Max-algebra, where the classical arithmetic operations of addition and multiplication are replaced by a ⊕ b := max(a, b) and a ⊗ b := a + b offers an attractive way for modelling discrete event systems and optimization problems in production and transportation. Moreover, it shows a strong similarity to classical linear algebra: for instance, it allows a consideration of linear equation systems ...

In this paper, we present a characteristic set method to solve polynomial equation systems in the finite field F2. Due to the special property of F2, the given characteristic set methods are much more efficient and simpler than the general characteristic set method. We also use our methods to solve equations raised from cryptanalysis of stream ciphers based on nonlinear filter generators.

Let ( ) ( ) ( ) ( ) be a sequence of mutually independent, identically distributed random variables following semi-stable distribution with characteristic function ( ( ) ) . In this work, we obtain the lower bound of the number of real zeros of the random algebraic equation∑ ( ) . ( ) denote the number of real roots must ( ⁄ ) , except for a set of measure at most .

This paper proposes a new index to determine the static voltage stability of the load buses in a power network for certain operating conditions and hence identifies load buses which are close to voltage collapse. The proposed index is formulated from the quadratic equation derived from a twobus network and is computed using the apparent power and the line impedance. The proposed index shows how...

Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9 or less, Positivity is decidable, with complexity in the Counting Hierarchy.