A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method (MLADM) has been proposed for solving the model for HIV infection of CD4+T cells. The proposed method is modification of the classical Laplace Adomian Decomposition Method (LADM) with multistep approach. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method is confirmed that MLADM performs with very high accuracy. Results show that MLADM is a very promising method for obtaining approximate solutions to the model for HIV infection of CD4+T cells. Some plots and tables are presented to show the reliability and simplicity of the methods. All computations have been made with the aid of a computer code written in Mathematica 7.

In this paper, combined Laplace transform-Adomian decomposition method is presented to solve differential equations systems. Theoretical considerations are being discussed. Some examples are presented to show the ability of the method for linear and non-linear systems of differential equations. The results obtained are in good agreement with the exact solution and Runge-Kutta method.

Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method. Results show that the numerical scheme is very effective and convenient for solving a large number of linear singularly perturbed two-point boundary value problems with high accuracy.

In this work, the applications of differential transform method were extended to singularly perturbed Volterra integral equations. To show the efficiency of the method, some singularly perturbed Volterra integral equations are solved as numerical examples. Numerical results show that the differential transform method is very effective and convenient for solving a large number of singularly perturbed problems with high accuracy.

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Günümüzde dijital iletişim içerisinde bilginin güvenliği çok önemli bir yer tutmaktadır. Uçtan uca iletişimlerde önemli bilgilerin şifrelenmesi veya bir taşıyıcı üzerine gömülerek gizlenmesi bilgi güvenliği için kullanılan yöntemlerinin başında gelir. Bazı durumlarda güvenliği artırmak için yöntemler karma bir şekilde kullanılıp bilgi iletişim kanalları içerisine bırakılabilir. Bu yöntemlerdeki ortak amaç, kaynaktan çıkan önemli bilgilerin, iletişimde ilgisi olmayan kişilerin eline geçmeden veya anlaşılmaz şekle dönüştürülerek hedefe gönderilmesidir. Bu çalışmada, steganografi ile ilgili temel bilgiler verildikten sonra önerilen renkli görüntü gizleme yöntemi anlatılmıştır. Yöntemde, önce gizlenecek görüntü veya metindeki veriler genişletilmiş 1B lojistik harita kullanılarak rastgele dağıtılmış ardından renkli örtü görüntüsündeki en az anlamlı k-bit ile değiştirilmiştir. Gizlenmek istenen bilgi şifrelenerek bilgi güvenliğinin artırılması hedeflenmiştir. Yöntemin başarısı, bilginin saklanacağı bit düzlem sayısına göre farklı boyutlarda görsel ve metinler üzerinde denenmiştir. Önemli güvenlik değerlendirme kriterlerinden PSNR ve MSE ölçütleri incelenmiştir. 1 bit düzlemin kullanıldığı 75x100 boyutlarındaki görselin gizlendiği işlemde

In this study, a novel Improved Affine Algorithm (IAA) for color image encryption is proposed. Affine Algorithm (AA) is generally known as an algorithm used for plain text encryption. In the proposed IAA algorithm, Linear Feedback Shift Register (LFSR), XOR encryption, and the AA are combined for color images encryption. The plane image is firstly split into three channels: R, G, and B. The RGB channel image is encrypted using AA encryption with ten keys based on pixel locations and pixel values. The rows and columns of the image are encrypted with LFSR keys and XOR encryption procedures. Finally, the proposed algorithm is tested in Matlab environment to obtain the Histogram, Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Unified Average Changing Intensity (UACI), Number of Pixel Change Rate (NPCR), and Entropy analyses. The values are compared with other algorithms. The results show that the proposed image encryption algorithm is secure and powerful, outperforming other algorithms.

Data hiding is done in different environments and with different techniques, and applications in this area attract a lot of attention. In data hiding, the method of securing the data in the image by hiding data is one of the steganography methods. Bit Plane Slicing, one of the techniques applied in image steganography, is a reliable technique applied on images such as data hiding or compression, which allows us to operate on some special bits by separating each pixel that makes up the image into planes. This technique is aimed to provide high image quality and data security. In this study, two encryption layers and a concealment stage are proposed. Here, the bit planes of the three channels of the color image were first extracted using the BPS technique. The message to be hidden later was encrypted using a double XOR operation using binary representation and a secret key (extracted from the MSB). Then, the stream of encrypted bits is hidden in the cover image using the least significant bit plane. Well-known evaluation criteria such as MSE, PSNR, and histogram distribution were calculated to ensure the quality of the proposed method. Experimental results show that the proposed method has acceptable results and maintains the security of confidential text messages.