This paper deals with the implementation of Adomian Decomposition Method (ADM) to solve the optimal control problem of linear time invariant singular systems with a quadratic cost functional. The idea is that the states and the input are expressed in terms of ADM. The method simplifies the system of state equations into a set of algebraic equations which can be solved using a digital computer. Illustrative example is included to demonstrate the validity and applicability of the technique.Mathematics Subject Classification: 65L05, 65L80

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The binary quadratic Diophantine equation 8 17 2 2   x y is analyzed for its non-zero distinct integral solutions. A few interesting relations among the solutions are given. Further, employing the solutions have obtained solutions of other choices of hyperbolas and parabolas.

This paper concerns with the problem of obtaining many Pythagorean triangles where, in each Pythagorean triangle, the expression Leg a H Perimeter Area * 2   is represented by a Harshadd number, Multiple Harshad number and Nivenmorphic number respectively. Also, we present the number of primitive and non-primitive Pythagorean triangles.