Given a family F and a host graph H, a graph G ⊆ H is F-saturated relative to H if no subgraph of G lies in F but adding any edge from E(H)−E(G) to G creates such a subgraph. In the F-saturation game on H, players Max and Min alternately add edges of H to G, avoiding subgraphs in F , until G becomes F-saturated relative to H. They aim to maximize or minimize the length of the game, respectively...

Applying the techniques of nonabelian duality to a system of Majorana fermions in 1+1 dimensions, invariant under a nonabelian group O L (N) × O R (N), we obtain the level-one Wess-Zumino-Witten model as the dual theory. This makes nonabelian bosonization a particular case of a nonabelian duality transformation, generalizing our previous result for the abelian case.

We show that any set of n pairwise disjoint ovals in a finite projective plane of even order has a unique common tangent. As a consequence, any set of q+1 pairwise disjoint ovoids in PG(3, q), q even, has exactly q2+1 common tangent lines, constituting a regular spread. Also, if q−1 ovoids in PG(3, q) intersect pairwise exactly in two given points x ̸= y and share two tangent planes πx, πy at th...

1 Department of Computer Science and Engineering, Michigan State University, East Lansing, MI 48824, USA; [email protected] 2 BEACON Center for the Study of Evolution in Action, Michigan State University, East Lansing, MI 48824, USA 3 Department of Microbiology & Molecular Genetics, Michigan State University, East Lansing, MI 48824, USA; [email protected] 4 Department of Integrative Biology, Michigan St...

In this paper n denotes a natural number, X denotes a set, and F1, G1 denote families of subsets of X. Let us consider X, F1. We say that F1 is finite-order if and only if: (Def. 1) There exists n such that for every G1 such that G1 ⊆ F1 and n ∈ CardG1 holds ⋂ G1 is empty. Let us consider X. Observe that there exists a family of subsets of X which is finite-order and every family of subsets of ...

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J.P. Roudnee as well as R. Aharoni and R. Ziv conjectured that every-critical linear hyper-graph has at most ? +1 2 edges. In this note we prove this conjecture for 5, and obtain a nontrivial upper bound for general .

We survey some known facts and open questions concerning the global properties of 3+1 dimensional space–times containing a compact Cauchy surface. We consider space–times with an l–dimensional Lie algebra of space–like Killing fields. For each l ≤ 3, we give some basic results and conjectures on global existence and cosmic censorship. For the case of the 3+1 dimensional Einstein equations witho...

We study the the Casimir effect of a massless conformally coupled scalar field in the background of a conformally flat brane-world geometries, where the scalar field satisfying Robin boundary conditions on two parallel plates. In the general case of Robin boundary conditions formula are derived for the vacuum expectation values of the energy-momentum tensor. Further the surface energy per unit ...