We study reachability problems for various nondeterministic polynomial maps in Z n . prove that the problem very simple three-dimensional affine (with independent variables) is undecidable and PSPACE -hard both two-dimensional one-dimensional quadratic maps. Then we show complexity of without functions form ± x + a 0 lower. In this case any dimension if not fixed, then -complete. Finally extend...

let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

We discuss four eigenvalue problems of increasing generality and complexity: rooting a univariate polynomial, solving the polynomial problem, set multivariate polynomials multi-parameter problems. In doing so, we provide unifying framework for these problems, where exploit properties (block-) (multi-) shift-invariant subspaces use multi-dimensional realization algorithms.

We present in this paper general pseudo-polynomial time algorithms to solve min-max and min-max regret versions of some polynomial or pseudo-polynomial problems under a constant number of scenarios. Using easily computable bounds, we can improve these algorithms. This way we provide pseudo-polynomial algorithms for the min-max and and min-max regret versions of several classical problems includ...

This is the final article in a series of four articles. Richard Karp has proven that a deterministic polynomial time solution to K-SAT will result in a deterministic polynomial time solution to all NP-Complete problems. However, it is demonstrated that a deterministic polynomial time solution to any NP-Complete problem does not necessarily produce a deterministic polynomial time solution to all...

a class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. convergence anal...