Journal of Advances in Mathematics and Computer Science

A modified solution of the nonlinear singular oscillator has been obtained based on the extended iteration procedure. We have used an appropriate truncation of the obtained Fourier series in each step of iterations to determine the approximate analytic solution of the oscillator. The third approximate frequency of the nonlinear singular oscillator shows a good agreement with its exact values. Earlier different authors presented the analytic solution of the oscillator by using various types of methods. We have compared the results obtained by the modified technique with some of the existing results. We see that some of their techniques deviate from higher-order approximations and the present technique performs comparatively better.  The rate of change of percentage of error of the presented modified solution shows the validity of convergence.

In this paper, we include stochastic perturbation into SIRS epidemic model incorporating media coverage and study their dynamics. Our model is obtained by taking into account both for demographic stochasticity and environmental fluctuations on contact rate before alert media β1. First, we show that the model is biologically well-posed by proving the global existence, positivity and boundedness of solution . Then, sufficient conditions for the extinction of infectious disease
is proved. We also established sufficient conditions for the existence of an ergodic stationary distribution to the model. Finally, the theoretical results are illustrated by numerical simulations; in addition we show that the media coverage can reduce the peak of infective individuals via numerical simulations.

Some stochastic epidemiological models are less significant. They do not take into account some sudden events that could disrupt the behavior of the studied phenomenon. In this work, we introduce a white noise and jumps in a deterministic SIRS model for smoking to take into account of the effects of randomly fluctuation and such sudden factors respectively. First of all we prove that the solution of the stochastic differential equation with jumps of the new model
is positive. Then we study the asymptotic behavior around the smoking-free equilibrium state and the smoking-present equilibrium state of the original deterministic model. Under certain conditions, we show that the solution oscillate respectively around these equilibrium states. We prove that the intensity of these oscillations depends on the magnitude of noise and the jump diffusion coefficient of our stochastic differential equation with jumps. To support our theoretical results, we realise numerical simulations. The observations confirm our conclusions.

This article proposed a new extension of the Inverse Lindley distribution called “Lomax-Inverse Lindley distribution” which is more flexible compared to the Inverse Lindley distribution and other similar models. The paper derives and discusses some Statistical properties of the new distribution which include the limiting behavior, quantile function, reliability functions and distribution of order statistics. The parameters of the new model are estimated by method of maximum likelihood estimation. Conclusively, three lifetime datasets were used to evaluate the usefulness of the proposed model and the results indicate that the proposed extension is more flexible and performs better than the other distributions considered in this study.

Cloud computing is a developing, very buoyant and nascent paradigm offering numerous solutions to the mirage of challenges and troubles confronting the IT world. It is an online computing solution for on-demand scaling, sharing and abstraction of unlimited resources. Since the significance of trust and confidence in cloud data or information transmission cannot be underestimated, it is obligatory that adequate mechanism be put in place to guarantee the safety of data provided on a Card-Not-Present (CNP) transaction mode. On this note, this paper presents an RSA algorithm with encryption and decryption-based solution to the problems of data confidentiality and integrity. While the encryption mechanism provides secured and safe representation of financial data (such as credit card details) on the cloud, a message digest mechanism is used to decrypt the encrypted files at the gateway as well as generate and send a digest message for the transaction instrument to the user for authentication. Decryption by unauthorized user is effectively checked because the security key is exclusive to data owner and financial data is not domiciled on the merchant network. Experimental study and online survey of the system reveal its very high ratings for guaranteeing data safety and confidentiality as well as the efficacy of the digital signature, the RSA modulus and security keys (public and private) for reliable and attack-proof transactions.