This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth–death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman–Kolmogorov differential equations are developed with the use of mnemonic rule and these equations are solved with Runga–Kutta fourth-order method. The long-run availability, reliability and mean time between failures are computed for various choices of failure and repair rates of subsystems of the system. The findings of the paper are discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the performance of the urea synthesis system of the fertilizer plant.

This study aims to achieve an efficient time-frequency representation of higher-dimensional signals by introducing the notion of a non-separable linear canonical wavelet transform in $L^2\left({\mathbb{R}}^n\right)$. The preliminary analysis encompasses the derivation of fundamental properties of the novel integral transform including the orthogonality relation, inversion formula, and the range theorem. To extend the scope of the study, we formulate several uncertainty inequalities, including the Heisenberg’s, logarithmic, and Nazorav’s inequalities for the proposed transform in the linear canonical domain. The obtained results are reinforced with illustrative examples.

The free metaplectic transformation (FMT) is a multidimensional integral transform that encompasses a broader range of integral transforms, from the classical Fourier to the more recent linear canonical transforms. The aim of this study is to introduce a novel shearlet transform by employing the free metaplectic convolution structures. Besides obtaining the orthogonality relation, inversion formula, and range theorem, we also study the homogeneous approximation property for the proposed transform. Towards the culmination, we formulate the Heisenberg and logarithmic-type uncertainty principles associated with the free metaplectic shearlet transform.

Electronic voting is most growing field in the area of voting system. Digital users are growing with the expo-national growth in every country. In the country like India where mobile or internet user are 391 million, e-voting system reduce a huge amount of current voting methods. But in this current scenario e-voting system are vulnerable and not threat proof. Blockchain is new emerging field in security and for distributed systems. Only few methods are applied in the past where E-Voting system used the blockchain technology. So, the objective of this research is to review the different algorithms applied in e-voting using blockchain through various parameters to help researchers working to provide more security using blockchain.

The aim of the present paper is to analysis the reliability of the system by using CAS Mathematica and also, it’s comparative study with CAS Maxima. The butter oil manufacturing plant consists of seven units i.e. separator, pasteurizer, continuous butter making, melting vats, butter oil clarifier, packaging and standby state. Model is developed by using Markov birth-death process. The first order differential equations are derived by using model and then solved for comparative study of reliability to give accuracy in result. By using Mathematica, we calculate probability of each state, which is beneficial to plant owners because better accuracy in result enhance reliability of the plant Graphs are plotted and tables are developed with the help of CAS Mathematica and Maxima, graphs show the variation and tables shows the fluctuations in reliability in comparative manner.