A regular covering projection ℘: X̃ → X of connected graphs is G-admissible if G lifts along ℘. Denote by G̃ the lifted group, and let CT(℘) be the group of covering transformations. The projection is called G-split whenever the extension CT(℘) → G̃ → G splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that G is transitive o...

We examine the relationship between the notion of Frobe-nius splitting and ordinarity for varieties. We show the following: a) The de Rham-Witt cohomology groups H i (X, W (OX)) of a smooth projec-tive Frobenius split variety are finitely generated over W (k). b) we provide counterexamples to a question of V. B. Mehta that Frobenius split varieties are ordinary or even Hodge-Witt. c) a Kummer K...

There are two main objectives of this paper. The first is to present a statistical framework for models with context specific indepen­ dence structures, i.e. conditional independen­ cies holding only for specific values of the con­ ditioning variables. This framework is consti­ tuted by the class of split models. Split mod­ els are an extension of graphical models for contingency tables and all...

This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme based on a local collocation on unstructured elements. Recently results for scalar transport equations and the Euler equations have been presented. For the extension to viscous flow several techniques are investigated, ...

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such as the isomorphism problem of general Coxeter groups. In the argument, some properties of certain special elements and of the fixed-point subgroups by graph...

Extension research has been conducted over the past three years over the various abattoirs, technological institutions and meat processing plants, in order to establish means of enhancing safety as well as shelf life extension. The technology applied was the process of electro-chemical activation of water by an on-site device. This device makes use of a powerful electrical field to split a sali...

Let G ≤ Sn be a permutation group of degree n with a quotient isomorphic to Ak. We show that if n < (1/2 − o(1))k then the extension splits. Motivated by this result, Guralnick and Liebeck have shown that the conclusion fails to hold if we allow n to be n = 2k(k − 1), establishing a tight quadratic growth rate for the smallest degree of a faithful permutation representation of a non-split exten...

Recall that a metric d on a finite set X is called antipodal if there exists a map σ : X → X: x 7→ x so that d(x, x) = d(x, y) + d(y, x) holds for all x, y ∈ X. Antipodal metrics canonically arise as metrics induced on specific weighted graphs, although their abundance becomes clearer in light of the fact that any finite metric space can be isometrically embedded in a more-or-less canonical way...

Let k be a field and V be an algebraic fc-scheme of dimension w—1. V is called a Severi-Brauer /;-scheme if there exists a separable algebraic extension L/k such that V xkL and Pw_1(L)=Proj L[XX, • • • , Xn] are isomorphic as /.-schemes [7]. V is said to be split by L/k. V is called a trivial Severi-Brauer ^-scheme if V and -Pw_i(fc) are isomorphic as fcschemes. Let K/k be a finite Galois exten...