International Journal of Mathematics and Mathematical Sciences

This paper explores the concept of almost positively closed models in the framework of positive logic. To accomplish this, we initially define various forms of the positive amalgamation property, such as h-amalgamation and symmetric and asymmetric amalgamation properties. Subsequently, we introduce certain structures that enjoy these properties. Following this, we introduce the concepts of -almost positively closed and -weekly almost positively closed. The classes of these structures contain and exhibit properties that closely resemble those of positive existentially closed models. In order to investigate the relationship between positive almost closed and positive strong amalgamation properties, we first introduce the sets of positive algebraic formulas and and the properties of positive strong amalgamation. We then show that if a model of a theory is a -weekly almost positively closed, then is a positive strong amalgamation basis of , and if is a positive strong amalgamation basis of , then is -weekly almost positively closed.

The SEIQHR model, introduced in this study, serves as a valuable tool for anticipating the emergence of various infectious diseases, such as COVID-19 and illnesses transmitted by insects. An analysis of the model’s qualitative features was conducted, encompassing the computation of the fundamental reproduction number, . It was observed that the disease-free equilibrium point remains singular and locally asymptotically stable when , while the endemic equilibrium point exhibits uniqueness when . Additionally, specific conditions were outlined to guarantee the local asymptotic stability of both equilibrium points. Employing numerical simulations, the graphical representation illustrated the influence of model parameters on disease dynamics and the potential for its eradication across different noninteger orders of the Caputo derivative. In essence, the adoption of a fractional epidemic model contributes to a deeper comprehension and enhanced biological insights into the dynamics of diseases.

The advection-diffusion-reaction (ADR) equation is a fundamental mathematical model used to describe various processes in many different areas of science and engineering. Due to wide applicability of the ADR equation, finding accurate solution is very important to better understand a physical phenomenon represented by the equation. In this study, a numerical scheme for solving two-dimensional unsteady ADR equations with spatially varying velocity and diffusion coefficients is presented. The equations include nonlinear reaction terms. To discretize the ADR equations, the Crank–Nicolson finite difference method is employed with a uniform grid. The resulting nonlinear system of equations is solved using Newton’s method. At each iteration of Newton’s method, the Gauss–Seidel iterative method with sparse matrix computation is utilized to solve the block tridiagonal system and obtain the error correction vector. The consistency and stability of the numerical scheme are investigated. MATLAB codes are developed to implement this combined numerical approach. The validation of the scheme is verified by solving a two-dimensional advection-diffusion equation without reaction term. Numerical tests are provided to show the good performances of the proposed numerical scheme in simulation of ADR problems. The numerical scheme gives accurate results. The obtained numerical solutions are presented graphically. The result of this study may provide insights to apply numerical methods in solving comprehensive models of physical phenomena that capture the underlying situations.

In this article, we define and discuss strongly nil-clean rings: every element in a ring is the sum of a nilpotent and three 7-potents that commute with each other. We use the properties of nilpotent and 7-potent to conduct in-depth research and a large number of calculations and obtain a nilpotent formula for the constant . Furthermore, we prove that a ring is a strongly nil-clean ring if and only if , where , , , , , and are strongly nil-clean rings with , , , , , and . The equivalent conditions of strongly nil-clean rings in some cases are discussed.

The main objective of this paper is to analyse investment returns using a stochastic model and inform investors about the best stock market to invest in. To this effect, a Markov chain random walk model was successfully developed and implemented on 450 monthly market returns data spanning from January 1976 to December 2020 for Canada, India, Mexico, South Africa, and Switzerland obtained from the Federal Reserves of the Bank of St. Louis. The limiting state probabilities and six-month moving crush probabilities were estimated for each country, and these were used to assess the performance of the markets. The Mexican market was observed to have the least probabilities for all the negative states, while the Indian market recorded the largest limiting probabilities. In the case of positive states, the Mexican market recorded the highest limiting probabilities, while the Indian market recorded the lowest limiting probabilities. The results showed that the Mexican market performed better than the others over the study period, whilst India performed poorly. These findings provide crucial information for market regulators and investors in setting regulations and decision-making in investment.

In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.