In current study, a particle swarm clustering method is suggested for clustering triangular fuzzy data. This clustering method can find fuzzy cluster centers in the proposed method, where fuzzy cluster centers contain more points from the corresponding cluster, the higher clustering accuracy. Also, triangular fuzzy numbers are utilized to demonstrate uncertain data. To compare triangular fuzzy ...

In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the associated graph of one specific triangular set computed in any algorithm for triangular decomposition in top-down style is a subgraph of the chordal graph of ...

Progress on two-dimensional materials has shown that valleys, as energy extrema in a hexagonal first Brillouin zone, provides new degree of freedom for information manipulation. Then valley Hall topological insulators supporting such-polarized edge states boundaries were set up accordingly. In this paper, photonic crystal composed six tunable dielectric triangular pillars unit cells is proposed...

This study aimed to analyze the treatment effects of miniscrew-assisted rapid palatal expansion using dental cone-beam computed tomography (CT) in adolescents. The group comprised 20 patients who underwent CT before and after (MARPE). Paired t-test analysis variance were used significant differences treatment. Skeletal dentoalveolar measurements indicated highly differences, with these expansio...

A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. We show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid graph can be found in polynomial time. 2000 Mathematics Subject Classification: 05C38 (05C45, 68Q25).

An attractive method for approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces is introduced. The main result is that the arbitrary given order derived vectors of a polynomial triangular surface converge uniformly to those of the approximated rational triangular Bézier surface as the elevated degree tends to infinity. The polynomial triangular surface is con...

This paper puts forward 3D model retrieval method based on normal-angle histogram. The method firstly makes the pretreatment for 3D model, and defines the calculation method of the normal at every vertex of the triangular mesh in 3D model and the included angle among the triangular meshes. Then it classifies the triangular mesh in accordance with the normal at three vertexes of the triangular m...

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...

Triangular B-splines are a new tool for modeling a broad class of objects defined over arbitrary, nonrectangular domains. They provide an elegant and unified representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additi...

Triangular B-splines are a new tool for modeling a broad class of objects deened over arbitrary, non-rectangular domains. They provide an elegant and uniied representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additio...