We find many conditions equivalent to the modeltheoretical property λ κ ⇒ μ introduced in [L1]. Our conditions involve uniformity of ultrafilters, compactness properties of products of topological spaces and the existence of certain infinite matrices. See Part I [L7] or [CN, CK, KM, KV, HNV] for unexplained notation. According to [L1], if λ ≥ μ are infinite regular cardinals, and κ is a cardina...

Given a simple connected graph Γ and a subset of its vertices C, the pseudodistance-regularity around C generalizes, for not necessarily regular graphs, the notion of completely regular code. Up to know, most of the characterizations of pseudodistance-regularity has been derived from a combinatorial definition. In this paper we propose an algebraic (Terwilliger-like) approach to this notion, sh...

In this paper, we classify 2-closed (in Wielandt’s sense) permutation groups which contain a normal regular cyclic subgroup and prove that for each such group G, there exists a circulant Γ such that Aut(Γ) = G.

Let Γ denote a group of finite virtual cohomological dimension and p a prime. If the cohomology ring H∗(Γ;Fp) has Krull dimension one, the p-period of Γ is defined; it measures the periodicity of H∗(Γ;Fp) in degrees above the virtual cohomological dimension of Γ. The Yagita invariant p(Γ) of Γ is a natural generalization of the p-period to groups with H∗(Γ;Fp) of Krull dimension larger than one...

In this paper, we consider the derivation of the modified Wenzel’s and Cassie’s equations for wetting phenomena on rough surfaces from a three-dimensional phase field model. We derive an effective boundary condition by asymptotic two-scale homogenization technique when the size of the roughness is small. The modified Wenzel’s and Cassie’s equations for the apparent contact angles on the rough s...

A Cayley graph Γ = Cay(G, S) is called normal for G, if GR, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ ) of Γ . In this paper we determine the normality of connected and undirected Cayley graphs of valency three for dihedral groups. 2000 Mathematics Subject Classification: 05C25, 20B25.

We investigate, using the framework of Γ-convergence, a phase-field model proposed in [Torabi et al, Proc. R. Soc. A, 2009] for strongly anisotropic systems; in particular, we prove a full Γ-convergence result for an anisotropic Modica-Mortolatype energy.

For Erdős-Rényi random graphs with average degree γ, and uniformly random γ-regular graph on n vertices, we prove that with high probability the size of both the Max-Cut and maximum bisection are n( γ 4 + P∗ √ γ 4 + o( √ γ)) + o(n) while the size of the minimum bisection is n( γ 4 − P∗ √ γ 4 + o( √ γ)) + o(n). Our derivation relates the free energy of the anti-ferromagnetic Ising model on such ...

Very often, strongly regular graphs appear associated with partial geometries. The point graph of a partial geometry is the graph whose vertices are the points of the geometry and adjacency is defined by collinearity. It is well known that the point graph associated to a partial geometry is a strongly regular graph and, in this case, the strongly regular graph is named geometric. When the param...

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integerm. Ifm > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 + m2,m4 + m2,m4 + m2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defi...