Pure Mathematics for Theoretical Computer Science

and Fuzzy Generalized Double Hurdle (FGPDH)—to estimate and predict patient outcomes. We used the Firefly Algorithm to optimize and estimate the parameters for these models. Among them, the FGPDH model consistently provided the most accurate predictions, closely matching the actual values. The Generalized Double Hurdle model also performed well, significantly improving accuracy by capturing the complexity of the data. In contrast, models like Poisson, Single Hurdle, and Double Hurdle Poisson showed less predictive accuracy due to higher error rates. Our proposed FGPDH model, enhanced with the Firefly Algorithm, effectively handles uncertainty and complexity, making it the most reliable and precise approach in this context.

This study introduces a precise numerical technique employing exponential splines for singly perturbed singularity boundary values problems. A numerical scheme is devised to address issues encountered in diverse scientific and engineering domains. The framework consists of a triad of nonlinear equations. The approach is employed in several test cases to demonstrate accuracy and implementation.

This paper provides a method to solve the discrete time Lyapunov equation. Identified and discussed. If the equation takes the following form: D (λy+μz) = λDy+ μDz , 𝑦,z∈ y; λ ,μ ∈𝐹 . If ∃ a constant e∈∞ ∋ ||Dy|| ≤ e ||y||, y ∀Y. and D is bounded, then D is called a linear operator equation. In particular, (Lyapunov and Sylvester operator equations) are very important in differential equations, integral equations and many other branches of mathematics. The study of solutions and of the above equestion We also discussed operator equations and special kinds of operators and studied some elementary operators. These operators are generalizations of operators τ𝐴𝐷:𝐷(𝐻)→𝐷(𝐻) τ𝐴𝐷:𝜏𝐴𝐷(𝑦)=𝐴𝑦−𝑦𝐷, 𝑦∈𝐷(𝐻)

In this article, the ZeroInflated Poisson Regression model (ZI-PRM) was used to predict the number of tuberculosis patients by estimating the model using the maximum likelihood method and compared with Poisson regression model (PRM). The results showed that the ZIPRM best represented TB data from PRM. The PRM showed that the importance of some variables, although they were not significant as a cause of the TB data. The ZIP model indicates that there will be more TB cases in 2027 than there were in 2023. These findings point to an improvement in the nation's health status.

In this paper, a new two-parameter estimator was proposed to estimate the parameters of the linear regression model that has the ability to face the problem of Multicollinearity based on the previous information about the parameters to be estimated and this estimator was compared with the two-parameter estimator of the linear regression model of Kaciranlar and the two-parameter estimator of the linear regression model (Lokman et al. [1]) using the mean square error criterion (MSE) for each model by conducting Monte-Carlo simulation to study the behavior of the proposed estimator. It was concluded that the proposed method is better than the rest of the estimation methods because it achieved the lowest comparison criteria, and in the case of high Multicollinearity between the explanatory variables, the proposed method was very effective in solving this problem. Data representing (100) observations of the number of women with Irritable Bowel Syndrome (IBS) for the years (2020-2023) from the Karbala Holy Health Department were used, which represents the dependent variable (y) and a group of variables affecting the incidence of the disease, with nineteen variables. It was concluded that irritable bowel syndrome among women is decreasing, as the predictive values ​​according to the proposed method are appropriate for the estimated values ​​during the next five years.