We determine the number of cubic surfaces with 27 lines over a finite field $${{\mathbb {F}}}_q$$ . This is based on exploiting relationship between non-conical six-arcs in projective plane embedded three-space and lines. revisit this classical relationship, which goes back to work Clebsch nineteenth century. Our result can be used as an enumerative check for computer classification fields.

PACS numbers: 11.10.Ef 02.30.Wd 02.30.Jr 03.40.Gc Abstract We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and...

There appear to be two standard ways of calculation C-G coefficients in quantum mechanics. One method is to combine the “ladder” operator approach with orthogonality conditions. The second method is to use some type of closed form [2] which allows the coefficients to be calculated directly. However, the latter approach is at times considered “tedious” [2] and does not reveal any new information...

The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1, 1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can occur, and the discrete terms are a finite number of discrete series representations or one complementary series representation. The interpretation of Meixne...

This paper characterizes the first cohomology group H(G,M) where M is a Banach space (with norm || ||M) that is also a left CG module such that the elements of G act onM as continuous C-linear transformations. We study this group for G an infinite, finitely generated group. Of particular interest are the implications of the vanishing of the group H(G,M). The first result is that H(G,CG) imbeds ...

The non-relativistic quark model has been a useful tool in the study of hadrons. Baryons and mesons are described by quantum mechanical wavefunctions for nonrelativistic constituent quarks. The lowest lying baryons, the 81/2 and 103/2, are three quark states with wavefunctions which are completely antisymmetric in color, and completely symmetric in position and spin-flavor. The properties of ba...

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A−G based on the explicit construction of weight states. This straightforward approach (which is slower and more memoryconsumptive than the standard methods to just calculate dimensions of the tensor product decomposition) produces Clebsch-Gordan coefficients that are of intere...

The study of the topological classiication of complex polynomials began in the XIX-th century by Luroth (1871), Clebsch (1873) and Hurwitz (1891). In the works of Zdravkovska 23] and Khovanskii and Zdravkovska 17] the problem is reduced to a purely combinatorial one, that of the study of a certain action of the braid groups on a class of tree-like gures that we, following 14], call \cacti". Usi...