In this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. Some characteristics of this polynomial which can be used for solvin

Due to the vast using of digital images and the fast evolution in computer science and especially the using of images in the social network.This lead to focus on securing these images and protect it against attackers, many techniques are proposed to achieve this goal. In this paper we proposed a new chaotic method to enhance AES (Advanced Encryption Standards) by eliminating Mix-Columns transformation to reduce time consuming and using palmprint biometric and Lorenz chaotic system to enhance authentication and security of the image, by using chaotic system that adds more sensitivity to the encryption system and authentication for the system.

The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

  The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] .  Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, in 2021, the wavelet Boubaker (WB) polynomials were used for the first time to study their properties and applications in detail. They were also utilized for solving the Lane-Emden equation. The aim of this paper is to show the truncated Wavelet Boubaker polynomials for solving variation problems. In this research, the direct method using wavelets Boubaker was presented for solving variational problems. The method reduces the problem into a set of linear algebraic equations. The fundamental idea of this method for solving variation problems is to convert the problem of a function into one that involves a finite number of variables. Diff

The derivation of 5^th order diagonal implicit type Runge Kutta methods (DITRKM5) for solving 3^rd special order ordinary differential equations (ODEs) is introduced in the present study. The DITRKM5 techniques are the name of the approach. This approach has three equivalent non-zero diagonal elements. To investigate the current study, a variety of tests for five various initial value problems (IVPs) with different step sizes h were implemented. Then, a comparison was made with the methods indicated in the other literature of the implicit RK techniques. The numerical techniques are elucidated as the qualification regarding the efficiency and number of function evaluations compared with another literature of the implic

Watermarking operation can be defined as a process of embedding special wanted and reversible information in important secure files to protect the ownership or information of the wanted cover file based on the proposed singular value decomposition (SVD) watermark. The proposed method for digital watermark has very huge domain for constructing final number and this mean protecting watermark from conflict. The cover file is the important image need to be protected. A hidden watermark is a unique number extracted from the cover file by performing proposed related and successive operations, starting by dividing the original image into four various parts with unequal size. Each part of these four treated as a separate matrix and applying SVD

new, simple and fast solid-phase extraction method for separation and preconcentration of trace theophylline in aqueous solutions was developed using magnetite nanoparticles (MIONPs) coated with aluminium oxide (AMIONPs) and modified with palmitate (P) as an extractor (P@AMIONPs). It has shown that the developed method has a fast absorbent rate of the theophylline at room temperature. The parameters that affect the absorbent of theophylline in the aqueous solutions have been investigated such as the amount of magnetite nanoparticle, pH, standing time and the volume, concentration of desorption solution. The linear range, limit of quantification (LOQ) and limit of detection (LOD) for the determination of theophylline were 0.05-2.450 μg mL-

     In this paper, the oscillation of a Hematopoiesis model in both cases delay and non-delay are discussed. The place and are continuous pstive -rdic functions. In the nn-dlay cse, we will exhibit that a nonlinear differential equation of hematopoiesis model has a global attractor  for all different pstive solutions. Also, in the delay case, the sufficient conditions for the oscillation of all pstive solutions of it aboutare presented and we establish sufficient cnditions for the global attractive of. To illustrate the obtained results some examples are given.

In this paper, a new modification was proposed to enhance the security level in the Blowfish algorithm by increasing the difficulty of cracking the original message which will lead to be safe against unauthorized attack. This algorithm is a symmetric variable-length key, 64-bit block cipher and it is implemented using gray scale images of different sizes. Instead of using a single key in cipher operation, another key (KEY2) of one byte length was used in the proposed algorithm which has taken place in the Feistel function in the first round both in encryption and decryption processes. In addition, the proposed modified Blowfish algorithm uses five Sboxes instead of four; the additional key (KEY2) is selected randomly from additional Sbox