This article aims to explain the principles of the leadership styles of madrasah heads in enhancing the quality of Islamic education in Lhokseumawe City. It turns out that the leadership of madrasah heads has a significant impact on the functioning of the madrasah leadership. The madrasah head plays a direct role in developing Islamic educational institutions through leadership characteristics, leader types, leader functions, and leader activities during their tenure as madrasah heads. A quantitative research method with a phenomenological approach is considered capable of addressing various issues in the research problem formulation. It simultaneously analyzes data obtained from observations, interviews, and in-depth documentation to find answers to the research problem. The research findings reveal that the leadership styles of madrasah heads can be divided into two categories: democratic leadership style and autocratic leadership style. The first principle of leadership style involves giving responsibilities and authority to all parties, encouraging active involvement in the organization. Members are given opportunities to provide suggestions, recommendations, and criticisms for the progress of the organization. The second principle, the autocratic leadership style, positions a leader as the source of policies.

Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.

In this study, we define the unrestricted Pell and Pell-Lucas quaternions. We give generating functions, Binet formulas and some generalizations of well-known identities such as Vajda’s, Catalan’s, Cassini’s d’Ocagne’s identities.

Lianghuai Mining Area is one of the 13 large coal bases in China. It is an important coal and coal production base in China. Mine water inrush accidents occur frequently, resulting in economic and human resource losses, reflecting the importance of the study of hydrogeology in mining areas. In this paper, the hydrogeological conditions of Bozhou and Huainan Panxie mine are analyzed, and the similarities and differences between the hydrogeological conditions of the two mines are summarized. The shallow pore water group in the Bozhou area is composed of the Quaternary system of the Quaternary system (Q4d) and the upper part of the upper part of the Mao Tong group (Q3m). The lithology of the aquifer is silt, silt and fine sand. The shallow pore water group of the Panxian Pancho Formation in Huainan is composed of the Upper Pleistocene of the Quaternary system and the Holocene strata. The lithology is mainly composed of fine sand. The main sources of shallow pore water supply in the two areas are precipitation infiltration, mainly for evaporation, lateral runoff, artificial mining and deep flow and discharge to the river.