Let the DRO (Diffeomorphism, Reparametrization, Observer) algebraDRO(N) be the extension of diff(N)⊕diff(1) by its four inequivalent Virasoro-like cocycles. Here diff(N) is the diffeomorphism algebra in N -dimensional spacetime and diff(1) describes reparametrizations of trajectories in the space of tensor-valued p-jets. DRO(N) has a Fock module for each p and each representation of gl(N). Anal...

We study the quotient of a completion of a symmetric variety G/H under the action of H . We prove that this is isomorphic to the closure of the image of an isotropic torus under the action of the restricted Weyl group. In the case the completion is smooth and toroidal we describe the set of semistable points. 2000 Math. Subj. Class. 14L30, 14L24, 14M17.

We subject the phenomenologically successful large volume scenario of hep-th/0502058 to a first consistency check in string theory. In particular, we consider whether the expansion of the string effective action is consistent in the presence of D-branes and O-planes. Due to the no-scale structure at tree-level, the scenario is surprisingly robust. We compute the modification of soft supersymmet...

Our model consists of intersecting 2255 brane configuration in M theory, distributed uniformly in the common transverse space and assumed to describe early universe. Equations of state are those following from U duality symmetries and a few standard assumptions. In this model, three spatial directions expand, and seven directions stabilise to constant sizes which depend on certain imbalance amo...

Let Φ be an embedding of graph G in a surface S. If there exists a subset K of S bounded by a subgraph of G which contains all the vertices of G, then K is called a spanning subset of Φ. Examples of spanning subsets include spanning discs, spanning annuli with some number of holes (called planarizing sets in some papers). A spanning subset may provide a simpler structure but still contain enoug...

Let X be a locally symmetric variety, i.e., the quotient of a bounded symmetric domain by a (say) neat arithmetically-defined group of isometries. Let X exc and X denote its excentric Borel-Serre and toroidal compactifications respectively. We determine their least common modification and use it to prove a conjecture of Goresky and Tai concerning canonical extensions of homogeneous vector bundl...

In this paper, we study the crossing number of the complete bipartite graph K4,n in torus and obtain crT (K4,n) = ⌊ n 4 ⌋(2n− 4(1 + ⌊ n 4 ⌋)).

A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G \ S is adjacent to only one vertex (dv ∈ {1, 2} vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol {3, 6} and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of thei...

As it is introduced by Bermond, Kodate, and Prennes, some Cayley graphs, including most popular models for interconnection networks, admit a special auto-morphism, called complete rotation. Such an automorphism is often used to derive algorithms or properties of the underlying graph. For example, optimal gossiping algorithms can be easily designed, and the constructions of the best known edge d...

Given a graph G that admits a perfect matching, we investigate the parameter η(G) (originally motivated by computer graphics applications) which is defined as follows. Among all nonnegative edge weight assignments, η(G) is the minimum ratio between (i) the maximum weight of a perfect matching and (ii) the maximum weight of a general matching. In this paper, we determine the exact value of η for...