‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

background: as various implant geometries present different biomechanical behaviors, the purpose of this work was to study stress distribution around tapered and cylindrical threaded implant geometries using three-dimensional finite element stress analysis.     methods: seven implant models were constructed using the cad system. after digitized models of mandibular section, the crowns were crea...

The design, implementation and performance of a parallel algorithm for reduction of a matrix pair in block upper Hessenberg-Triangular form (Hr, T ) to upper Hessenberg-triangular form (H, T ) is presented. This reduction is the second stage in a two-stage reduction of a regular matrix pair (A, B) to upper Hessenberg-Triangular from. The desired upper Hessenberg-triangular form is computed usin...

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

In this article, by using the method of finite difference time domain (FDTD) and PML boundary conditions, we have studied the photonic band gaps for TE and TM modes in square and triangular lattices consisting of air holes in dielectric medium and compared the results. In addition, the effect of nonlinearity of the photonic crystal background on the photonic band gaps and comparison with the re...

Sparse triangular solvers are typically parallelized using levelscheduling techniques, but parallel efficiency is poor on high-throughput architectures like GPUs. We propose using an iterative approach for solving sparse triangular systems when an approximation is suitable. This approach will not work for all problems, but can be successful for sparse triangular matrices arising from incomplete...

We present the result and accuracy comparison of generalized positivitypreserving schemes for triangular Bézier patches of 1 C and 2 C scattered data interpolants that have been constructed. We compare three methods of 1 C schemes using cubic triangular Bézier patches and one 2 C scheme using quintic triangular Bézier patches. Our test case consists of four sets of node/test function pairs, wit...