Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ , where ρ is (m,n)semiregular for some integers m ≥ 1, n ≥ 2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ has at least one fixed vertex. A halfarc-transitive graph is a vertexand edgebut not arc-transitive graph. In this arti...

2 The reciprocity problem 3 2.1 Quadratic reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Cubic reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Biquadratic reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Hilber...

In this paper, we prove the generalized Hyres–Ulam–Rassias stability of the mixed type cubic and quartic functional equation f (x + 2y) + f (x − 2y) = 4(f (x + y) + f (x − y)) − 24f (y) − 6f (x) + 3f (2y) in non-Archimedean ℓ-fuzzy normed spaces.

Let c 3 be positive integer such that c; 4c+ 1; c 1 are square-free integers relatively prime in pairs. In this paper we …nd minimal index and determine all elements with minimal index in bicyclic biquadratic …eld K = Q p (4c+ 1) c; p (c 1) c .

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.