In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio

Abstract The study aims to clarify the value of auditing economic units and how it can be measured, which is one of the most important challenges to matching the Value Relevance of Accounting Information. The problem of the study was identified with questions that revolve around the extent to which it is possible to measure the value of auditing in Iraqi economic units and the extent to which the value of auditing affects the adequacy of accounting information. Through reviewing the studies discussing this topic, it was found that auditing can provide value through the performance of the auditor and adding value to the economic unit subject to audit. The study recommended the need to study the situational factors of auditing, whether exter

The research aims to know the impact of science, technology, engineering, and mathematics education on both creative thinking and mathematical achievement. To achieve it, the two researchers followed the quasi-experimental approach with an experimental design for two groups, one experimental and the other a control. The research sample consisted of (32) female students from the fourth scientific grade in Al-Intisar Preparatory School for Girls/ AlRasafa, First Directorate. The sample was chosen intentionally and was divided into two groups: a control group studying by the traditional method, their number (16), and an experimental group that applied the STEM approach, their number also (16). There was parity between the two research groups i

This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

Hard water does not pose a threat to human health but may cause precipitation of soap or results stone in the boilers. These reactions are caused by the high concentrations of Ca and Mg. In the industry they are undesirable because of higher fuel consumption for industrial use .Electromagnetic polarization water treatment is a method which can be used for increasing the precipitation of Ca ²⁺ and CO₃ ^2- ions in hard water to form CaCO₃ which leads to decrease the water hardness is research has been conducted by changing the number of coil turns and voltage of the system. The spectroscopy electron microscope was used for imaging the produced crystals. Results of the investigation indicated that

The aerodynamic characteristics of general three-dimensional rectangular wings are considered using non-linear interaction between two-dimensional viscous-inviscid panel method and vortex ring method. The potential flow of a two-dimensional airfoil by the pioneering Hess & Smith method was used with viscous laminar, transition and turbulent boundary layer to solve flow about complex configuration of airfoils including stalling effect. Viterna method was used to extend the aerodynamic characteristics of the specified airfoil to high angles of attacks. A modified vortex ring method was used to find the circulation values along span wise direction of the wing and then interacted with sectional circulation obtained by Kutta-Joukowsky theorem of

In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection. This study intro- duces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least abso- lute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD). These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to en- sure sparse and interpretable models. The performance of both methods is evaluated through simulations using the mean squared error and variable selection cri