Journal of Applied & Computational Mathematics

This paper proves the log-concavity of polygonal and centered polygonal figurate number sequences and derives two recurrence formulas for these sequences. The log-concavity property is established by examining the second-order difference between consecutive terms, showing its non-negativity. The derived recurrence relations offer a practical method to compute subsequent terms based on previous ones. The proofs for both the log-concavity property and the recurrence formulas are provided, enhancing our understanding of these sequences and their mathematical properties.

This study investigates the effects of the MHD flow via an exponentially extending surface of a Casson hybrid nanofluid made of graphene and carbon nanotubes with basic Casson fluid. The directions of flow were subjected to the standard Lorentz force. The velocity, temperature and concentration profiles are simulated using a mathematical model established under the flow suppositions by utilizing boundary exponentially layer surface approximations in equations using Partial Differentials (PDEs). The lie symmetry method was used to achieve a suitable performance of mathematical transformations. After applying the necessary transformations, Partial Differential Equations (PDEs) were transformed into Ordinary Differential Equations (ODEs). The dimensionless system was explained using a numerical with 4th-order Runge–Kutta method called bvp4c. Both tabular and depicted graphical representations were used to show the influence of relevant flow parameters on skin friction, Nusselt number, velocity, temperature and concentration distributions. Furthermore, the Casson fluid parameter, magnetic field strength, Brownian motion, random motion, volume fraction and radiation parameter cause the temperature profiles to rise at the surface can be observed. Also, increasing with Brownian motion, thermophoretic parameter and radiation parameter increases the primary velocity while decreasing with Casson fluid parameter and magnetic field parameter. Furthermore, insight into system irreversibility and demonstrates actual system transit from a low entropy configuration to a high entropy configuration.

Communication over the internet must be secure to prevent intercepting or accessing sensitive information. Attempts are being made to protect confidential information by providing maximum security over the network. One of such techniques is using matrix multiplication for Hill Cipher cryptosystem, which is not easily breakable. The traditional Hill Cipher algorithm uses 2 × 2 and 3 × 3 matrix for generating keys. In this paper, we enhance the existing algorithm by using 4 × 4 matrix to generate the keys and to demonstrate the application of this algorithm created in MATLAB programming language. We also compare the time consumed to encode and decode the message by the traditional Hill Cipher algorithm. The enhanced Hill Cipher algorithm to get a clear idea which algorithm is more efficient and reliable and not easily breakable by the intruders.