In this paper a new macroscopic k-ε model is developed and validated for turbulent flow through porous media for a wide range of porosities. The morphology of porous media is simulated by a periodic array of square cylinders. In the first step, calculations based on microscopic v2 − f model are conducted using a Galerkin/Least-Squares finite element formulation, employing equalorder bilinear ve...

If {A(V)} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V1 and V2 are spacelike separated spacetime regions, then the system (A(V1),A(V2), f) is said to satisfy the Weak Reichenbach’s Common Cause Principle iff for every pair of projections A ¥ A(V1), B ¥A(V2) correlated in the normal state f there exists a projection C belo...

Let (M,ω) and (N, η) be symplectic manifolds. A symplectomorphism F : M → N is a diffeomorphism such that ω = F ∗η. Recall that for x ∈ M and v1, v2 ∈ TxM , (F η)x(v1, v2) = ηF (x)((TxF )v1, (TxF )v2); TxF : TxM → TF (x)N . (A tangent vector at x ∈ M is pushed forward to a tangent vector at F (x) ∈ N , while a differential 2-form on N is pulled back to a differential 2-form on M .) In these not...

1 PAIRS OF DUAL CONES Around 1900 Voronoï [10] formulated his fundamental algorithm to enumerate all similarity classes of perfect lattices in a given dimension. This algorithm has far reaching generalisations ([7], [6], [4]) used to compute generators and relators for arithmetic groups. A quite general situation, where one may apply Voronoï’s algorithm, is described in [7]: Let σ : V1 ×V2 → R ...

Let F be a family of graphs. Two graphs G1 = (V1, E1), G2 = (V2, E2) are said to have the same F-structure if there is a bijection f : V1 → V2 such that a subset S induces a graph belonging to F in G1 if and only if its image f(S) induces a graph belonging to F in G2. We prove that graph H is perfect if and only if it has the {P3, P 3}-structure of some perfect graph G.

In this paper, we study the vector invariants, F[m V2] Cp , of the 2-dimensional indecomposable representation V2 of the cylic group, Cp, of order p over a field F of characteristic p. This ring of invariants was first studied by David Richman [18] who showed that this ring required a generator of degree m(p−1), thus demonstrating that the result of Noether in characteristic 0 (that the ring of...

Let V = V1 ⊕ V2 be a finite-dimensional vector space over an infinite locally-finite field F . Then V admits the torus action of G = F • by defining (v1 ⊕ v2) = v1g−1 ⊕ v2g. If K is a field of characteristic different from that of F , then G acts on the group algebra K[V ] and it is an interesting problem to determine all G-stable ideals of this algebra. In this paper, we consider the special c...

Note that the three vector spaces involved aren’t necessarily the same. What these examples have in common is that in each case, the product is a bilinear map. The tensor product is just another example of a product like this. If V1 and V2 are any two vector spaces over a field F, the tensor product is a bilinear map: V1 × V2 → V1 ⊗ V2 , where V1 ⊗ V2 is a vector space over F. The tricky part i...

A vertex colouring f: V(G) → C of a graph G is complete if for any c1, c2 ∈ with c1 ≠ there are in adjacent vertices v1, v2 such that f(v1) = and f(v2) c2. The achromatic number the maximum achr(G) colours proper G. Let G1▫G2 denote Cartesian product graphs G1 G2. In paper achr(Kr2 + r 1▫Kq) determined an infinite q’s provided finite projective plane order.