in this paper, the lorentzian version of beltrami-euler formula is investigated in 1n . initially,the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the help of the christoffel symbols, riemann-christoffel curvatures are obtained. thus, the curvatures of spacelike and timelike tangential sections of generalized timelike ruled surf...

let a; b; k 2 k and u ; v 2 u(k). we show for any idempotent e 2 k, ( a 0 b 0 ) is e-clean i ( a 0 u(vb + ka) 0 ) is e-clean and if ( a 0 b 0 ) is 0-clean, ( ua 0 u(vb + ka) 0 ) is too.

Based on Lagrange and Hermite interpolation two novel versions of weak form quadrature element are proposed for a non-classical Euler-Bernoulli beam theory. By extending these concept two new plate elements are formulated using Lagrange-Lagrange and mixed Lagrange-Hermite interpolations for a non-classical Kirchhoff plate theory. The non-classical theories are governed by sixth order partial di...

In this paper, the finite element discretization of non-classical continuum models with micro-inertia is analysed. The focus on extensions one-dimensional rod model, beam bending theories Euler–Bernoulli and Rayleigh, two-dimensional membrane model. performance a variety mass matrices assessed by comparing natural frequencies their modes those associated discrete systems, it demonstrated that u...

High-order entropy-stable discontinuous Galerkin (DG) methods for nonlinear conservation laws reproduce a discrete entropy inequality by combining conservative finite volume fluxes with summation-by-parts (SBP) discretization matrices. In the DG context, on tensor product (quadrilateral and hexahedral) elements, SBP matrices are typically constructed collocating at Lobatto quadrature points. Re...

Abstract Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely Hamilton–Jacobi–Bellman (HJB) equation. In general, this cannot be solved analytically, thus numerical algorithms are only tools provide accurate approximations. The aims paper is introduce novel fitted finite volume method solve high dimensional degenerated HJB from stochastic control...

In this paper, we address the numerical solution of optimal transport problem on undirected weighted graphs, taking shortest path distance as cost. The is obtained from long-time limit gradient descent dynamics. Among different time stepping procedures for discretization dynamics, a backward Euler scheme combined with inexact Newton--Raphson method results in robust and accurate approach graphs...

In this article, we analyze the effect of transverse cracks on natural frequencies a Euler-Bernoulli functional gradient beam. The studied beam was discretized into finite elements and global matrices motion equation are determined by applying Lagrange to kinetic deformation energies. material properties considered vary in directions thickness, gradation is described power-law distribution, sti...

Abstract We consider the approximation of Navier-Stokes equations for a Newtonian fluid by Euler type systems with relaxation both in compressible and incompressible cases. This requires to decompose second-order derivative terms velocity into first-order ones. Usual decompositions lead approximate tensor variables. construct vector variables using Hurwitz-Radon matrices. These are written form...