In the present paper, we introduce theH-wavelet method for the fast solution of nonlocal operator equations on unstructured meshes. On the given mesh, we construct a wavelet basis which provides vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates is compressed to O(N logN) relevant matrix coefficients, where...

Introduction The axillary nerve comes from the posterior cord of the brachial plexus at the level of the axilla and carries nerve fibers from C5 and C6. The axillary nerve travels through the quadrangular space with the posterior circumflex humeral vessels, and divides into anterior and posterior branches. It supplies deltoid and teres minor. It carries sensory information from the shoulder joi...

Mitral valve repair is currently considered the standard treatment for mitral regurgitation. Posterior leaflet prolapse has been treated by quadrangular resection and ring annuloplasty for many years. Although it is a classic and reproducible method, this technique may predispose to systolic anterior motion (SAM) of the anterior leaflet of the mitral valve. The incidence of SAM has been reporte...

A set S ⊆ V is called an q-set (q−-set, respectively) if S has at least two vertices and, for every u ∈ S, there exists v ∈ S, v 6= u such that N(u) ∩ N(v) 6= ∅ (N−(u)∩N−(v) 6= ∅, respectively). A digraph D is called s-quadrangular if, for every q-set S, we have | ∪ {N+(u) ∩ N(v) : u 6= v, u, v ∈ S}| ≥ |S| and, for every q−set S, we have | ∪ {N−(u) ∩ N−(v) : u, v ∈ S)} ≥ |S|. We conjecture that...

We derive an O(n)-time algorithm for calculating the genus distribution of a given 3-regular Halin graph G; that is, we calculate the sequence of numbers g0(G), g1(G), g2(G), . . . on the respective orientable surfaces S0, S1, S2, . . . . Key topological features are a quadrangular decomposition of plane Halin graphs and a new recombinant-strands reassembly process that fits pieces together thr...

We consider the problem of designing space efficient solutions for representing triangle meshes. Our main result is a new explicit data structure for compactly representing planar triangulations: if one is allowed to permute input vertices, then a triangulation with n vertices requires at most 4n references (5n references if vertex permutations are not allowed). Our solution combines existing t...

BACKGROUND The procedure of quadrangular resection and suture for prolapsed posterior leaflet of the mitral valve is a reliable and reproducible method that achieves excellent long-term results. However, triangular resection and suture of a prolapsed anterior leaflet is not widely supported and different techniques have been advocated. The aim of this study was to review our experience of mitra...