ABSENCE OF POSITIVE ROOTS OF SEXTIC POLYNOMIALS
نویسندگان
چکیده
منابع مشابه
Roots of polynomials with positive coefficients
We describe the limit zero distributions of sequences of polynomials with positive coefficients. We also characterize the polynomials with real coefficients for which some power has positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.
متن کاملImproved Computation of Bounds for Positive Roots of Polynomials
A new lower bound for computing positive roots of polynomial equations is proposed. We discuss a twostage algorithm for computing positive roots of polynomial equations. In the first stage, we use the continued fraction method based on Vincent’s theorem, which employs the lower bound of real roots, for isolating the positive roots into intervals. In the second stage, we apply a bisection method...
متن کاملSextic anharmonic oscillators and orthogonal polynomials
Under certain constraints on the parameters a, b and c, it is known that Schrödinger’s equation −d2ψ/dx2 + (ax + bx + cx)ψ = Eψ, a > 0 with the sextic anharmonic oscillator potential is exactly solvable. In this article we show that the exact wave function ψ is the generating function for a set of orthogonal polynomials {P (t) n (x)} in the energy variable E. Some of the properties of these pol...
متن کاملSize Optimization of Sextic Polynomials in the Number Field Sieve
The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some methods to optimize the size property of sextic polynomials.
متن کاملconstruction of vector fields with positive lyapunov exponents
in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2011
ISSN: 1027-5487
DOI: 10.11650/twjm/1500406488