Research Article On the Lower Bound for the Number of Real Roots of a Random Algebraic Equation

An Lower Estimate for the Number of Level Crossing of a Random Algebraic Curve when the Coefficients follow Semi-Stable Distribution

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 .

On Classifications of Random Polynomials

 Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...

On the Number of Real Roots of a Random Algebraic Equation

1 . SOME time ago Littlewood and Offordt gave estimates of the number of real roots that an equation of degree n selected at random might be expected to have for various classes of equations in which the coefficients were selected on some probability basis . They found that, when each coefficient was treated on the same basis, the results were practically the same in all cases considered and ag...

On the average number of sharp crossings of certain Gaussian random polynomials

ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...