It may prove useful in cosmology to understand the behavior of the energy distribution in a scalar field that interacts only with gravity and with itself by a pure quartic potential, because if such a field existed it would be gravitationally produced, as a squeezed state, during inflation. It is known that the mean energy density in such a field after inflation varies with the expansion of the...

In this article we compute fundamental units for three parametric families of number fields of degree 4 with unit rank 2 and 3 generated by polynomials with Galois group D4 and S4.

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation 3(f(x+ 2y) + f(x− 2y)) = 12(f(x + y) + f(x− y)) + 4f(3y)− 18f(2y) + 36f(y)− 18f(x).

We show that the quartic generalised KdV equation ut + uxxx + (u )x = 0 is globally wellposed for data in the critical (scale-invariant) space Ḣ −1/6 x (R) with small norm (and locally wellposed for large norm), improving a result of Gruenrock [8]. As an application we obtain scattering results in H x(R) ∩ Ḣ −1/6 x (R) for the radiation component of a perturbed soliton for this equation, improv...

We show that for all integers m and n there are no non-trivial solutions of Thue equation x − 2mnxy + 2 ( m − n + 1 ) xy + 2mnxy + y = 1, satisfying the additional condition gcd(xy,mn) = 1.

Richter-Gebert proved that every non-Euclidean uniform oriented matroid admits a biquadratic final polynomial. We extend this result to the non-uniform case.

We searched up to height 107 for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright.

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x+ y) + f(2x− y) = 4(f(x+ y) + f(x− y))− 3 7 (f(2y)− 2f(y)) + 2f(2x) − 8f(x).

following result. THEOREM 1. The only (n,m)eZ with n^2 and m5=4 satisfying © = ( 7 ) a r e {n> m)=(2> 4)> (6> 6)> and (21> Our binomial diophantine equation represents an elliptic curve, since it can be rewritten as a quartic polynomial being a square. Indeed, on putting u = 2/i 1 and v = 2m 3, we see at once that Theorem 1 follows from the following result. THEOREM 2. The only (u, v) e Z with ...

By making use of the duality transformation, gauge field correlators of the Abelian Higgs Model are studied in the London limit. The obtained results are in a good agreement with the dual Meissner scenario of confinement and with the Stochastic Model of QCD vacuum. The nontrivial contribution to the quartic correlator arising due to accounting for the finiteness of the coupling constant is disc...