International Journal of Mathematics And its Applications

1-6

Authors: A. George Maria Selvam and D. Vignesh

This paper considers a two dimensional model of Series RLC circuit. Existence of equilibrium points is established and local stability conditions are discussed. The phase portraits are obtained for different sets of parameter values. Numerical simulations are performed.

15−18

Authors: B. Stephen John and S. Andrin Shahila

Let G=(V,E) be an undirected simple graph. The transformation graph G−−− of G is a simple graph with vertex set V(G)∪E(G) in which adjacency is defined as follows: (a) two elements in V(G) are adjacent if and only if they are non-adjacent in G, (b) two elements in E(G) are adjacent if and only if they are non-adjacent in G, and (c) an element of V(G) and an element of E(G) are adjacent if and only if they are non-incident in G. In this paper, we determine the chromatic number of Transformation graph G−−− for Complete, Wheel and Friendship graph.

1-6

Authors: Albert william, Indra Rajasingh and S.Roy

The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi:V(G)\longrightarrow \{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, we compute the packing chromatic number for enhanced hypercubes.

17-27

Authors: S.K.Vaidya and N.H.Shah

We prove that the graphs alternate triangular snake, alternate quadrilateral snake, double alternate triangular snake and double alternate quadrilateral snake admit cordial labeling.

53-62

Authors: Manish Kumar

In the present paper, we prove a coupled coincidence fixed point theorem in the setting of two pairs of mappings in G-metric space. The main result is illustrated by an example.

73-83

Authors: Dr. SK. Samsul Alam and Dr.Partha Karmakar

In this paper, an attempt has been made to study status of mathematical education at degree level in West Bengal, India. For this study, descriptive research design- normative survey research method has been applied on four degree colleges including one women's college under different universities of West Bengal. The findings of the analysis of survey data have been presented.

1-14

Authors: Lorenc Ekonomi and Argjir Butka

When the observations are dependent, like in time series, Kunsch introduced the bootstrap with blocks forming by a x number of consecutive observations. Dierent versions of block bootstrap has been formulated. In this paper we have proposed a bootstrap estimation with blocks formed from recalculated values of a statistic. We call it bootstrap with re-blocks. We have shown that this bootstrap works in time series strictly stationary -mixing or m-dependent under some conditions. We have done simulations to compare the bootstrap with re-blocks with other block bootstrap methods.

23-28

Authors: Vineeta Yadav, A.K.Verma and Rizwana Zamal

The present research article represent the mathematical analysis of objective function for training new hidden units in constructive algorithms for multi-layer feed-forward networks. Neural research, now days, is highly attractive wing under research community which may lead the development of some hidden prospects by using mathematical modeling which involve the design of neurons network. The network size is highly important for neural network. Small network as well as large network size cannot be learned very well, but there is an optimum size for which the neural network can be involved for good results. Constructive algorithms started with a small network size and then grow additional hidden units until a satisfactory solution is found. A network, having n-1 hidden units, is directly connected to the output unit, which is modeled as $f_{n-1}=\sum\limits_{j=1}^{n-1}\beta_{j}g_{j}$ and $e_{n-1}=f-f_{n-1}$ is the residual error function for current network with $n-1$ hidden units. A new hidden unit is added under a process in input as a linear combination of $g_n$ with the current network $f_{n-1}+\beta_n g_n$ which governed the minimum residual error $\|e_n\|$ in the output process by keeping $g_n$ fixed and adjusted value of $\beta_n$ so as to minimize residual error. The function to be optimized during input training is $\frac{\langle e_{n-1},g_n\rangle^2}{\|g_n\|^2}$ and corresponding objective function is $s_1=\frac{(\Sigma_pE_p H_p)^2}{\|g_n\|^2}$, where $H_p$ is the activation function of the new hidden unit and $E_p$ is the corresponding residual error before this new hidden unit is added.

37-46

Authors: Albert William, Indra Rajasingh and S.Roy

Given an undirected graph, finding a minimum 2-edge connected spanning subgraph is NP-hard. We solve the problem for silicate network, brother cell and sierpi\'{n}ski gasket rhombus.