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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