Wavelet-based methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all waveletbased methods is a hierarchy of meshes that satisfies subdivisionconnectivity: this hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree unifor...

We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group AutHopf (E(n)). Using this result we show that for any triangular structure R on E(n) the Brauer group BM(k,E(n), R) is the direct product of the Brauer-Wall group of the base field k and the group Symn(k) of symmetric matrices of order n with entri...

Let E be a finite set, R be the set of real numbers and f:2E-+R be a symmetric submodular function. The pair (E,f) is called a symmetric submodular system. We examine the structures of symmetric submodular systems and provide a decomposition theory of symmetric submodular systems. The theory is a generalization of the decomposition theory of 2-connected graphs developed by Tutte and can be appl...

The hexagonal and the triangular grids are duals of each other. These two grids are the first and second ones in the family of triangular grids (we can call them as oneand two-planes triangular grids). This family comes from the mapping their points to Z3. Their symmetric properties are triangular. The next grid is the three-planes triangular grid, which looks like the mix of them. In this pape...

Let n ≥ 2 be an integer. The complete graph Kn with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that Kn − F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≡ 2, 4 mod 8. We also show that the complete bipartite graph Kn,n has a symmetric Hamilton cycle decomposition if and only if n ...

We give an $\mathrm{SL}\_3$ analogue of the triangular decomposition Kauffman bracket stated skein algebras described by Lê. To any punctured bordered surface, we associate algebra which contains closed webs. These admit natural morphisms associated to splitting surfaces along ideal arcs. explicit basis for and show that are injective describe their images. By a surface edges triangulation, see...

In this paper, we present a sum-of-rank-1 type decomposition and its differential model for symmetric tensors and investigate the convergence properties of numerical gradient-based iterative optimization algorithms to obtain this decomposition. The decomposition we propose reinterprets the orthogonality property of the eigenvectors of symmetric matrices as a geometric constraint on the rank-1 m...