Recently, fuzzy linear programming problems have been considered by many. In the literature of fuzzy linear programming several models are offered and therefore some various methods have been suggested to solve these problems. One of the most important of these problems that recently has been considered; are Fully Fuzzy Linear Programming (FFLP), which all coefficients and variables of the prob...

We study the three-dimensional lens partition function for $\mathcal{N}=2$ supersymmetric gauge dual theories on ${S}^{3}/{\mathbb{Z}}_{r}$ by using gauge/Yang-Baxter equation correspondence. This correspondence relates to exactly solvable models of statistical mechanics. The equality functions can be written as an integral identity hyperbolic hypergeometric functions. obtain such which star-tr...

We present a method to produce a hierarchy of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithm produces a sequence of meshes 00, 01, 02, ..., 0n, where each mesh 0i can be transformed to mesh 0i+1 through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of...

BACKGROUND The benefits of triangle tilt surgery in children with OBPI have been previously validated through measurements of statistical improvements in Mallet scores and in glenohumeral congruity. The purpose of the current study was to evaluate the effectiveness of triangle tilt surgery through the application of the Pediatric Outcomes Data Collection Instrument, a well validated questionnai...

We often need to refer to adjacent elements (e.g., vertices, edges and faces) in triangle meshes for rendering, mesh simplification and other processes. It is, however, sometimes impossible to prepare the enormous memory needed to represent element connectivity in gigantic triangle meshes. We proposed a memory efficient scheme for referring to adjacent faces around a vertex in non-manifold tria...

A tool for constructing a “good” 3D triangulation of a given set of vertices in 3D is developed and studied. The constructed triangulation is “optimal” in the sense that it locally minimizes a cost function which measures a certain discrete curvature over the resulting triangle mesh. The algorithm for obtaining the optimal triangulation is that of swapping edges sequentially, such that the cost...

Isosceles trapezoids are dissected into three similar triangles and rearranged to form two additional isosceles trapezoids. Moreover, triangle centers, one from each similar triangle, form the vertices of a centric triangle which has special properties. For example, the centroidal triangles are congruent to each other and have an area one-ninth of the area of the trapezoids; whereas, the circum...

About 300 years ago Sébastien Truchet systematically studied patterns that could be formed from square tiles that were divided by a diagonal into a white triangle and a black triangle. Other pattern creators have been inspired by him to make Truchet-like tilings composed of circular arcs and other motifs. These tilings are all based on Euclidean tessellations, usually the tiling by squares. In ...

Nadler. E., Nonnegativity of bivariate quadratic functions on a triangle. Computer Aided Geometric Design 9 (1992) 19.5-205. A necessary and sufficient condition for the nonnegativity of a bivariate quadratic defined on a triangle is presented in terms of the Bernstein-Bkzier form of the function. Keywfords. Nonnegativity, bivariate quadratic function, Bernstein-BCzier form, positiviry preservi...