iosr-Jm   Volume-3 ~ Issue-2

Abstract :This paper proposed fast Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L) iterative method for solving path planning problem for a mobile robot operating in indoor environment model. It is based on the use of Laplace's Equation to constraint the distribution of potential values in the environment of the robot. Fast computation with half-sweep iteration is obtained by considering only half of whole points in the configuration model. The inclusion of SOR and 9-point Laplacian into the formulation further speeds up the computation. The simulation results show that HSSOR9L performs much faster than the previous iterative methods in computing the potntial values to be used for generating smooth path from a given initial point to a specified goal position.
Keywords - Robot path planning, Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L), Laplace's Equation, Harmonic functions

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Abstract :There are well known formulas approximating the circumference of the Ellipse given in different periods in history. However there lacks a formula to calculate the Arc length of a given Arc segment of an Ellipse. The Arc length of the Elliptical Arc is presently given by the Incomplete Elliptical Integral of the Second Kind, however a closed form solution of the Elliptical Integral is not known. The current solution methods are numerical approximation methods, based on series expansions of the Elliptical Integral. This paper introduces a Geometric Method (procedure) to approximate the Arc length of any given Arc segment of the ellipse. An analytical procedure of the defined geometric method is detailed.

[1] Wikipedia Article: Ellipse
[2] Wikipedia Article: Elliptic integral
[3] Wikipedia Article: Trigonometric functions:
[4] Wikipedia Article: Eccentric Anomaly
[5] Wikipedia Article: Elliptical Integral
[6] Appendices
[7] Appendix A: Determine the side of an Isosceles Triangle given the Angle opposite to the Base and Base length
[8] Appendix B: Approximating the Incomplete Elliptical Integral of Second Kind
[9] Appendix C: Sample Problem & Solution Algorithm

Abstract :Agriculture is the back bone of Indian economy and provides livelihood to about 70 percent of the population and about one third of our national income gets generated in this sector. After independence, in early years, there was a problem of a food shortage. The position at the food front became a matter of concern in the early sixties. To meet the situation efforts were made to develop the agriculture sector of the economy. Toward the mid of sixties the new agriculture technology emphasizing the use of fertilizer and irrigation, ushered an era popularly could as green revaluation. However it was confined to few states and few crops. In present state, the nation's objective is not only to increase the food grain production but also to increase the employment ventures. While individual farmer may be interested in maximizing his cash income risks aversion etc. The mathematical programming approach to the modeling of agricultural decisions rests on certain basic assumptions about the situation being modeled and the decision maker himself. One fundamental assumption is that the decision maker (DM) seeks to optimize a well defined single objective. In reality this is not the case, as the DM is usually seeking an optimal compromise amongst several objectives, many of which can be in conflict, or trying to achieve satisfying levels of his goals. For instance, a subsistence farmer may be interested in securing adequate food supplies for the family, maximizing cash income, increasing leisure, avoiding risk etc. but not necessarily in that order. Similarly a commercial farmer may wish to maximize gross margin, minimize his indebtedness, acquire more land, reduce fixed costs etc.
Keywords - Decision Making, Optimization, Mathematical programming, Minimization & maximization

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Abstract :TIn the present paper the concept of qpI-Irresolute mappings have been introduced and studied.
Keywords - Ideal bitopological spaces, qpI- closed sets, qpI- open sets and qpI- Irresolute mappings AMS Subject classification 54A05, 54C08

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Abstract :Various kinds of deterministic models for the spread of infectious disease have been analyzed mathematically and applied to control the epidemic. A vaccine is a biological preparation that improves immunity to a particular disease. In this paper, a deterministic model for the dynamics of an infectious disease in the presence of a preventive vaccine and natural death rate is formulated. The model has various kinds of parameter. In this paper, we try to present a model for the transmission dynamics of an infectious disease In order to control the epidemic by changing the value of the parameters. AMS: 92C60, 92D30, 92B05, 92D25.
Keywords - Basic reproduction number, diseases free equilibrium, Infectious diseases, Stability analysi

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London. Series A, Vol. 115 (1927), pp. 700–721.
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Abstract :The aim of this work is to find the Ehrhart polynomial for a certain type of a convex polytope and the Ehrhart polynomial for the dual of these polytopes together with a comparison between them; two theorems that related with the number of lattice points and the volume are also given. Different examples are presented in order to demonstrate our results.
Keywords - Ehrhart polynomial, dual,polytope.

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Abstract :The governing equations for the description of turbulence with reacting and mixing n-chemical elements described by R. S. Brodkey 1 and E. E. O'Brien 2 are considered. For convenience, we consider a turbulent reaction mixture with two reacting and mixing chemical elements A and B. The reactions are irreversible, isothermic, second order and the type of reactions is A+B→ Product. A brief account of derivation of the equations describing the dynamics of the energy spectrum density functions for the velocity field and the concentration fields A and B derived on using Lewis-Kraichnan 3 space-time version of the Hopf 4 functional formalism and multiple-scale-cumulant-expansion method is given. The equations for spectrum functions of the velocity field and the concentration fields derived on employing multiple-scale-cumulant-expansion method by Joshi N. E. and Meshram M. C. 5 are considered. The equations for spectrum functions are rewritten by using a modified-zero-fourth-order-cumulant-expansion (MZFOCE) approximation method which are first written in dimensionless form and then integrated numerically. The numerical values of the energy of velocity field as well as that of concentration fields are obtained. These values are used to evaluate the statistical quantities describing the turbulence with reacting and mixing chemical elements for large Reynolds numbers up to R=106 .The quantities include energy transfer functions of concentration fields , enstropy of the concentration fields, skewness of concentration fields, dissipation energy of concentration fields and Taylor's micro-scales for concentration fields. We present these in the form of graphs for the representative values of Reynolds number R=104 and R=106.The analysis of the numerical values of statistical parameters thus obtained is carried out and the laws governing these quantities are investigated. Also, we discuss the merits and scope of the present closure scheme for studying similar types of turbulent flows.
Keywords - Hopf functional formalism, Cumulants, Multiple scales, Turbulence with reacting and mixing chemical elements

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