Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracy--higher than the traditional condition numbers for linear systems suggest. This phenomenon is investigated by use of condition numbers appropriate to the componentwis...

The main purpose of this paper was to evaluate the performance of the triangular vanes located on the bed and their effect on the bed topography considering different flow conditions. For this purpose, tests were carried out on a straight flume for different flow conditions (five Froude numbers of 0.18, 0.20, 0.22, 0.24 and 0.26) by installing a series of triangular vanes at a space of 4Le (Le ...

This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-pat...

Abstract In this paper, multi-objective optimization (MOO) of Al2O3-water nanofluid flow in microchannel heat sinks (MCHS) with triangular ribs is performed using Computational Fluid Dynamics (CFD) techniques and Non-dominated Sorting Genetic Algorithms (NSGA II). At first, nanofluid flow is solved numerically in various MCHS with triangular ribs using CFD techniques. Finally, the CFD data will...

We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. Contrary to intuition, we show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a square tile assembly ...

Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...

in this paper a linear fuzzy fredholm integral equation(ffie) with arbitrary fuzzy function input and symmetric triangular (fuzzy interval) output is considered. for each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (ffie).

Polyphilic self-assembly leads to compartmentalization of space and development of complex structures in soft matter on different length scales, reaching from the morphologies of block copolymers to the liquid crystalline (LC) phases of small molecules. Whereas block copolymers are known to form membranes and interact with phospholipid bilayers, liquid crystals have been less investigated in th...

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solv...