International Journal of Mathematics And its Applications

1-11

Authors: D. Pradeep

In \cite{Pr1}, the authors have suggested a modified iterative Laverentiv method for solving nonlinear ill-posed equations involving monotone operators. In this paper, we propose the finite-dimensional approximation of the scheme considered in \cite{Pr1}. We have shown the regularization parameter and the error estimates are optimal order. Finally, we also present some numerical results to verify the theoretical estimates.

21-27

Authors: Kalan Nguyen

Number theory is the branch of pure mathematics which studies positive whole numbers also called natural numbers and integers. The goal of number theory is to discover relationships between numbers that may not be apparent at face value. Cryptography is the study of encryption and decryption of information. By encrypting information the data can be transmitted to the intended recipient securely across the internet (insecure network). The use of numbers in cryptography is inextricably linked.

35-39

Authors: T. J. Rajesh Kumar and Antony Sanoj Jerome

Gaussian integers are the complex numbers of the form a + bi where $a, b \in Z$ and $i^{2} =-1$ and it is denoted by $ Z[i]$. A Gaussian prime labeling on G is a bijection from the vertices of G to $[\psi_{n}]$, the set of the first n Gaussian integers in the spiral ordering such that if $uv \in E(G)$, then $\psi(u)$ and $\psi(v)$ are relatively prime. Using the order on the Gaussian integers, we discuss the Gaussian prime labeling of super subdivision of star graphs.

49-53

Authors: S. Mbala, M. M. Manene and J. A. M Ottieno

Examinations across the world play a vital role in the education system. Unfortunately, the process of examinations is greatly affected by the act of cheating hence giving a wrong impression on the results. The research on examination dishonesty among secondary school students is considered to be a sensitive issue, thus direct questioning techniques are not useful as the respondents will either refuse to answer the survey questions or even if they do, may give false answers for fear of being known to have been involved in the cheating. In this paper we have tested the validity of Symmetric truth detection models using examination dishonesty research. This research was done in a national Secondary school in Kenya. The results were used to validate the Symmetric Truth detection models by comparing the results with the results of the Asymmetric questioning technique. We have shown that the Symmetric truth detection models are more reliable when investigating sensitive information compared to Asymmetric truth detection models.

59-68

Authors: P. R. Hampiholi, A. S. Joshi and J. P. Kitturkar

For any two vertices $u$ and $v$ of a graph $G$, $d(u, v)$ is the length of the shortest path between the vertices $u$ and $v$. D. Reddy Babu and P.L.N. Varma introduced the concept of D-distance. D-distance considers the degree of all vertices present in a path while defining its length. In this paper, D-eccentricity spectra of D-eccentricity matrix of some class of graphs are computed.

75-83

Authors: Shweta Wasnik and Subhashish Biswas

In this paper, we prove Chatterjea - Pata type fixed point theorem in modular spaces which generalizes and improves some old results. Also we give an application for the existence of solutions of integral equations in modular function spaces.

91-94

Authors: S. R. Nayaka

A dominating set of a graph $G$ is said to be pendant dominating set if the induced subgraph contains at least one pendant vertex. A subset $F$ of edges of $G$ is said to be an edge dominating set if every edge not in $F$ is incident to at least one edge in $F$. An edge dominating set is said to be pendant edge dominating set if an edge induced subgraph $\langle F\rangle$ contains an edge of degree one. In this article, we initiate the study of pendant edge domination of graph and compute exact values for some standard graphs.

103-112

Authors: S. Singh and R. K. Srivastava

This paper analyses the single server bulk arrival Markovian queueing system where customers arrive according to the general bulk rule and follows the Poisson distribution. Customers are served with three types of services, one is essential service and two of them are optional services. Server is giving service to the customers according to Exponential distribution with the bulk service rule. After providing service to the bulk, server goes for a vacation according to the exponentially distribution. Server returns from the vacation when there are sufficient number of customers is available for receiving the service. Again server go back for a vacation if arrived number of customers is not enough to get the essential service. The server returns when arrived bulk is sufficient. After receiving the essential service, customers have the choice that they take first essential service, second essential service or take both. We have also include the impatience behaviour of customers i.e. the bulk of customers also balks from the system if the server is busy to giving service to other customers or server is on the vacation. We have computed the time dependent probability generating functions with the help of corresponding steady state results. Also we determine the number of customers waiting in the queue for this system.