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International Journal of Mathematics and Mathematical Sciences publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.
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More articlesPlanar Graphs without Cycles of Length 3, 4, and 6 are (3, 3)-Colorable
For non-negative integers and , if and are two partitions of a graph ’s vertex set , such that and induce two subgraphs of , called with maximum degree at most and with maximum degree at most , respectively, then the graph is said to be improper -colorable, as well as -colorable. A class of planar graphs without , and is denoted by . In 2019, Dross and Ochem proved that is -colorable, for each graph in . Given that , this inspires us to investigate whether is -colorable, for each graph in . In this paper, we provide a partial solution by showing that is (3, 3)-colorable, for each graph in .
Modeling the Impact of Air Pollution and Meteorological Variables on COVID-19 Transmission in Western Cape, South Africa
Understanding the factors that influence COVID-19 transmission is essential in assessing and mitigating the spread of the pandemic. This study focuses on modeling the impact of air pollution and meteorological parameters on the risk of COVID-19 transmission in Western Cape Province, South Africa. The data used in this study consist of air pollution parameters, meteorological variables, and COVID-19 incidence observed for 262 days from April 26, 2020, to January 12, 2021. Lagged data were prepared for modeling based on a 6-day incubation period for COVID-19 disease. Based on the overdispersion property of the incidence, negative binomial (NB) and generalised Poisson (GP) regression models were fitted. Stepwise regression was used to select the significant predictors in both models based on the Akaike information criterion (AIC). The residuals of both NB and GB regression models were autocorrelated. An autoregressive integrated moving average (ARIMA) model was fitted to the residuals of both models. ARIMA (7, 1, 5) was fitted to the residuals of the NB model while ARIMA (1, 1, 6) was fitted for the residuals of the GP model. NB + ARIMA (7, 1, 5) and GP + ARIMA (1, 1, 6) models were tested for performance using root mean square error (RSME). GP + ARIMA (1, 1, 6) was selected as the optimal model. The results from the optimal model suggest that minimum temperature, ambient relative humidity, ambient wind speed, , and at various lags are positively associated with COVID-19 incidence while maximum relative humidity, minimum relative humidity, solar radiation, maximum temperature, NO, PM load, , , and at various lags have a negative association with COVID-19 incidence. Ambient wind direction and temperature showed a nonsignificant association with COVID-19 at all lags. This study suggests that meteorological and pollution parameters play a vital independent role in the transmission of the SARS-CoV-2 virus.
Almost Existentially Closed Models in Positive Logic
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.
Analysis of COVID-19 Disease Model: Backward Bifurcation and Impact of Pharmaceutical and Nonpharmaceutical Interventions
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.
Numerical Solution of Two-Dimensional Nonlinear Unsteady Advection-Diffusion-Reaction Equations with Variable Coefficients
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.
Rings in Which Every Element Is a Sum of a Nilpotent and Three 7-Potents
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.