prolate-shape dominance enhances with the proton number increasing from 52 to 56. The dominance and its enhancement can be well understood by the microscopic canonical single-particle energies obtained in the DRHBc theory, in good agreement with the schematic interpretation based on the Nilsson diagram. Finally, pairing correlations are found to bring more energy displacements to oblate minima on average but do not play a decisive role in prolate-shape dominance.

The deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) has garnered significant attention for its ability to describe the properties of nuclei across the entire nuclear chart, from light to heavy nuclei, including both stable and exotic ones. As part of ongoing efforts to construct a mass table using the DRHBc theory, determining the ground states of nuclei is a crucial task in the systematic studies of deformed nuclei. In this work, a strategy for identifying the ground state in the superheavy nuclei region is proposed and evaluated, by taking $Z=134$ and 135 isotopes as examples. First, we examine how the step size of the initial quadrupole deformation parameter, $\Delta {\beta }_2$, affects the pattern of the potential energy curves (PECs) and the determination of the ground state. Our findings indicate that $\Delta {\beta }_2=0.05$ producing smooth and well-defined PECs while maintaining an acceptable numerical cost. Next, we explore the convergence of PECs with respect to the angular momentum cutoff, $J_{\max }$. Based on the results, we recommend using $J_{\max }=31/2\hslash$, especially for nuclei with competing oblate and prolate minima. Finally, we conclude that the accurate identification of the ground state can be achieved by performing unconstrained calculations around the minima of the PECs.

The impact of the Lipkin–Nogami (LN) method on a giant halo is investigated within the relativistic continuum Hartree–Bogoliubov (RCHB) theory. The ground-state properties of Ca isotopes obtained from RCHB and RCHB+LN calculations are presented. The results show that the LN correction does not change the range of Ca isotopes with a giant halo. Taking ⁶⁶Ca as an example, the neutron density distribution with LN correction is found to be slightly more diffused, which can be illustrated by the enlargement of the root mean square radius and the enhancement of the relative contribution in neutron $3s_{1/2}$ level.

The investigation of magic numbers for nuclei in the hyperheavy region $(Z>120)$ is an interesting topic. The neutron magic number $N=350$ is carefully validated by the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), via analysing even-even nuclei around $N=350$ of the $Z=136$ isotopes in detail. Nuclei with $Z=136$ and $340\le N\le 360$ are all found to be spherical in their ground states. A big drop of the two-neutron separation energy $S_{2n}$ is observed from $N=350$ to $N=352$ in the isotopic chain of $Z=136$, and a peak of the two-neutron gap ${\delta }_{2n}$ appears at $N=350$. There exists a big shell gap above $N=350$ around the spherical regions of single-neutron levels for nucleus with $(Z=136,N=350)$. These evidences from the DRHBc theory support $N=350$ to be a neutron magic number in the hyperheavy region.

At present, water pollution has become an important factor affecting and restricting national and regional economic development. Total phosphorus is one of the main sources of water pollution and eutrophication, so the prediction of total phosphorus in water quality has good research significance. This paper selects the total phosphorus and turbidity data for analysis by crawling the data of the water quality monitoring platform. By constructing the attribute object mapping relationship, the correlation between the two indicators was analyzed and used to predict the future data. Firstly, the monthly mean and daily mean concentrations of total phosphorus and turbidity outliers were calculated after cleaning, and the correlation between them was analyzed. Secondly, the correlation coefficients of different times and frequencies were used to predict the values for the next five days, and the data trend was predicted by python visualization. Finally, the real value was compared with the predicted value data, and the results showed that the correlation between total phosphorus and turbidity was useful in predicting the water quality.