Research on automated reasoning systems based on a number of paradigms that support human activity in formalized text processing began in the late 1950s – early 1960s, when computer performance and memory space became sufficient for programming of complex intelligent processes. The so-called evidential paradigm was among them and it can be viewed as a way for integrating all reasonable paradigms oriented to the development of computer languages for representing formalized texts in the form most suitable for a user, formalization and development of the evidence of a computer-made proof step, creation of the information environment having influence on a current evidence of a machine proof step, and an active human-machine interaction. This work contains a brief description of the evidential paradigm and its implementation in the form of intelligent systems intended for the symbolic and deductive processing of mathematical texts focusing main attention on their features and peculiarities.

Public key cryptographic schemes are vastly used to ensure confidentiality, integrity, authentication and non-repudiation. Schmidt-Samoa cryptosystem (SSC) is a public key cryptosystem, which depends on the difficulty of large integer factorization problem. The implementation of SSC to secure different recent communication technologies such as cloud and fog computing is on demand due to the assorted security services offered by SSC such as data encryption/decryption, digital signature and data integrity. In this paper, we provide a systematic review of SSC public key cryptosystem to help crypto-designers to implement SSC efficiently and adopt it in hardware or software-based applications. According to the literature, the effective utilization and design SSC can place it as a viable alternative of RSA cryptosystems and many others.

This study describes the Bayesian approach as an alternative approach for estimating time axes parameters and the periodogram (power spectrum) associated with sinusoidal model when the white noise (sigma) is known or unknown. The conventional method of estimating the time axes parameters and the periodogram has been via the Schuster method that relies solely on Maximum Likelihood Estimation (MLE). The Bayesian alternative approach proposed in this work, on the other hand, adopted the Maximum A Posteriori (MAP) via the Markov Chain Monte Carlo (MCMC) in order to checkmate the problem of re-parameterization and over- parameterization associated with MLE in the conventional practice. The rates of heartbeat variability at exactly an hour and two hours after birth of one thousand eight hundred (1800) newly born babies in a state hospital were recorded and subjected to both the Bayesian approach and Schuster approach for inferences. The periodogram estimates, exactly an hour and two hours of after birth, were estimated to be 0.7395 and 0.7549, respectively - and it was deduced that rates of heartbeat (frequency) variability moderated and stabilized the pulse among the babies after two hours of birth. In addition, MAP mean estimates of the parameters approximately equals to the true mean of estimates when round up to curb the problem of re-parameterization and over- parameterization that do affect Schuster method via MLE.

When we live in a global village, then maintaining privacy and confidentiality becomes reasonably challenging. Short Message Service (SMS) is the oldest application for exchanging messages between communicating parties in cellular network used by mobile phones. These messages are encrypted over-the-air with A5/1 algorithm and stored as clear text at network operator. Recent developments have shown that this algorithm is not secure any more. Compromising an access to network operator registers gains access to SMS also. Current scenarios of hacks and exploitation demands confidentiality, and encryption is one of the techniques, which is used, in this subsequent project of designing a secure SMS android application. Cryptographic manipulation of the data is performed using AES 128 -bit algorithm to secure the data, which is essential to us and the safe transmission of confidential data over the GSM network. AES (Advanced Encryption Standards) algorithm is the considered impregnable even to super computers brute force attacks. The AES algorithm technique uses very befuddled and sporadic encryption making data impregnable to attackers or hackers. This android app will allow the user to encrypt and decrypt the SMS (Short Message Service) efficiently and just at one click. Subsequent explanation is given afterwards.

The present study is concerned with the estimation of Inverse Exponential distribution using various Bayesian approximation techniques like normal approximation, Tierney and Kadane (T-K) Approximation. Different informative and non-informative priors are used to obtain the Baye’s estimate of Inverse Exponential distribution under different approximation techniques. A simulation study has also been conducted for comparison of Baye’s estimates obtained under different approximation using different priors.