Energy balance method EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the firstand second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreemen...

We present a construction of nested spaces of C2 macro-elements of degree 5 on triangulations of a polygonal domain obtained by uniform refinements of an initial triangulation and a Powell-Sabin-12 split.

We develop a general classification theory for Brumer’s dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.

We study standing wave solutions in a parabolic partial diierential equations which consists of a cubic-quintic equation stabilized by global coupling A 2 (y) dy : We classify the existence and stability of all posssible standing wave solutions.

We present efficient algorithms to construct both C1 and C 2 smooth meshes of cubic and quintic A-patches to approximate a given polyhedron P in three dimensions. The A~patch is a smooth and single-sheeted zero-contour patch of a trivariate polynomial in Bernstein-Bezier (BB) form defined within a tetrahedron. The smooth mesh constructions rely on a novel scheme to build an inner simplicial hul...

Aim of this paper is to describe how the so called Variable Degree Polynomial Spaces can be used for the construction of C spatial curves, approximating or interpolating a given set of data. Their main advantages rely in the easy control on their shape, provided by the variable degrees, and in the low computational cost, comparable with that of standard quintic splines. 1 – Introduction Geometr...

In this paper, we show the global well-posedness for periodic gKdV equations in the space H(T), s ≥ 1 2 for quartic case, and s > 5 9 for quintic case. These improve the previous results of Colliander et al in 2004. In particular, the result is sharp in the quartic case.

Let Pn(x) = xm + pm−1(n)x m−1 + · · · + p1(n)x + pm(n) be a parametrized family of polynomials of a given degree with complex coefficients pk(n) depending on a parameter n ∈ Z≥0. We use Rouché’s theorem to obtain approximations to the complex roots of Pn(x). As an example, we obtain approximations to the complex roots of the quintic polynomials Pn(x) = x5 + nx4 − (2n + 1)x3 + (n + 2)x2 − 2x + 1...

For a class of primes p = 1 (mod 20) for which 2 is a quintic nonresidue, unambiguous evaluations of parameters of bidecic Jacobi and Jacobsthal sums (modp) are presented, in terms of the partition p = a + 5b+5c+5d, ab = d — c—cd. Similar results for sums of other orders have been obtained by E. Lehmer and by K. S. Williams. Subject classification (Amer. Math. Soc. (MOS) 1970): 10G05.

According to Hermite there exists only a finite number of number fields having a given degree, and a given value of the discriminant, nevertheless this number is not known generally. The determination of a maximum number of number fields of degree 10 having a given discriminant that contain a subfield of degree 5 having a fixed class number, narrow class number and Galois group is the purpose o...