The governing equations of three dimensional elasticity problems include the six Beltrami– Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usually used to achieve a solution. Stress-based formulation methods, and displacement-based formulation methods are two common simplified methods for solving elasticity problems. This work adopts a stress-based formulation for a three dimensional elasticity problem. In this work, the Maxwell’ s stress functions for solving three dimensional problems of elasticity theory are derived from fundamental principles. It is shown that the three Maxwell stress functions identically satisfy all the three differential equations of static equilibrium when body force components are ignored. It is further shown that the three Maxwell stress functions are solutions to the six Beltrami-Michell stress compatibility equations if the Maxwell stress functions are potential functions. It is also shown that the Airy’ s stress functions for two dimensional elasticity problems are special cases of the Maxwell stress functions.

The Maxwell-Dagum distribution is a continuous statistical distribution suitable for modeling data sets relating to various fields including finance, business, medical sciences, survival analysis, and related areas. This article aimed to propose some important properties of the Maxwell-Dagum distribution and obtained the parameters of its estimates by using different methods of estimation including maximum likelihood estimation, the maximum product of spacings, least squares estimation, and weighted least squares estimation. The first and second derivatives of this distribution are studied. We present two real data sets relating to the COVID-19 mortality rate belonging to Canada and the waiting time of bank customers to assess the performance of the proposed distribution. It is discovered that the Maxwell-Dagum distribution can be chosen as the best distribution by having a minimum value of Akaike information and Bayesian information criteria.

To consider the cosmic magnetic effects on the rate of cosmic inflation, instead of unknown dark sector of matter/energy, some authors presented non-minimally coupled exotic Einstein-Maxwell (EM) gravity theories which we address in this work. We  use one of these models and add Dirac action functional interacting with gauge Maxwell field to the exotic EM gravity and then investigate the formation and stability of a relativistic fermion star by using the dynamical system approach. Mathematical calculations predict important role of frequencies of the Dirac waves in formation of the Dirac star and whose critical energy density. Dirac star is a particular kind of fermionic relativistic star which has spherically symmetric static metric field. In this context, the directional interaction parameter between the gravity, and the electromagnetic fields play more important role, particularly in size of the star. Large values of that parameter  makes larger Dirac star.  Furthermore, we apply the dynamical system approach to find stabilization conditions of the Dirac star. These conditions are linked to specific values of the total angular momentum quantum numbers (including both spin and orbital contributions).

In this paper, the investigation is carried out to study the structural responses of two adjacent structures connected with Maxwell dampers under various earthquake excitations. The specific objective of this study is to evaluate the optimum damper parameter and its importance in response reduction of adjacent structures coupled by Maxwell dampers. The optimum damper parameter is investigated for the adjacent coupled structures subjected to four different types of earthquake ground motions. A formulation of the equations of motion for the two adjacent multi-degree-of-freedom (MDOF) structures connected with Maxwell dampers is presented. The numerical study is carried out for two adjacent MDOF structures connected with Maxwell dampers having same damper parameter in all dampers as well as, having different damper parameter in the dampers. The investigation is also carried out for effectiveness of the damper in terms of the structural response reduction, namely, displacement, acceleration and shear forces of adjacent connected structures. In addition, to minimize the cost of the dampers, the optimal location of the dampers, rather than providing the dampers at all floor levels is also investigated. Results show that using Maxwell dampers of appropriate parameter to connect the adjacent structures of different fundamental frequencies can effectively reduce earthquake-induced responses of either structure. Further, lesser dampers at appropriate locations can significantly reduce the earthquake response of connected system, thereby reducing cost of damper significantly.