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Category: Volume 25

Further characterization of induced paired domination number of a graph

G. MAHADEVAN1, A. NAGARAJAN2, A. RAJESWARI3 and SELVAM AVADAYAPPAN4

ABSTRACT:

A set S  V is a induced -paired dominating set if S is a dominating set of G and the induced subgraph is a perfect matching. The induced – paired domination number ip(G) is the minimum cardinality taken over all paired dominating sets in G. The minimum number of colours required to colour all the vertices so that adjacent vertices do
not receive the same colour and is denoted by (G). The authors4characterized the classes of graphs whose sum of induced paired domination number and chromatic number equals to 2n 6, for any n  4.

In this paper we extend the above result and characterize the classes of all graphs whose sum of induced paired domination number and chromatic number equals to 2n – 7, for any n  4.

KEYWORDS: Paired domination number, Chromatic number


A set S  V is a induced -paired dominating set if S is a dominating set of G and the induced subgraph <S> is a perfect matching. The induced –...

MHD flow of a conducting visco-elastic Rivlin- Ericksen (1955) fluid through porous medium in a long uniform rectangular duct due to an impulsive pressure gradient acting at the central part of a section

ANIL TRIPATHI*, A. K. SHARMA* and K.K. SINGH**

ABSTRACT:

The aim of present problem is to study the unsteady flow of a conducting visco-elastic Rivlin-Ericksen10 type fluid through porous medium in a long uniform rectangular duct under the influence of an impulsive pressure gradient acting at the central part of a section and uniform magnetic field applied normally to the flow of fluid. The analytical expressions for velocity profile and flux have been determined by the application of transform technique. Some particular cases have been
discussed in detail. The results for the flow of ordinary viscous fluid have also been deduced by taking parameter

KEYWORDS: unsteady flow


The aim of present problem is to study the unsteady flow of a conducting visco-elastic Rivlin-Ericksen10 type fluid through porous medium in a long uniform rectangular duct under the influence of...

Some Identities Involving Common Factors of Negafibonacci and Lucas Numbers

SANJAY HARNE1, V.H. BADSHAH2 and SAPNA SETHIYA3

ABSTRACT:

In this paper we present some identities involving common factors of Negafibonacci and Lucas numbers. Binet’s formula of Negafibonacci will employ to obtain the identities.

KEYWORDS: Fibonacci numbers,Negafibonacci numbers, Binet’s formula.


In this paper we present some identities involving common factors of Negafibonacci and Lucas numbers. Binet’s formula of Negafibonacci will employ to obtain the identities.

LRS Bianchi Type II Bulk Viscous Stiff Fluid Cosmological Models with Variable G and Λ

GAJENDRA PAL SINGH1 and ATUL TYAGI2

ABSTRACT:

We have investigated the Bianchi type II bulk viscous stiff fluid cosmological models with variable gravitational constant G and cosmological constant Λ. To obtain the deterministic model, we have assumed that the expansion θ in the model is proportional to the shear σ. Various physical and geometrical features of the models are also discussed.

KEYWORDS: Bianchi Type-II, Stiff fluid, Bulk viscosity, Variable Λ, Variable G.


We have investigated the Bianchi type II bulk viscous stiff fluid cosmological models with variable gravitational constant G and cosmological constant Λ. To obtain the deterministic model, we have assumed that the...

On 0g – Homeomorphism in topological spaces

1MANOJ GARG, 2MRADUL DIXIT and 2P.K. TRIPATHI

ABSTRACT:

In this paper we introduce a new class of closed maps namely 0g -closed maps which settled in between the class of g*-closed maps12 and the class of gs-closed maps12. We also introduce and study new class of homeomorphisms called 0g -homeomorphisms and 0g *- homeomorphisms. Further we show that the set of all 0g*-homeomorphisms form a group under the operation composition of maps.

KEYWORDS: 0g-closed maps; 0g *-closed maps; 0g *-homeomorphisms.


In this paper we introduce a new class of closed maps namely 0g -closed maps which settled in between the class of g*-closed maps12 and the class of gs-closed maps12. We also...

Variable Selection for Multivariate Survival data

1A. LOKESHMARAN* and 2R. ELANGOVAN

ABSTRACT:

It is assumed for the Cox’s proportional hazards model that the survival times of subjects are independent. This assumption might be violated in some situations, in which the collected data are correlated. The well-known Cox model is not valid in this situation because independence assumption among individuals is violated. For this purpose Cox’s proportional hazard model is extent to the analysis of multivariate failure time data, which includes frailty models and marginal model. In this paper frailty and marginal hazard models are discussed using nonconcave penalized likelihood approach. Detailed illustrations are also provided.

KEYWORDS: Cox’s Proportional Hazards Model, Multivariate Failure Time Data, Frailty Model, Marginal Model, Nonconcave Penalized Likelihood Approach.


It is assumed for the Cox’s proportional hazards model that the survival times of subjects are independent. This assumption might be violated in some situations, in which the collected...

Viscous Fluid Cosmological Model with Two Degrees of Freedom in General Relativity

RAJ BALI1, MAHESH KUMAR YADAV2 and VIMAL CHAND JAIN3

ABSTRACT:

Viscous fluid cosmological model with two degrees of freedom is investigated. We assume the coordinates to be comoving. In presence of viscosity our model is non-degenerate Petrov Type- I. There is a real physical singularity at T=0. Moreover in the absence of viscosity, we get the stiff fluid case. Some significant physical and geometrical aspects
of the model are also discussed.

KEYWORDS: Viscous Fluid cosmology, Cylindrically symmetric metric with two degrees of freedom


Viscous fluid cosmological model with two degrees of freedom is investigated. We assume the coordinates to be comoving. In presence of viscosity our model is non-degenerate Petrov Type- I. There is...

Analytical solution of Burgers-like equation

S.M. KUMBHAR and SARITA THAKAR

ABSTRACT:

In this paper we determine optimal system for one-dimensional Burgers-like equation, Lie group analysis is used to obtain invariant vector fields of one-dimensional Burgers-like equation. These invariant vector fields forms the Lie algebra. Certain choice of invariant vector field defines the transformation to convert the equation into a solvable partial differential
equation. With help of adjoint representation table one-dimensional optimal system is obtained.

KEYWORDS: invariant vector fields, optimal system of Lie subalgebras.


In this paper we determine optimal system for one-dimensional Burgers-like equation, Lie group analysis is used to obtain invariant vector fields of one-dimensional Burgers-like equation. These invariant vector fields forms the Lie algebra....

On studying antibiotic in the bloodstream by the method of dynamical model

R. SOPHIAPORCHELVI1 and R. VANITHA2

ABSTRACT:

Primarily the antibiotics-the group drugs intended to inhibit or destroy bacteria, should be used only against bacterial infection. The antibiotic Norfloxacin is prescribed for treating bacterial infections, including urinary tract infections, prostatitis, and gonorrhea infections of the urethra or cervix. This antibiotic works to kill bacteria by interfering
with specific enzymes, which prevents the bacteria from multiplying. When taking an antibiotic, it is important to keep the amount of the bloodstream fairly constant. If the amount gets too low, they can begin to regrow. If the amount gets too high, it could cause other Complications. In this paper, a dynamical model has been constructed to find the amount
of the Norfloxacin in the blood stream.

KEYWORDS: Antibiotic, Half-life period of the drug, dosage of the drug, Discrete Dynamical system


Primarily the antibiotics-the group drugs intended to inhibit or destroy bacteria, should be used only against bacterial infection. The antibiotic Norfloxacin is prescribed for treating bacterial infections, including urinary tract infections, prostatitis,...

Stochastic model to determine the optimal manpower reserve at four nodes in series

1R. ARULPAVAI and 2R. ELANGOVAN

ABSTRACT:

The purpose of manpower planning is to best match future manpower demand and supply in the light of multiple objectives such as economic conditions, production/scale trends, people skills inventory, government regulations, as well as organization history and policies regarding personnel hearing, training, promotion, firing and retirement. One of the essential components of a manpower planning system is manpower forecasting, the process of anticipating the future size and nature of the manpower force. Stochastic models have been widely used in the study of manpower systems with different modes in series like training, promotion, placement, etc. There are many industries and organizations where the skilled personnel are to be recruited and they must be given prior training before employment. In human resource planning the training and induction of the right type of personnel is a pressing problem. In this paper, we consider the optimal solution for the manpower to be kept as reserve inventory at four different nodes in series. Two different models have been discussed. Numerical illustrations are provided using simulation studies.

KEYWORDS: Human Resource Planning, Reserve Inventory and Optimal Solution.


The purpose of manpower planning is to best match future manpower demand and supply in the light of multiple objectives such as economic conditions, production/scale trends, people skills inventory,...