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...

We determine all exceptional units among the elements of certain groups of units in quartic number fields. These groups arise from a oneparameter family of polynomials with two real roots.

In this paper a technique for the construction of quartic polynomial B-spline patches fitting on analytical surfaces and triangle meshes is presented. The input data are curvature values and principal directions at a given surface point which can be computed directly, if the surface is represented by a vector function. In the case of discrete surface representation, i.e. on a triangle mesh the ...

We consider the constraints on the effective Lagrangian of the rank-one gauge field on Dbranes imposed by the equivalence between the description by ordinary gauge theory and that by non-commutative gauge theory in the presence of a constant B field. It is shown that we can consistently construct the two-derivative corrections to the Dirac-Born-Infeld Lagrangian up to the quartic order of field...

The Picard curves are genus three curves with a non trivial automorphism, which have been intensively studied due their connection with interesting number theoretic problems. In 1989, R. Pellikaan obtained an algorithm decoding geometric codes up to b(d ? 1)=2c-errors, where d is the designed distance of the code. His algorithm is not completely eeective, but recently some authors have given an...

We show that it is possible to obtain spontaneous CP violation in the minimal SU(2)L × SU(2)R ×U(1)B−L, i.e. in a left right symmetric model containing a bidoublet and two triplets in the scalar sector. For this to be a natural scenario, the non-diagonal quartic couplings between the two scalar triplets and the bidoublet play a fundamental role. We analyze the corresponding Higgs spectrum, the ...

Andrea Blanco-Redondo, C. Martijn de Sterke, J.E. Sipe, Thomas F. Krauss, Benjamin J. Eggleton & Chad Husko Nature Communications 7:10427 doi: 10.1038/ncomms10427 (2016); Published 29 Jan 2016; Updated 9 Mar 2016 The original version of this article contained an error in the spelling of the author C. Martijn de Sterke, which was incorrectly given as de Sterke C. Martijn. This has now been corre...