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.

Mathematical integration techniques rely on mathematical relationships such as addition, subtraction, division, and subtraction to merge images with different resolutions to achieve the best effect of the merger. In this study, a simulation is adopted to correct the geometric and radiometric distortion of satellite images based on mathematical integration techniques, including Brovey Transform (BT), Color Normalization Transform (CNT), and Multiplicative Model (MM). Also, interpolation methods, namely the nearest neighborhood, Bi-linear, and Bi-cubic were adapted to the images captured by an optical camera. The evaluation of images resulting from the integration process was performed using several types of measures; the first type depend

     Transformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He’s Polynomials is provided as the transformation plays an essential role in solving differential linear and non-linear equations. Here is the α-Sumudu technique to find the relevant results of the gas dynamics equation in fractional order. To calculate the non-linear fractional gas dynamical problem, a consumer method created on the new homotopy perturbation a-Sumudu transformation method (HP TM) is suggested. In the Caputo type, the derivative is evaluated. a-Sumudu homotopy pe

Enhanced Thematic Mapper Plus (ETM+) onboard the Landsat-7 remotely sensor satellite was launched on 15 April 1999. On May 31, 2003, image acquisition via the ETM+ was greatly impacted by the failure of the system’s Scan Line Corrector (SLC). Consequently, the ETM+ has lost approximately 22% of the data due to the increased scan gap. In this work, several gap-filling methods will be proposed to restore the ETM+ image malfunctions. Some of the proposed methods will be carried by estimating the missed pixel’s values from the same image pixel’s neighborhood, while others will utilize the pixel values extracted from different temporal scene acquired in different time. Mean average filter, median filter, midpoint filter, and several int

In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

This paper demonstrates a new technique based on a combined form of the new transform method with homotopy perturbation method to find the suitable accurate solution of autonomous Equations with initial condition.  This technique is called the transform homotopy perturbation method (THPM). It can be used to solve the problems without resorting to the frequency domain.The implementation of the suggested method demonstrates the usefulness in finding exact solution for linear and nonlinear problems. The practical results show the efficiency and reliability of technique and easier implemented than HPM in finding exact solutions.Finally, all algorithms in this paper implemented in MATLAB version 7.12.

In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.
The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.

Deepfake is a type of artificial intelligence used to create convincing images, audio, and video hoaxes and it concerns celebrities and everyone because they are easy to manufacture. Deepfake are hard to recognize by people and current approaches, especially high-quality ones. As a defense against Deepfake techniques, various methods to detect Deepfake in images have been suggested. Most of them had limitations, like only working with one face in an image. The face has to be facing forward, with both eyes and the mouth open, depending on what part of the face they worked on. Other than that, a few focus on the impact of pre-processing steps on the detection accuracy of the models. This paper introduces a framework design focused on this asp