Integral Geometry and Real Zeros of Thue - Morse Polynomials

Integral Geometry and Real Zeros of Thue-Morse Polynomials

On the real roots of generalized Thue-Morse polynomials

In this article we investigate real roots of real polynomials. By results of M. Kac 8, 9, 10] we know that a polynomial of degree n has in average 2 log n real zeros. See also results of Edelman and Kostlan 5] on the same subject. Some 10 years later Erdds and OOord 7] proved that the mean number of real roots of a random polynomial of degree n with coeecients 1 is again 2 log n: This leads us ...

Acoustic Wave propagation through multilayer Thue-Morse structures containing two, three and four materials of Cu, Al, MgO and Pb

In this paper, the acoustic wave propagation in multilayer Thue-Morse structures has theoretically been studied. The composing layers were assumed do be Cu, Al, Mgo and Pb materials. Two, three or four different materials have been used in a typical structure. By using a perpendicular incident acoustic wave, the transmission coefficient was calculated and then by its old, the frequency gaps was...

Domain of attraction of normal law and zeros of random polynomials

Let$ P_{n}(x)= sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraicpolynomial, where $A_{0},A_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. Thus $A_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}H_{j}(t)}$, where $H_j(t)$'s are complex slowlyvarying functions.Under the assumption that there exist ...

On Sums of Powers of Zeros of Polynomials

Due to Girard’s (sometimes called Waring’s) formula the sum of the r−th power of the zeros of every one variable polynomial of degree N , PN (x), can be given explicitly in terms of the coefficients of the monic P̃N (x) polynomial. This formula is closely related to a known N − 1 variable generalization of Chebyshev’s polynomials of the first kind, T (N−1) r . The generating function of these po...