A k-decomposition (G1, . . . , Gk) of a graph G is a partition of its edge set to form k spanning subgraphs G1, . . . , Gk. The classical theorem of Nordhaus and Gaddum bounds χ(G1) + χ(G2) and χ(G1)χ(G2) over all 2-decompositions of Kn. For a graph parameter p, let p(k;G) denote the maximum of ∑k i=1 p(Gi) over all k-decompositions of the graph G. The clique number ω, chromatic number χ, list ...

An integral representation for the functional F(m, M) := inf { lim inf k→+∞ ∫ Ω f(x, mk(x),∇mk(x)) dx + ∫ Ω∩S(mk) |[mk](x)|dH : mk ∈ SBV (Ω;R ), |mk(x)| = 1 a.e. in Ω, mk → m in L(Ω;R ), ∇mk ⇀ M in L(Ω;R ) } . This problem is motivated by equilibria issues in micromagnetics.

This paper presents 2-D finite volume method for computation of viscous drag based on Reynolds-averaged Navier-Stokes (RANS) equations. Computations are performed on bare submarine hull DREA and six axisymmetric bodies of revolution with a number of length-diameter (L/D) ratios ranging from 4 to 10. Both structured and unstructured grids are used to discretize the domain around the bodies. Diff...

which implies a UV-cutoff. Here O(ν) denotes the orthogonal group. The physically interesting choices for the dispersion relations Ω and ω are Ω(η) = η/2M , Ω(η) = √ η2 + M2 and ω(k) = √ k2 + m2, where M,m > 0 are the electron and boson masses. We will however work with general forms of both Ω and ω. As for ω, this is partly motivated by the similarity with the Polaron model, cf. [5, 11], where...

A temperature controlled 1 Ω–10 kΩ Standard resistors setup was developed at National Institute of Metrological Research, (INRIM). The aim of this realization was the involvement of the setup resistors in the traceability transfer process to high accuracy multifunction electrical instruments used in Secondary Electrical Calibration Laboratories or even their use as primary Standards in high lev...

Let G be a connected linear semisimple Lie group with Lie algebra g, and let K C → Aut(p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that Ω is a nilpotent G-orbit in g and O is the nilpotent K C -orbit in p C associated to Ω by the Kostant-Sekiguchi correspondence. We show that the complexity of O as a K C variety measures ...

Denote by Ω = {1, . . . , n} an n–element set. For all A,B ∈ Ωk ) , the k–element subsets of Ω, define the relation ∼ as follows: A ∼ B iff A and B have a common shadow, i.e. there is a C ∈ ( Ω k−1 ) with C ⊂ A and C ⊂ B. For fixed integer α, our goal is to find a family A of k–subsets with size α, having as many as possible ∼ –relations for all pairs of its elements. For k = 2 this was achieve...

We consider the boundary value problem ∆u+ε k(x) e = 0 in a bounded, smooth domain Ω in R with homogeneous Dirichlet boundary conditions. Here ε > 0, k(x) is a non-negative, not identically zero function. We find conditions under which there exists a solution uε which blows up at exactly m points as ε→ 0 and satisfies ε ∫ Ω keε → 8mπ. In particular, we find that if k ∈ C(Ω̄), infΩ k > 0 and Ω is...

Lower semicontinuity properties of multiple integrals u ∈W (Ω;R) 7→ ∫ Ω f(x, u(x), · · · ,∇u(x)) dx are studied when f may grow linearly with respect to the highest-order derivative, ∇ku, and admissible W k,1(Ω;Rd) sequences converge strongly in W k−1,1(Ω;Rd). It is shown that under certain continuity assumptions on f, convexity, 1-quasiconvexity or k-polyconvexity of ξ 7→ f(x0, u(x0), · · · ,∇...