This paper first presents a Gauss Legendre quadrature method for numerical integration of I 1⁄4 R R T f ðx; yÞdxdy, where f(x,y) is an analytic function in x, y and T is the standard triangular surface: {(x,y)j0 6 x, y 6 1, x + y 6 1} in the Cartesian two dimensional (x,y) space. We then use a transformation x = x(n,g), y = y(n,g) to change the integral I to an equivalent integral R R S f ðxðn;...

In this paper we apply the ADER one step time discretization to the Discontinuous Galerkin framework for hyperbolic conservation laws. In the case of linear hyperbolic systems we obtain a quadrature-free explicit single-step scheme of arbitrary order of accuracy in space and time on Cartesian and triangular meshes. The ADERDG scheme does not need more memory than a first order explicit Euler ti...

The fault detection and diagnosis of complicated production processes is one of essential tasks needed to run the process safely with good final product quality. Unexpected events occurred in the process may have a serious impact on the process. In this work, triangular representation of process measurement data obtained in an on-line basis is evaluated using simulation process. The effect of u...

danehkhoshk anticline is a typical growing anticline in kermanshah province which is located in folded zagros belt. the purpose of this research is to evaluate the effect of tectonic on the triangular facet characteristics, the drainage density and on the drainage pattern formed on anticline. dimensions of triangular facets were determined by means of quickbird satellite images and field works....

The U(1) Calogero Sutherland Model (CSM) with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered state space is obtained in an upper triangular form. Consequently the diagonal elements become the energy eigenvalues.

We construct a hierarchical tiling of 3 dimensional Euclidean space based on a triangular prism, using repeated rotations, about orthogonal axes, by angles 2=m and 2=n. To analyze the structure of the tiling we are led to determine the group G(m; n) generated by such a pair of rotations, for m = n = 3 and for m = 3; n = 4.

We present an approximation method to compute geodesic distances on triangulated domains in the three dimensional space. Our particular approach is based on the Fast Marching Method for solving the Eikonal equation on triangular meshes. As such, the algorithm is a wavefront propagation method, a reminiscent of the Dijkstra algorithm which runs in O(n log n) steps.

In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.

An exceptional point in moduli space is a unique surface class whose full group of conformal automorphisms acts with a triangular signature. In this paper we determine, up to topological conjugacy, the full group of conformal and anticonformal automorphisms of a symmetric exceptional point in the elliptic-hyperelliptic locus in moduli space. We determine the number of ovals of any symmetry of s...

We study parametrized dynamics of the Weierstrass elliptic ℘ function by looking at the underlying lattices; that is, we study parametrized families ℘Λ and let Λ vary. Each lattice shape is represented by a point τ in a fundamental period in modular space; for a fixed lattice shape Λ = [1, τ ] we study the parametrized space kΛ. We show that within each shape space there is a wide variety of dy...