Present work of this paper deals with the unification classical polynomials in which we have defined a generalized polynomial set analogous to that associated Legendre P (x) m n by taking 5the use Operator. Also derived explicit form, Operational Formulae generating functions for function.

When engineering an automated planning model, domain authors typically assume a static, unchanging ground-truth world. Unfortunately, this assumption can clash with reality, where domain changes often rapidly occur in best practices, effectors, or known conditions. In these cases, remodeling the domain causes domain experts to ensure newly captured requirements integrate well with the current m...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

economists were interested in economic stabilization policies as early as the 1930’s but the formal applications of stability theory from the classical control theory to economic analysis appeared in the early 1950’s when a number of control engineers actively collaborated with economists on economic stability and feedback mechanisms. the theory of optimal control resulting from the contributio...