# RAIMS 2017- Recent Advances in Mathematical Sciences

"RAIMS-2017 Conference Papers "

**Some Properties of the Lattice of Convex Edge Setsofa Connected Directed Graph****[Full-Text ]**

Asha Saraswathi B. And Lavanya S.Let G be a connected directed graph and E(G) be the directed edge set of G. A subset C of E(G) is said to be convex if for any e_i (,e)_j "∈"C , there is a directed path containing e_i (,e)_j and the edge set of every e_i-e_j geodesic is contained in C. Let Con(G) be the set of all convex edge sets of G together with empty set partial ordered by set inclusion relation. Then Con(G) forms a lattice if and only if G has an Euler trial. In this paper cardinality of the lattice Con(G) is discussed. Also some of the properties of the lattice Con(G) are studied.

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**Double Diffusive Phenomenon in a Gravity Modulated Environment****[Full-Text ]**

Dr. H.G. Deepak, Prof. Dr. P.K.SrimaniAnalytical investigation of onset of double diffusive convection in a two component two phase system under gravity modulation to study the effects of salinity gradient and temperature gradient ; the gradients are of opposite nature employing the method of normal mode and the modified perturbation technique is presented. Analysis is carried out for Viscous , Brinkmann and Darcy models by deriving solvability condition and computing the first non - zero correction to the Rayleigh number. Possibility of enhancing or suppressing convection by suitable choice of the governing parameters is studied.

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**Evaluation of Reliability Parameters of a Double Unit Repairable System with Preventive Maintenance under Warranty****[Full-Text ]**

Dr.M.Gayathri, Dr. S. Sree LakshmiThis paper presents Evaluation of Reliability Parameters of a Double Unit Repairable System with Preventive Maintenance under Warranty. If the Unit under goes PM and works as new after PM. There is a single repairman who always remains with the system. The failure time of the system follows negative exponential distribution while PM and repair time distributions are taken as arbitrary. Supplementary variable technique is adopted to derive the expressions for Reliability, Mean time to system failure and Availability. To highlight the behaviour of Reliability numerical results are considered for particular values of various parameters.

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**A Graph Theory Algorithm To Find Shortest Path In Routing Protocol****[Full-Text ]**

Hamela KIn Computer Networks, routing protocol performs the task of communicating between the nodes and the way to establish path be-tween the two nodes. It also has a responsibility of sharing information among the entire network from the source location to the destination location. For this to achieve, the route connected between source node to destination node is to be found. There are various algorithms to find the path between the two nodes. But we focus on finding the route between source to the destination node through shortest path. The main emphasis of this paper is to find the shortest path between the source node and destination node in Open Shortest Path First Protocol(OSPF) using Dijkstra’s graph theory algorithm.

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**A Study on Graph Coloring****[Full-Text ]**

Bharathi S NThe Swiss Mathematician Leonhard Euler is considered as the Father of Graph theory. Today graph theory has matured into a full-fledged theory from a mere collection of challenging games and interesting puzzles. Peculiarity of Graph theory is that it depends very little on other branches of Mathematics and is independent in itself. Graph coloring enjoys many practical applications as well as theoretical challenges. Graph coloring is still a very active field of research. This paper consists of III Sections. Section I involves Introduction to Graph theory and Introduction to Graph Coloring. Section II is Vertex Coloring and Upper Bounds: in which Chromatic Polynomials and Chromatic Partitioning, Properties of Chromatic Numbers, Color Class, some important Theorems, Propositions, are discussed. In Section III Edge Coloring, Enumerative Aspects are discussed.

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**Deriving Vertices, Shape Functions for Elliptic Duct Geometry and Verified Two Verification Conditions****[Full-Text ]**

Dr. P. Reddaiah, Prof. D.R.V. Prasada RaoIn this paper we derived vertices for elliptic duct geometry and derived shape functions for elliptic duct geometry and verified the conditions that sum of all the shape functions is equal to one and each shape function has a value of one at its own node and zero at the other nodes.

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**Fuzzification of Gamma-semigroups satisfying the identity the****[Full-Text ]**

SHASHIKUMAR.H.C., Dr.T.RAMI REDDYIn this paper, we consider some properties and characterizations of fuzzy - ideals and fuzzy bi - ideals of - semi groups and investigate some of their properties. We also characterize the properties related to - semi groups and Fuzzy - ideals using an identi-ty .

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**Effect of Rayleigh number and buoyancy ratio on heat and mass transfer in an inclined parallelo-grammic porous enclosure in the presence of magnetic field and heat source****[Full-Text ]**

Jagadeesha R D, B M R Prasanna, M. SankarA numerical investigation of the double diffusive natural convection in an inclined porous parallelogrammic enclosure has been performed in this paper. The vertical sloping sidewalls of the enclosure are maintained at different, uniform temperatures and concentrations, while the top and the bottom walls are kept as insulated and impermeable. In addition, the enclosure contains a heat source and a constant magnetic field is applied in the horizontal direction. The governing equations are modeled and are solved using an implicit finite difference method. The numerical algorithm used in the present analysis has been validated and is in good agreement with different benchmark solutions available in the literature. Detailed numerical computations are performed for wide range of Rayleigh numbers, and buoyancy ratio. It is found that the streamlines, isotherms, isoconcentrations and average Nusselt and Sherwood numbers are significantly altered by varying the Rayleigh number and buoyancy ratio.

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**Solution of Heat equation using Adomian Decomposition Method****[Full-Text ]**

Krishna B. ChavaraddiIn this paper, the Adomian Decomposition Method (ADM) is applied to some parabolic (heat) equations subjected to the initial and non-local boundary conditions to obtain the approximate solution. The method shows an accurate and efficient technique in comparison with existing exact solutions.

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**Mathematical Modelling of Air Pollutants Emitted from a Line Source with Chemical Reaction and Mesoscale Wind****[Full-Text ]**

Krishna S, Lakshminarayanachari K, Pandurangappa CA mathematical model for air pollutants emitted from a line source along with the mesoscale wind and chemical reaction is presented. The Crank-Nicolson finite difference scheme is employed to solve the model numerically. The realistic forms of large-scale, mesoscale wind velocities and eddy diffusivity profiles are used in the model. The results have been analysed for the dispersion of air pollutants for stable and neutral conditions of the atmosphere in the presence of mesoscale wind. The effect of mesoscale wind on pollutants is non-uniform over the simulated urban region and the effect of chemical reaction decreases the concentration of pollutants everywhere.

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**Radiation effect on Non-Darcy Convective Heat Transfer through a porous medium in a vertical channel with heat generating source****[Full-Text ]**

P.Raveendra Nath, S.T.Dinesh Kumar ,N.B.V.Ramadeva PrasadIn this study the effect of radiation on the Non-Darcy convection heat transfer flow of a viscous electrically conducting fluid through a porous medium confined in a vertical channel investigated by taking into account both heat generating source and Radiation effect in the presence of heat sources. The non-linear, coupled equations governing the flow and heat transfer have been solved by employing a perturbation technique with Î´ the porous parameter as perturbation parameter. The velocity and temperature dissipation are analysed for different values of G,D-1, , and M .From the analysis, new expressions for Nusselt number and Shear Stress on the walls are numerically evaluated for different sets of parameters

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**Mathematical Model for Future Population Scenario In India And China â€“ An Econometric Approach****[Full-Text ]**

Dr. G. Michael Rosario, Dr. M. James AntonyMathematical modeling is a broad interdisciplinary science that uses mathematical and computational techniques to model and elucidate the phenomena arising in life sciences. A mathematical model including dynamical systems, statistical models and differential equations involves variety abstract structures. Population growth is one of the main issues in India and China which are located in Asia. These two countries are over populated and the growth in resources has not been keeping pace with the growth in population. So the increasing trend in population is great threat to the nations. The use of the logistic growth model is widely established in many fields of modeling and forecasting . In this paper, we will determine the carrying capacity and the vital coefficients governing the population growth of India and China. Further this study gives an insight on how to determine the carrying capacity and the vital coefficients, governing population growth, by using the least square method. Future Population growth rates and Global ranks of India and China are predicted.

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**Fourier Analysis of Equation of Centre ****[Full-Text ]**

Shailaja M, Vanaja V, S Balachandra RaoIn Indian astronomy, the heavenly bodies were assumed to move around the Sun in a circular orbit with uniform angular velocities. But by observation it was found that these motions were not uniform, hence some corrections were devised to obtain the true positions of planet.

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**A Hamiltonian Approach for a Traveling Salesman****[Full-Text ]**

Shyamala VenkatramanIn this modern era, various applications of Hamiltonian’s graph have come into existence and serve as very good measures over a large class of optimization problems. The Travelling Salesman Problem (TSP) is a problem in combinatorial optimization studied in operation research and theoretical computer science. Given a list of cities and their pair wise distances, the task is to find a shortest possible tour that visits each city exactly once. This paper analyzes various types of algorithms such as The nearest Neighbor Algorithm to find a (reasonably good) Hamiltonian cycle, Lower Bound Algorithm to find a lower bound for a Hamiltonian cycle , Tour Improvement Algorithm to look for possible improvement in the tour etc. In this research paper, we have taken a locality in Meghalaya state which is under development, having lesser main resources viz. roadways, telecome links etc.

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**On Meromorphic Solutions of a Certain Type of System of Complex Differential â€“Difference equations****[Full-Text ]**

A. TanujaIn this article, we study meromorphic solutions of the type of system of complex differential and difference equation of the following form

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**Application of Mathematics to Eclipse Analysis****[Full-Text ]**

Vanaja.V, Shailaja.M, S. Balachandra RaoEclipses are astronomical aspects occurs in nature periodically. The two types of eclipses are lunar and solar eclipses. The computation of occurrence and periodicity of these eclipses are based on the positions (longitudes) of the celestial bodies, namely the Sun, the Moon and the Earth. Geometrically the ‘conjunction’ of the Sun and the Moon refers to solar eclipse and ‘opposition’ of the Sun and the Moon refers to lunar eclipse. To find the occurrence of eclipse different mathematical methods are used. In Indian classical siddhÄntic texts eclipse computation is based on the true positions (longitudes) of the Sun, the Moon and the ascending or the descending node, in Indian parlance it is called RÄhu or Ketu. Modern computation of eclipse is based on the International Astronomical Union terms (IAU). Both Indian and Modern computation of eclipses are mathematically compared and analyzed.

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**Mathematical Modelling of Transport of Pollutants in Unsaturated Porous Media for One-Dimensional Flow ****[Full-Text ]**

Shobhankumar D.M. and Vijayalakshmi A.R.Contaminants containing different chemicals will pass through different hydro geologic zones as they migrate through the soil to the water table. The water table is the upper surface of the groundwater system. The pore space between soil particles above the water table are occupied by both air and water. Flow in this unsaturated zone is taken to be vertically downward, as liquid contaminants or solutions of contaminants and precipitation move under the force of gravity. The upper most region of the soil, the unsaturated zone, is the site of important process leading to pollutant attenuation. In responding to the growing concern over deteriorating groundwater quality, groundwater flow models are rapidly coming to play a crucial role in the development of protection and rehabilitation strategies. These models provide forecasts of the future state of the groundwater aquifer systems.The objective of the present work is to demonstrate how mass transport, flow of pollutants and other technologies can be applied to define the behaviour of pollutants in the unsaturated and saturated soil zones. The present study is concerned with the development of analytical models for unsaturated and saturated flow behaviour in soils.

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