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Issue 3
Volume 6 (2018)

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Authors |
: | A. George Maria Selvam and D. Vignesh |

Title |
: | Dynamics in a Series RLC Circuit with Damping |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 1−6 |

**Abstract: ** 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.

**Keywords: ** RLC circuit, Differential Equation, Numerical Simulation, Stability.

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Authors |
: | R. Vimala Devi and S. Suganya |

Title |
: | Two Heterogeneous Service Queue With Second Optional Repair Subject to Reneging During Compulsory Vacation and Breakdown Time |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 7−14 |

**Abstract: ** This paper deals with a single server batch arrival queue, two stages of heterogeneous service with different (arbitrary) service time distribution subject to random breakdowns followed by a repair and compulsory server vacations with general (arbitrary) vacation periods. After first stage service the server must provide second stage service. However after the completion of each second stage service the server will take compulsory vacation. The system may breakdown at random and it must be send to repair process immediately. If the server could not be repaired with first essential repair, subsequent repairs are needed for the restoration of the server. Both first essential repair and second optional repair times follow exponential distribution. We consider reneging to occur when the server is unavailable during the system breakdown or vacation periods. The steady state solutions have been found by using supplementary variable technique.

**Keywords: ** Batch Arrivals, Breakdowns, Steady state, First essential repair, Second optional repair, Reneging.

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Authors |
: | B. Stephen John and S. Andrin Shahila |

Title |
: | Chromatic Number to the Transformation $(G^{---})$ of $K_n$, $W_n$ and $F_n$ |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 15−18 |

**Abstract: ** Let $G=(V,E)$ be an undirected simple graph. The transformation graph $G^{---}$ of G is a simple graph with vertex set $V(G)\cup E(G)$ 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.

**Keywords: ** Complete Graph, Wheel Graph, Friendship graph, Chromatic Number, Transformation Graph.

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Authors |
: | D. Stephen Dinagar and M. Mohamed Jeyavuthin |

Title |
: | Fully Fuzzy Integer Linear Programming Problems Under Robust Ranking Techniques |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 19−25 |

**Abstract: ** The focus of this paper is to find fuzzy optimal solution of fully fuzzy integer linear programming problems (FFILPP) with pentagonal fuzzy numbers under robust ranking technique. A new approach for solving fully fuzzy integer linear programming problems with pentagonal fuzzy number is proposed, based on ranking function. The proposed method is very easy to understand. This is illustrated with relevant numerical examples.

**Keywords: ** Ranking function, Robust ranking function, Pentagonal fuzzy number, Fully fuzzy integer linear programming.

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Authors |
: | A. V. Paparao and N.V.S.R.C. Murty Gamini |

Title |
: | Dynamical Behaviour of Prey Predators Model with Time Delay |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 27−37 |

**Abstract: ** This paper describes a Prey and Two predators Ecological model. Continuous type gestational delay is incorporated in the interaction of Prey and first predator is taken for investigation. The system dynamics is studied at its equilibrium points. We construct a suitable Lyapunov function for global stability. The effect of Time delay on the dynamical behiviour of the system is studied. Using Numerical simulation, it is shown that the delay arguments with different kernels exhibit rich dynamics.

**Keywords: ** Equilibrium points, Local stability, Global stability, Time delay.

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Authors |
: | T. Geetha and S. Usha |

Title |
: | Application of Fuzzy Membership Matrix in Yoga on Insomnia |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 39−44 |

**Abstract: ** Fuzzy Set Theory and fuzzy logic are highly suitable and applicable for developing knowledge based system in medicine for the tasks of medical findings. There are variety of models involving fuzzy matrices to deal with different complicated aspects of medical diagnosis. In this paper, procedures are presented for medical diagnosis and for fuzzy decision models.

**Keywords: ** Triangular fuzzy number, Triangular fuzzy number matrix, addition and subtraction, operation on triangular fuzzy number matrix, New membership function, Max-Min composition on fuzzy membership Value matrices, insomnia.

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Authors |
: | Rajesh Kumar, Gaurav Gupta, Amita Bhagat and Kapil Kumar Kalkal |

Title |
: | A Study on Magneto-thermodiffusive Wave Propagation in Dual-phase-lag Thermoelasticity with Temperature-dependent Properties |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 45−61 |

**Abstract: ** The present paper is concerned with the analysis of magneto-thermodiffusive wave propagation in a homogeneous, isotropic, thermally and perfectly conducting elastic medium with temperature dependent mechanical properties. The formulation is established under the purview of dual-phase-lag thermoelasticity theory with diffusion. The modulus of elasticity is taken as a linear function of reference temperature. The resulting non-dimensional coupled equations are applied to a specific problem of a half-space whose surface is subjected to a time dependent mechanical shock. The analytical expressions for the displacement components, stresses, concentration and temperature field in the physical domain are obtained by employing normal mode analysis. Finally, numerical solution is carried out for copper material and corresponding graphs are plotted to illustrate and compare theoretical results. Discussions have been made to highlight the effects of phase lag parameters, temperature dependent modulus of elasticity, frequency and time on the physical fields. Some particular cases of interest have been deduced from the present investigation. The phenomenon of a finite speed of propagation is observed graphically for each field.

**Keywords: ** Dual-phase-lag, Diffusion, Magneto-thermoelasticity, Temperature-dependent elastic modulus, Normal mode analysis.

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Authors |
: | Ashok S. Kulkarni and A. D. Lokhande |

Title |
: | Semi Prime Ideal in a-Distributive Lattice |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 63−68 |

**Abstract: ** In this paper we define semi prime ideal in a a-distributive lattice L. For a non empty subset B of a a-distributive lattice L, we observe if L is a a-distributive lattice then annihilator of B as $B^{a} = \{x \in L / x \wedge b \le a\ \ \forall\ \ b \in B \}$ is a semi prime ideal for any non empty subset B of L and observe some properties.

**Keywords: ** Prime Ideal, Semi Prime Ideal, Distributive Lattice.

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Authors |
: | Vinita Dewangan and Amitabh Banerjee |

Title |
: | Common Best Proximity Point Theorem of Two Non-self Mappings Satisfying a Generalized Weak Contractive Condition |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 69−75 |

**Abstract: ** In this paper, we use the notion of weakly contractive non-self mappings and establish the existence of common best proximity points for two mappings which satisfy a generalized weak contractive condition in metric spaces. We also provide an example to illustrate our result.

**Keywords: ** Common fixed point, weakly contractive non-self mappings, best proximity points, P-property.

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Authors |
: | R. Gokilam |

Title |
: | Existence and Continuous Dependence of the Solutions of the Benjamin-Bona-Mahony-Peregrine-Burger's Equation on the Circle |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 77−88 |

**Abstract: ** In this paper, we show the existence and continuous dependence of the solutions of the Benjamin-Bona-Mahony-Peregrine-Burger's(BBMPB) equation in Sobolev spaces $H^s$, for $s>\frac{3}{2}$. We employ a Galerkin approximation argument to show the existence of solutions of BBMPB
equation.

**Keywords: ** Continuous dependence, Sobolev space, Galerkin approximation.

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Authors |
: | S. Pinelas, M. Arunkumar and P. Agilan |

Title |
: | Generalized Ulam-Hyers Stability of $n-$Dimensional AQCQ Functional Equation in Fuzzy Banach Spaces in Two Different Methods |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 89−136 |

**Abstract: ** In this paper, the authors achieve the generalized Hyers-Ulam-stability of $n-$dimensional additive-quadratic-cubic-quartic functional equation
\begin{align*}
f\left(\sum_{k=1}^{n-1}x_k+2x_n\right)+f\left(\sum_{k=1}^{n-1}x_k-2x_n\right)&=4f\left(\sum_{k=1}^{n}x_k\right)+4f\left(\sum_{k=1}^{n-1}x_k-x_n\right)-6f\left(\sum_{k=1}^{n-1}x_k\right)\notag\\
&\quad+f(2x_n)+f(-2x_n)-4f(x_n)-4f(-x_n)
\end{align*}
in fuzzy Banach spaces using direct and fixed point methods.

**Keywords: ** Fuzzy normed space, additive, quadratic, cubic and quartic functional equation, Generalized Hyers-Ulam-Rassias stability.

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Authors |
: | R. Sureshkumar and S. Murugesan |

Title |
: | Centered Polygonal Sum Labeling of Graphs |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 137−144 |

**Abstract: ** Let G be a $(p,q)$ graph. A graph G admits centered polygonal sum labeling if a one to one function $f:V(G)\rightarrow N$ (where $N$ is a set of all non-negative integers) that induces a bijection $f^+: E(G)\rightarrow\{\mathbf{_CP_k(1)},\mathbf{_CP_k(2)},\cdots ,\mathbf{_CP_k(n)}\}$ of the edges of G defined by $f^+(uv) = f(u) + f(v)$ for every $e=uv \epsilon E(G),$ where $\mathbf{_CP_k(1)},\mathbf{_CP_k(2)},\cdots ,\mathbf{_CP_k(q)} $, $k\ge3$ are the first q centered polygonal numbers. A graph which admits such labeling is called centered polygonal sum graph. In this paper we characterize some families of graphs such as Path, Comb, Star graph, Subdivision of star, Bistar, $S_{m,n,r}$, Coconut tree admit centered polygonal sum labeling.

**Keywords: ** Centered polygonal numbers, Centered polygonal sum labeling, Centered polygonal sum graph.

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Authors |
: | Tara Dhakate, Vinod Varghese and Lalsingh Khalsa |

Title |
: | Transient Thermoelastic Analysis of a Multi-layered Oblate Spheroidal Shell with Internal Heat Generation |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 145−158 |

**Abstract: ** The principal aim of this paper is to investigate the thermoelastic responses in a generalised oblate spheroid subjected time-independent volumetric heat sources in each layer and sectional heat supply on the inner and outer curved surfaces. The closed-form solution is obtained for transient temperature distributions by establishing Sturm-Liouville integral transform considering series expansion function in terms of an eigenfunction of Sturm-Liouville boundary value problem for the composite region consisting of multilayered composites in an oblate spheroidal coordinate system. The relations obtained in this paper can be applied to any arbitrary boundary and initial conditions to avoid structural failure due to thermal stress response. Some results which are derived using computational tools are accurate enough for the practical purpose were depicted graphically. The three-layer elliptic region has been computed numerically and exhibited in a graphical form, by using dimensionless values and therefore discussed.

**Keywords: ** Multilayer oblate spheroid, transient heat conduction, thermal stresses, integral transform, composite.

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Authors |
: | Mahesh Boda and V. Dharmaiah |

Title |
: | A Hermite - Type Collocation Method for the Solution of an Integral Equation With a Certain Weakly Singular Kernel |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 159−167 |

**Abstract: ** In this paper we apply A Hermite-type collocation method is considered for the solution of a volterra integral equation of second kind with a certain weakly singular kernel. The constructed approximated is a cubic spline in the continuity class $ c'.$ The approximation is shown to be convergent of order four.

**Keywords: ** A Hermite - type collocation method, Preliminaries, Convergence analysis.

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Authors |
: | Keerthi G. Mirajkar and B. Pooja |

Title |
: | A Hermite - Type Collocation Method for the Solution of an Integral Equation With a Certain Weakly Singular Kernel |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 169−176 |

**Abstract: ** The Wiener index $W(G)$ of a graph $G$ is the sum of distances between all (unordered) pairs of vertices of $G$. In this paper, we obtain the Hosoya polynomial and Wiener index of semitotal point graph and its complement of certain graph families. Further, we obtained sharp upper and lower bounds for Wiener index of semitotal point graph and its complement.

**Keywords: ** Wiener index, Hosoya polynomial, semitotal point graph, complement of a graph.

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Authors |
: | S. S. Sandhya, E. Ebin Raja Merly and G. D. Jemi |

Title |
: | Some Results on Super Heronian Mean Number of Graphs |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 177−180 |

**Abstract: ** We add to some fresh outcomes for Super Heronian Mean Number of graphs. It has been found that the graphs obtained by the collection of Super Heronian Mean Number of Ladder, Triangular snake, Double Triangular snake also admit Super Heronian Mean Number.

**Keywords: ** Super Heronian mean number, $S_{hm}( L_{n}\odot K_{1,2})$, $S_{hm}(T L_{n}\odot K_{1})$, $S_{hm} (T_{n}\odot K_{1})$,
$S_{hm}(D(T_{n}) \odot K_{1})$.

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Authors |
: | Yadaiah Arupula and V. Dharmaiah |

Title |
: | Oscillation of Third-order Nonlinear Delay Difference Equation |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 181−191 |

**Abstract: ** Third-order nonlinear difference equation of the form $\Delta \left(c_{n} \Delta \left(d_{n} \Delta x_{n} \right)\right)+p_{n} \Delta x_{n+1} +q_{n} f\left(x_{n-\sigma } \right)=0,n\ge n_{0} $ are considered. Here, $\left\{c_{n} \right\}$, $\left\{d_{n} \right\}$, $\left\{p_{n} \right\}$, and $\left\{a_{n} \right\}$ are sequence of positive real number for $n_{0} \in N,f$ is a continuous function such that ${f\left(u\right) \mathord{\left/{\vphantom{f\left(u\right) u}}\right.\kern-\nulldelimiterspace} u} \ge k>0$ for $u\ne 0$. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results.

**Keywords: ** Difference equation, Delay, Third order, Oscillation. Nonoscillation, Riccati transformation.

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Authors |
: | T. L. Dewangan and M. M. Singh |

Title |
: | Interval Valued Fuzzy Ideals and Anti Fuzzy Ideals of $\Gamma$-Near-ring |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 193−201 |

**Abstract: ** The aim of this paper is to study the notion of an interval valued fuzzy ideal of a near ring and interval valued anti fuzzy ideal of a near-ring and to discuss some of their properties.

**Keywords: ** Near-ring, Near-subring, Fuzzy Ideals of near-ring, Fuzzy subring, Interval Valued Fuzzy ideals of near-ring, Interval Valued Anti fuzzy ideals of near-ring.

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Authors |
: | S. Mari Maheswari and M. J. Jeyanthi |

Title |
: | Interval Valued Fuzzy Ideals of $\Gamma$-Semirings |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 203−209 |

**Abstract: ** In this paper, we introduce the concept of interval valued fuzzy ideals of $\Gamma$-Semirings. We also characterize some of its properties and illustrate with examples of interval valued fuzzy ideals of $\Gamma$-Semirings.

**Keywords: ** $\Gamma$-Semiring, Ideals in $\Gamma$-Semiring, Fuzzy Ideals in $\Gamma$-Semiring, Interval valued fuzzy ideals in $\Gamma$-Semiring.

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Authors |
: | Ghulam Murtaza |

Title |
: | On 3-absorbing Hyperideals of Multiplicative Hyperring |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 211−214 |

**Abstract: ** Let $R$ be a multiplicative hyperring. In this research, we learn 3-absorbing hyperideal which is an extension of prime hyperideal. A non zero hyperideal $ J $ of a multiplicative hyperring $ R $ is called a 3-absorbing hyperideal of $ R $ if whenever $ x, y, z, w \in Q $ and $ x\cdot y\cdot z\cdot w\cdot \in J ,$ then either $ x\cdot y\cdot\cdot z \in J $ or $ y\cdot z\cdot w \in J $ or $ x\cdot z \cdot w \in J $ or $ x\cdot y\cdot w \in J $. A number of results concerning 3-absorbing hyperideals and examples of 3-absorbing primary ideals are given.

**Keywords: ** Hyperideal, 2-absorbing Hyperideals 3-absorbing Hyperideal.

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Authors |
: | M. Najarian, Z. Sarmast, S.M. Ghasemi and S. Sarmadi |

Title |
: | Evolutionary Vertical Size Reduction: A novel Approach for Big Data Computing |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 215−225 |

**Abstract: ** Complexity of model based machine learning techniques depends mainly on the size of feature vector, so various feature selection and feature extraction methods are widely employed for size reduction. Although horizontal size reduction approaches can exponentially subside the complexity of learning algorithms, utilizing all instances to build and train any models can potentially be problematic. As illustration, not only problematic data can lead for over-fitting and over-generalization, but using noisy data can cause no proper decision makings. Furthermore, performance and complexity of instance/memory based classifiers (e.g. k-NN) are highly depends on train samples. In this paper, evolutionary vertical size reduction approach is introduced to identify and filter problematic and noisy data, not only for enhancing the performance and robustness of machine learning techniques but for ebbing the needs for remarkable system resources. To this end, genetic algorithms are proposed to label problematic instances in datasets. To evaluate the performance of proposed approach, benchmark classification datasets are employed to quantify the impacts of filtering noisy and problematic data in classification applications. Despite the fact that proposed vertical size reduction approach enhances machine learning techniques (mainly supervised learning methods), real world applications which contain big data would require remarkable system resources. To address this drawback, cloud computing frameworks (such as MapReduce on Hadoop) is recommended to make the proposed vertical size reduction more applicable for big data processing.

**Keywords: ** Big Data, Data-Mining, Gene p53 Mutant, High-Performance Computing, Instance Selection, Size Reduction.

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Authors |
: | Wei-Kai Lai |

Title |
: | Generalization of an Inequality with Sum of Fractions |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 227−230 |

**Abstract: ** Cvetkovski introduced the inequality: $\frac{a^2+b^2}{a+b}+\frac{b^2+c^2}{b+c}+\frac{c^2+a^2}{c+a}\geq a+b+c$ in his book \textit{Inequalities: Theorems, Techniques and Selected Problems}. Starting from there we generalize this inequality to the case with non-negative real number exponents: $\frac{a^m+b^m}{a^n+b^n}+\frac{b^m+c^m}{b^n+c^n}+\frac{c^m+a^m}{c^n+a^n}\geq a^{m-n}+b^{m-n}+c^{m-n}$ for $m\geq n$. Moreover, we also discuss the order of the sum of fractions when the exponents in the fractions change, and prove the inequality $\frac{a^m+b^m}{a^n+b^n}+\frac{b^m+c^m}{b^n+c^n}+\frac{c^m+a^m}{c^n+a^n}\geq\frac{a^{m-l}+b^{m-l}}{a^{n-l}+b^{n-l}}+\frac{b^{m-l}+c^{m-l}}{b^{n-l}+c^{n-l}}+\frac{c^{m-l}+a^{m-l}}{c^{n-l}+a^{n-l}}$ for real numbers $m\geq n\geq l\geq 0$. Versions of the two inequalities with $k$-variables are also examined.

**Keywords: ** Chebyshev's Sum Inequality, Rearrangement Inequality, Fibonacci Number.

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Authors |
: | G. Ayyappan, P. Gayathri and V. Mahadevan |

Title |
: | Oscillation of Third Order Quasilinear Advanced Differential Equation with ``Maxima'' |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 231−236 |

**Abstract: ** This paper study the asymptotic properties of third order advanced differential equation with ``maxima'' of the form
$$\left(a(t)(x''(t))^\gamma \right)'+q(t)\max_{[t, \tau(t)]}x^\gamma(s)=0,~~t\geq t_0,$$
where $\gamma$ is ratio of odd positive integers. Give an example to illustrate the main results.

**Keywords: ** Third order, delay differential equation, oscillation, quasilinear.

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Authors |
: | K. E. Sathappan and R. Sumathi |

Title |
: | L-Fuzzy Bi-ideal of a Ring |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 237−242 |

**Abstract: ** In this paper the concept of L-fuzzy bi-ideal is introduced and some of its properties are discussed and studied.

**Keywords: ** L-fuzzy set, fuzzy sub ring, L-fuzzy sub ring, bi-ideal, fuzzy bi- ideal, L-fuzzy bi-ideal.

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Authors |
: | J. Ruth and S. Selvam |

Title |
: | New Fuzzy Soft Topologies Via Fuzzy Soft Ideals |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 243−251 |

**Abstract: ** The aim of this study is to define fuzzy soft topology in Lowen's sense and to introduce the notion of fuzzy soft ideal in fuzzy soft set theory. The concept of fuzzy soft local function is also introduced and we obtain some of its properties. The basic structure for generated fuzzy soft topologies are also studied here. These concepts are discussed with a view to find new fuzzy soft topologies from original one via fuzzy soft ideals.

**Keywords: ** Fuzzy soft set, fuzzy soft topology, fuzzy soft ideal, fuzzy soft local function.

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Authors |
: | Prabhas Dash |

Title |
: | Triple Mixed Quadrature for Analytic Functions Through Extrapolation |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 253−259 |

**Abstract: ** This paper deals with the mixed quadrature rule of degree of precision eleven for the numerical evaluation of analytic functions through Richardson extrapolation. The numerical results are convergent to the exact results which are tested by taking some suitable texts and also error bound is determined.

**Keywords: ** Mixed quadrature, Analytic functions, Degree of precision, Maclaurin's theorem, Richardson extrapolation, Error bound.

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Authors |
: | R. Rohini and K. Krishnan |

Title |
: | Analysis of Two-Echelon Inventory System With Two Demand Classes With Direct Demand |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 261−271 |

**Abstract: ** This paper deals with a continuous review two-echelon inventory system with two demand classes.. The demand at retailer is of two types. The First type of demand is usual single unit and the second type is of bulk or packet demand. The arrival distribution for single and packet demands are assumed to be independent Poisson with rates $\lambda_{1}\ (>0)$ and $\lambda_{q}\ (>0)$ respectively. The model permits a direct demand of distributor which follows Poisson with rate $\lambda_{d}\ (>0) $. The operating policy at the lower echelon for the (s, S) that is whenever the inventory level drops to `\textbf{s'} on order for $Q = (S-s)$ items is placed, the ordered items are received after a random time which is distributed as exponential with rate $\mu>0$. We assume that the demands occurring during the stock-out period are lost. The retailer replenishes the stock from the distributor which adopts $(0, M)$ policy. The objective is to minimize the anticipated total cost rate by simultaneously optimizing the inventory level at all the equations. The joint probability disruption of the inventory levels at retailer and the distributor are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated. Several instances of numerical examples, which provide insight into the behavior of the system, are presented.

**Keywords: ** Markov Inventory System, Two-echelon, Two demand classes, Cost Optimization, Direct demand.

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Authors |
: | S. Pious Missier and K. M. Arifmohammed |

Title |
: | Functions Associated with $^*g \hat{\alpha}$-Closed Sets in Topological Spaces |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 273−283 |

**Abstract: ** In this paper, we introduce $^*g \hat{\alpha}$-continuous maps and study their relation with various generalized continuous maps. We also discuss certain properties of $^*g \hat{\alpha}$-continuous maps. We then introduce $^*g \hat{\alpha}$-irresolute maps, strongly $^*g \hat{\alpha}$-continuous maps and perfectly $^*g \hat{\alpha}$-continuous maps in topological spaces and some properties of these maps are discussed.

**Keywords: ** $^*g \hat{\alpha}$-closed set, Continuous function, $^*g \hat{\alpha}$-continuous map, $^*g \hat{\alpha}$-irresolute map, strongly $^*g \hat{\alpha}$-continuous map, perfectly $^*g \hat{\alpha}$-continuous map.

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Authors |
: | S. K. Hui, P. Mandal and S. Kishor |

Title |
: | Submanifolds of Generalized Sasakian-space-forms with Respect to Certain Connections |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 285−294 |

**Abstract: ** The present paper deals with some results of submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3}
with respect to semisymmetric metric connection, semisymmetric non-metric connection,
Schouten-van Kampen connection and Tanaka-webster connection.

**Keywords: ** Generalized Sasakian-space-forms, Semisymmetric metric connection, Semisymmetric non-metric connection, Schouten-van Kampen Connection, Tanaka-Webster connection.

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Authors |
: | A. R. Sudamani Ramaswamy and P. Ponmani |

Title |
: | Time Truncated Special Purpose Double Sampling Plan for Weighted Exponential Distribution |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 295−300 |

**Abstract: ** Special purpose Double Sampling Plan DSP (0,1) is developed for a
truncated life test when the life time of an item follows weighted exponential
distribution. The minimum sample sizes are determined when the consumerâ€™s risk and
the test termination time are specified. Tables are constructed and examples are
provided. The Operating Characteristic values are also provided in the table.

**Keywords: ** Double sampling plan, Probability of acceptance, Consumerâ€™s risk,
Truncated life test, Operating Characteristic curve, Weighted exponential distribution.

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Authors |
: | V. T. Chandrasekaran and R. Sangeetha |

Title |
: | Fuzzy Dominating Set |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 301−305 |

**Abstract: ** In this paper, we define effective vertex, vertex effective fuzzy graph, fuzzy dominating set of a fuzzy graph. Some properties of minimum fuzzy dominating set are discussed. Bounds of fuzzy dominating number is also studied.

**Keywords: ** Effective vertex strong arc, strong degree, strong
neighbor, vertex effective fuzzy graph, fuzzy dominating set, minimum fuzzy dominating set.

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Authors |
: | Dhruti B. Joshi and A. K. Desai |

Title |
: | Stability of Finite Difference Formula of Implicit Type for IBVP of Heat Equation |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 307−314 |

**Abstract: ** In the paper entitled ``A Finite Difference Formula of Implicit Type for IBVP of Heat Equation" \cite{Joshi} we have derived a Finite Difference Formula to get numerical solutions of Initial-Boundary Value Problem of Heat Equation. As, we all know that only stable Formulas can give Numerical Solutions which are almost close to the Exact Solution. Here in this paper the stability of the Finite Difference Formula is checked with the help of Eigen Values and using the concept of Diagonalization of matrix.

**Keywords: ** Heat Equation, Solution of First Order Linear PDE, Eigen values, Diagonalization of Matrix, Tridiagonal Matrix.

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Authors |
: | M. Arunkumar, T. Namachivayam, E. Sathya and P. Sentamil |

Title |
: | Generalized Ulam - Hyers - Rassias Stability of Additive - Quadratic Functional Equation in $(\beta;p)-$ Banach Space |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 315−323 |

**Abstract: ** The main aim of this research article is to analyze the generalized Ulam-Hyers-Rassias stability of additive-quadratic functional equation in $(\beta;p)-$ Banach spaces.

**Keywords: ** Additive functional equation, quadratic functional equation, Generalized Ulam-Hyers stability, quasi beta Banach spaces.

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Authors |
: | A. Ponmoni, S. Navaneetha Krishnan and A. Nagarajan |

Title |
: | Lucas Mean Labeling for Some Graphs |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 325−332 |

**Abstract: ** A function $f$ is called Lucas mean labeling of graph $G$ if $f:V\left(G\right)\to\{0,1,2,\dots ,L_{p+q}\}$ is injective and the induced function $f:E\left(G\right)\to\{L_1,L_2,\dots ,L_q\}$ defined as
\[
f^*\left(e=uv\right)=\left\{\begin{array}{ll}
\frac{f\left(u\right)+f(v)}{2}& \hbox{if $f\left(u\right)+f\left(v\right)$ is even} \\
\frac{f\left(u\right)+f\left(v\right)+1}{2}& \hbox{if $f\left(u\right)+f\left(v\right)$ is odd}\end{array}
\right.
\]
is bijective. A graph which admits Lucas mean labeling is called Lucas mean graph. In this paper, we proved for some graphs such as path $P_n$, Twigs $T_n$, $P_n\odot K_1$, the graph obtained by the subdivision of the edges of the path $P_n$ in comb $P_n\odot K_1$, $(C_3\odot K_{1,n})$, $\left\langle C_3, K_{1,n} \right\rangle $, $\left\langle C_3^*, K_{1,n} \right\rangle $, $(3,n)$ kite graph, $B_{m,n}$, $K_{1,n,n}\cup K_{1,m,m} $ are Lucas mean graph.

**Keywords: ** Mean Labeling, Lucas Mean Labeling.

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Authors |
: | B. Meera Devi, R. Vinitha and D. K. Nathan |

Title |
: | $\alpha g\delta$-Continuous and Irresolute Functions |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 333−339 |

**Abstract: ** The purpose of this paper is to define a new class of functions called $\alpha g\delta$-continuous functions. We obtain several characterizations and some their properties. Also we investigate its relationship with other types of generalized continuous functions. Further we introduce and study a new class of function namely $\alpha g\delta$-irresolute.

**Keywords: ** $\alpha g\delta$-closed sets, $\alpha g\delta$-continuous and $\alpha g\delta$-irresolute.

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Authors |
: | Pallavi P. Chopade and Prabha S. Rastogi |

Title |
: | Formulation of Finite Difference Method Algorithm for solution of One Dimensional Systems |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 341−347 |

**Abstract: ** In this paper, algorithm for effective numerical method (finite difference method) is designed for the solution of one dimensional systems (Laplace equation). Finite Difference method with Dirichlet boundary conditions is used to obtain the solutions of differential equations. We have solved one dimensional Laplace equation with analytical and numerical approach. These approaches are developed in MATLAB and their solutions are compared and verified for different step size.

**Keywords: ** Differential equation, Dirichlet boundary condition, Finite Difference method, Laplace equation, Poisson equation.

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Authors |
: | B. Amudhambigai, G. Vasuki and A. Ramya |

Title |
: | A View on Contra-Fr-B-Continuous M-Set Functions in Multiset Topological Spaces |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 349−356 |

**Abstract: ** In this paper, the concepts of Fr-B-open M-sets, contra-Fr-B-continuous M-set functions are studied with necessary examples. In this connection, the concepts of Fr-B-connected M-spaces, Fr-B-normal M-spaces, ultra normal M-spaces, strongly S-closed M-spaces and Fr-B-compact M-spaces are studied. Finally, the applications of contra-Fr-B-continuous M-set functions on various M-spaces are discussed.

**Keywords: ** B-open M-sets, t-open M-sets, Fr-B-open M-sets, contra-Fr-B-continuous M-set functions, Fr-B-connected M-spaces, Fr-B-normal M-spaces, ultra normal M-spaces, strongly S-closed M-spaces and Fr-B-compact M-spaces.

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Authors |
: | Suhrid Saha |

Title |
: | Exploring the Properties of m-bonacci Sequences |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 357−363 |

**Abstract: ** This paper formalized the definition of an m-bonacci sequence, a generalization of the more commonly known Fibonacci and Tribonacci sequences. Four theorems are then introduced to discuss the properties of these sequences and establish a relationship between the terms of the sequence with the related characteristic equation. A generating function is obtained that expresses all the terms of the sequence, and with an elaborate analysis of the function the last theorem-to limit the ratio of consecutive terms to 2-is proved using an alternate method.

**Keywords: ** Number theory, Fibonacci sequences, Mathematical Induction, Generating Functions.

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Authors |
: | A. Victor Devadoss and M. Rekha |

Title |
: | A Study on Gender Inequality in Education by Using Fuzzy Associative Memories |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 365−368 |

**Abstract: ** Education plays a major role for the development of human beings to recognize their rights in terms of social, political and economic growth of the country. More than one-third of women around the world who are illiterate are Indian women. Thus, the inequalities of women in education not only affects the women's lives but also on the economic developments of the country. This papers explores how Gender inequality in education affects the development of the society by using Fuzzy logic as it helps to study the uncertainties with the help of appropriate Fuzzy model.Here Section one deals with Introduction. Section two gives definitions of Fuzzy Associative Memories. Section three description of the problem is explained. Section four deals with the adaptation of the problem. Ultimately section five reveals the conclusion.

**Keywords: ** Fuzzy Associative Memories, Gender inequality, Education.

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Authors |
: | Vadivelan Urkalan, Thomas Rosy and S. Sunil Varma |

Title |
: | Radius Problem for Subclasses of Harmonic Univalent Functions |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 369−375 |

**Abstract: ** Let $f=h+\bar{g}$ be harmonic functions in the unit disk $D=\left\{z\in \mathbb{C}:\left|z\right| < 1\right\}$ normalized by $f(0)=0=f_{z} (0)-1$. In this paper we find the radius of the Goodman-Ronning type starlikeness and convexity of $D_{f}^{\varepsilon } =zf_{z} -\varepsilon \bar{z}f_{\bar{z}} \,\, (\left|\varepsilon \right|=1)$, when the coefficients of $h$ and $g$ satisfy the harmonic Bieberbach coefficients conjecture conditions.

**Keywords: ** FUnivalent functions, Harmonic functions, Goodman-Ronning type functions.

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Authors |
: | Sushomita Mohanta |

Title |
: | $\Delta^{m}$-lacunary Statistical Convergence of Order $\alpha$ Defined by a Modulus Function |

Volume, Issue, Year |
: | 6(3)(2018) |

Pages |
: | 377−385 |

**Abstract: ** In this paper, we introduce the concepts of lacunary $\Delta^{m}$-statistically
convergent sequence of order $\alpha$ and strongly
$N_{\theta}^{\alpha}(\Delta^{m},f,p)$-summable sequences of order $\alpha$
are introduced. Some inclusion relations between the set of lacunary
$\Delta^{m}$-statistically convergent sequences of order $\alpha$
and strongly $N_{\theta}^{\alpha}(\Delta^{m},f,p)$-summable sequences
of order $\alpha$ and the relations between two arbitrary lacunary
sequences are discussed.

**Keywords: ** Statistical convergence, Lacunary sequence, Lacunary refinment, modulus function.