Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction o...

Low energy weak interactions calculations with fermions frequently involve a superposition of quartic products of Dirac spinors, in which the order of the spinors is not the same in all the contributing terms. A common trick that is used to bring them to a uniform ordering is the Fierz transformation. We show that the standard Fierz rearrangement formula quoted in textbooks is one element of a ...

We consider the adaptive refinement of bivariate quartic C-smooth box-spline spaces on the three-directional (type-I) grid G. The polynomial segments of these box splines belong to a certain subspace of the space of quartic polynomials, which will be called the space of special quartics. Given a finite sequence (G)l=0,...,N of dyadically refined grids, we obtain a hierarchical grid by selecting...

A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature. 1. A quartic integral The problem of explicit evaluation of definite integrals has been greatly simplified due to the advances in symbolic languages like Mathematica and Maple. Some years ag...

In this paper we study to what extent the canonical equivalence and the identity of the geometric phases of dissipative and conservative linear oscillators, established in a preceeding paper, can be generalized to nonlinear ones. Considering first the 1-D quartic generalized oscillator we determine, by means of a perturbative time dependent technic of reduction to normal forms, the canonical tr...

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 .