We present a useful formula for the expected number of maxima of a normal process ξ(t) that occur below a levelu. In the derivation we assume chiefly that ξ(t), ξ(t), and ξ(t) have, with probability one, continuous 1 dimensional distributions and expected values of zero. The formula referred to above is then used to find the expected number of maxima below the level u for the random algebraic p...

We build a new kind of random polynomial model, Massive Algebraic System (MAS), which is equivalent to algebraic polynomial system in solvability. This model focused on Finite Fields, especially on Z2, is NPcomplete. By results of Population Dynamics, we find these systems undergo 1-Replica Symmetry Breaking (1RSB) and high order Replica Symmetry Breaking. This phenomenon indicates subtle struc...

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field