In recent years, compared with stream ciphers more attention has been to block ciphers because of their proved security and wide application. Design of most block ciphers are based on substitution-permutation network (SPN) or Fiestel structure. Although Fiestel structures compared with SPN has many benefits, but since they have less active S-boxes in round function, it has a security weakness. In this paper, we introduce two new methods for designing 192-bit block cipher algorithms that use Switching Structure and Recursive Diffusion Layers to increase active S-boxes. The first method is based on switching structure and 3×3 multiple Recursive Diffusion Layers and the second method used switching structure and 2×2 multiple Recursive Diffusion Layers. Security of tow structures using linear programming offered analysed with linear programming and evaluated the results show of resistance to linear and DIFFERENTIAL CRYPTOANALYSIS. Also, since the Recursive Diffusion Layers are more efficient than MDS matrices in software and hardware, thus designed algorithms with these methods have high performance in various platforms.

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of generalized DIFFERENTIAL squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

We expand a new generalization of the two-dimensional DIFFERENTIAL trans-form method. The new generalization is based on the two-dimensional differ-ential transform method, fractional power series expansions, and conformable fractional derivative. We use the new method for solving a nonlinear con-formable fractional partial DIFFERENTIAL equation and a system of conformable fractional partial DIFFERENTIAL equation. Finally, numerical examples are pre-sented to illustrate the preciseness and effectiveness of the new technique.

In this paper, an extension of DIFFERENTIAL Transformation Method (DTM) which is an analytical-numerical method for solving the fuzzy partial DIFFERENTIAL equation (FPDE) by using the strongly generalized differentiability concept is investigated. The proposed algorithm is illustrated by numerical example.