We determine those cubic graphs with at most 22 vertices which are leaves of partial triple systems. As a first step towards a complete characterization of cubic leaves, we also show several classes of cubic graphs to be leaves.

For diagonal cubic surfaces, we study the behaviour of the height of the smallest rational point versus the Tamagawa type number introduced by E. Peyre.

In the context of low-energy effective theory of multiple M2-branes, we construct the interaction terms between the world-volume fields of M2-branes and the antisymmetric tensor fields of threeand six-forms. By utilizing the compactification procedure, we show coincidence between the dimensionally reduced coupling and the R-R coupling to D-branes in type II string theory. We also discuss that a...

From May 26 to May 3

Integrity, a measure of network reliability, is defined as I(G) = minS⊂V {|S|+m(G− S)} , where G is a graph with vertex set V and m(G−S) denotes the order of the largest component of G− S. In this article the integrity of the cubic cage graphs (3, g) up to g = 10 and the integrity of the known small cages with less than or equal to 60 vertices is computed.

This paper describes a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1. The technique is based on Voronoi’s algorithm for generating a chain of successive minima in a multiplicative cubic lattice which is used for calculating the fundamental unit and regulator of a purely cubic number field.

In this paper we present the first example of a primitive, totally geodesic subvariety F ⊂ Mg,n with dim(F ) > 1. The variety we consider is a surface F ⊂M1,3 defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmüller curves in M4, and new SL2(R)–invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.

We argue that the rolling-tachyon solution in cubic OSFT proceeds at late times to precisely the analytic tachyon-vacuum solution constructed by Schnabl. In addition, we demonstrate the relationship between the rolling-tachyon solution and the standard BCFT description by showing that there is a finite gauge transformation which relates the two.

In this paper, we study the construction of α-conformally equivalent statistical manifolds for a given symmetric cubic form on a Riemannian manifold. In particular, we describe a method to obtain α-conformally equivalent connections from the relation between tensors and the symmetric cubic form.