##### Integrated and Differentiated Sequence Spaces and Weighted Mean

Murat Kirişci

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2018/44143

The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix transformations are characterized. Secondly, examples between new spaces with classical sequence spaces and sequence spaces which are derived by an infinite matrix are given in the table form.

##### Orbital Motion Around the Collinear Libration Points of the Restricted Three-Body Problem

A. H. Ibrahim, M. N. Ismail, A. S. Zaghrout, S. H. Younis, M. O. El Shikh

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2018/43370

In this work, the special solutions of the Restricted Three-Body Problem (RTBP) are presented which specify the locations of the equilibrium points. The periodic orbits around these libration points are obtained analytically and numerically. The Lissajous orbits around the collinear libration points are focused in this work. Earth-Moon-Spacecraft system is carried out to illustrate this study.

##### One-Step Five Offgrid Implicit Hybrid Block Method for the Direct Solution of Stiff Second-Order Ordinary Differential Equations

D. Raymond, E. O. Anyanwu, A. I. Michael, L. Adiku

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/JAMCS/2018/43363

A one-step five off-grid implicit hybrid block method for the solution of stiff Second Order Ordinary Differential Equations is developed. The continuous hybrid linear multistep method was generated using power series approximation via interpolation and collocation at the grid points. The discrete block method was recovered by evaluating the continuous block method at some selected grid points. The method is convergent. Numerical experiments on some Second Order Ordinary differential equations show that the method is more accurate than some existing methods.

##### Error Analysis and Detection Procedures for Signature and Authentication Schemes

Naglaa F. Saudy, Ihab A. Ali, Reda Al Barkouky

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2018/43056

In this paper, a fault discovery structure is presented to increase the protection and reliability of the Elliptic Curve Digital Signature Algorithm (ECDSA) under practical considerations. As the ECDSA will work in real systems, which have their own arrangement of transient errors, being able to handle faults that happen when examining the ECDSA execution turns into an unquestionable requirement. Since even one transient mistake was to occur amid the ECDSA procedure, will bring out enormous errors in the information. We introduce applying nonlinear fault detection codes to protect ECDSA operations against fault attacks. We also apply the same idea to protect Guillou-Quisquater authentication scheme (GQ) against fault injection attacks. These codes give almost perfect error detection capacity (aside from an exponentially small probability) at sensible overhead. We present a fault detection scheme by using the nonlinear error detecting code. This fault detection scheme has shown to have over 99% fault detection coverage.

##### Type II Half Logistic Rayleigh Distribution: Properties and Estimation Based on Censored Samples

Muhammad Ahsan Ul Haq, Abdullah M. Almarashi, Amal S. Hassan, M. Elgarhy

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/JAMCS/2018/44266

In this paper, we introduce a new model called the Type II half logistic Rayleigh (TIIHLR) with U-shaped, increasing and decreasing hazard rate function. Some structural properties of the current distribution are derived including; explicit expressions for moments, incomplete moments, order statistics and Rényi entropy. Maximum likelihood estimators of the model parameters, based on complete and censored samples, are obtained. A numerical study is demonstrated to illustrate the theoretical results. The superiority of the new model over some new existing distributions is illustrated through two real data sets. In both applications, the TIIHLR model produces better fits than; the transmuted Rayleigh; transmuted generalised Rayleigh; exponentiated transmuted generalised Rayleigh and transmuted exponentiated inverse Rayleigh distributions.