Statistical Condition Estimation for the Roots of Polynomials

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)+...

A Statistical Analysis of the Numerical Condition of Multiple Roots of Polynomials

Some new families of definite polynomials and the composition conjectures

The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...

Rotor Sizing of Helicopters Using Statistical Approach

This paper is concerned with the statistical model development issues, necessary for rapid estimation of the rotor sizing for single main rotor helicopters at the preliminary design stage. However, Central Composite Design (CCD) method, simulation-based data collection, linear regression analysis, mathematical modelsdevelopmentand validations through the analysis of variance (ANOVA) were perfor...

A Robust Distributed Estimation Algorithm under Alpha-Stable Noise Condition

Robust adaptive estimation of unknown parameter has been an important issue in recent years for reliable operation in the distributed networks. The conventional adaptive estimation algorithms that rely on mean square error (MSE) criterion exhibit good performance in the presence of Gaussian noise, but their performance drastically decreases under impulsive noise. In this paper, we propose a rob...