The diagonalisation of the transfer matrices of solvable vertex models with alternating spins is given. The crystal structure of (semi-)infinite tensor products of finite dimensional Uq(ŝl2) crystals with alternating dimensions is determined. Upon this basis the vertex models are formulated and then solved by means of Uq(ŝl2) intertwiners.

A graph G is said to be hyper-connected if the removal of every minimum cut creates exactly two connected components, one of which is an isolated vertex. In this paper, we first generalize the concept of hyper-connected graphs to that of semi-hyper-connected graphs: a graph G is called semi-hyper-connected if the removal of every minimum cut of G creates exactly two components. Then we characte...

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Given a graph G = (V, E), we define the transpose degree sequence d T j to be equal to the number of vertices of degree at least j. We define L G , the graph Laplacian, to be the matrix, whose rows and columns are indexed by the vertex set V , whose diagonal entry at v is the degree of v and whose value at a pair (v, w) is −1 if (v, w) ∈ E and 0 otherwise. Grone and Merris conjectured [GM] Conj...

A semi-perturbative calculation of the ghost-gluon vertex in Landau gauge YangMills theory in four and three Euclidean space-time dimensions is presented. Nonperturbative gluon and ghost propagators are employed, which have previously been calculated from a truncated set of Dyson–Schwinger equations and which are in qualitative and quantitative agreement with corresponding lattice results. Our ...

Non-radiative surface plasma oscillations in a semi-infinite metal are quantized by using a hydrodynamic jellium model for electrons in the metal. In consequence of the quantization, the electronSF (surface plasmon) vertex function is obtained for the overall region of the surface plasmon wave vector k. In the electrostatic limit, it coincides with the usual electrostatic vertex function obtain...

Inhomogeneous dynamical mean-field theory is employed to calculate the vertex-corrected electronic charge transport for multilayered devices composed of semi-infinite metallic lead layers coupled through a strongly correlated material barrier region. The barrier region can be tuned from a metal to a Mott insulator through adjusting the interaction strength and the particle filling. We use the F...

In a graph Γ = (V,E) a vertex v is resolved by a vertex-set S = {v1, . . . , vn} if its (ordered) distance list with respect to S, (d(v, v1), . . . , d(v, vn)), is unique. A set A ⊂ V is resolved by S if all its elements are resolved by S. S is a resolving set in Γ if it resolves V . The metric dimension of Γ is the size of the smallest resolving set in it. In a bipartite graph a semi-resolving...

One of the main objectives of aircraft and automotive manufacturers is related to improvement of the crash behaviour of lightweight structures. The absorbed energy is an important parameter for the development of the vehicle passive security concept. In present paper, the composite laminate of conical shell structures subjected to slip loading are studied by using finite element method. ANSYS/L...

let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...