In this paper, the second order boundary value problem −∇·(A(x, y)∇u) = f is discretized by the Finite Element Method using piecewise polynomial functions of degree p on a triangular mesh. On the reference element, we define integrated Jacobi polynomials as interior ansatz functions. If A is a constant function on each triangle and each triangle has straight edges, we prove that the element sti...

In this paper we describe a new method for constructing a multi-resolution representation for complex triangle meshes and we describe a new algorithme to reene and to coarsen a simpliied mesh at variable resolution with respect to a given error function. Using this algorithm we show how view-dependent adaptive approximations of the triangle nets with guaranteed approximation error can be genera...

We propose a simple algorithm for lattice point counting in rational polygons. A rational polygon is one whose vertices have rational coordinates. The algorithm decomposes a given polygon into right trapezoids and counts the number of lattice points in the right trapezoids. Each right trapezoid can be dissected into a rectangle and a right-angled triangle in the obvious way. The number of latti...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Abstract The equilateral triangle is one of the few planar domains where Dirichlet and Neumann eigenvalue problems were explicitly determined, by Lamé in 1833, despite not admitting separation variables. In this paper, we study Robin spectrum triangle, which was determined McCartin 2004 terms a system transcendental coupled secular equations. We give uniform upper bounds for Robin-Neumann gaps,...

This paper presents a method, along with some optimizations, for computing whether or not two triangles intersect. The code, which is shown to be fast, can be used in, for example, collision detection algorithms.

Objective: Brachial Plexus Birth palsy usually result in Shoulder deformities lead to poor function, loss of quality of life and pain. The purpose of our study is to examine the results of combined in one step shoulder soft tissues reconstruction and triangle tilt procedure on improvement of shoulder function and development. Method: A major treatment goal in children with obstetric brachial pl...

This paper aims to share new knowledge about tensions in establishing a school marketised educational landscape, with special focus on teachers’ experiences of enacting highly profiled vision. The is based single case study using observations, surveys, interviews and document studies. To cover the complex enactment process, we have created multilayered triangle analyse process strategies teache...

We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.

We propose a general approach for constructing bounds required for the “Big Triangle Small Triangle” method for the solution of planar location problems. Optimization problems which constitute a sum of individual functions, each a function of the Euclidean distance to a demand point, are analyzed and solved. These bounds are based on expressing each of the individual functions in the sum as a d...