This paper presents a new regular expression matching method by using Dual Glushkov NFA. Dual Glushkov NFA is the variant of Glushkov NFA, and it has the strong property that all the outgoing edges to a state of it have the same labels. We propose the new matching method Look Ahead Matching that suited to Dual Glushkov NFA structure. This method executes NFA simulation with reading two input ch...

The primal-dual method (or primal-dual schema) is another means of solving linear programs. The basic idea of this method is to start from a feasible solution y to the dual program, then attempt to find a feasible solution x to the primal program that satisfies the complementary slackness conditions. If such an x cannot be found, it turns out that we can find a better y in terms of its objectiv...

Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of divergence-free vector fields, which obey a particular set of chiral equations. Upon imposing the Jacobi identity upon these vector fields, we reproduce a pre...

Multiscale finite element numerical methods are used to solve flow problems when the coefficient in the elliptic operator is heterogeneous. A popular mixed multiscale finite element has basis functions which can be defined only over pairs of elements, so we call it a “dual-support” element. We show by example that it can fail to reproduce constant flow fields, and so fails to converge in any me...

A Legendre and Chebyshev dual-Petrov–Galerkin method for hyperbolic equations is introduced and analyzed. The dual-Petrov– Galerkin method is based on a natural variational formulation for hyperbolic equations. Consequently, it enjoys some advantages which are not available for methods based on other formulations. More precisely, it is shown that (i) the dual-Petrov–Galerkin method is always st...

The effects of dual consistency on discontinuous Galerkin (DG) discretizations of solution and solution gradient dependent source terms are examined. Two common discretizations are analyzed: the standard weighting technique for source terms and the mixed formulation. It is shown that if the source term depends on the first derivative of the solution, the standard weighting technique leads to a ...

By J. Douglas, Jr., R. B. Kellogg, and R. S. Varga We consider the iterative solution of the system of linear equations (1 ) (Xi + X-, + • ■ ■ + Xn)z = /, n 2; 2, where each Xj, 1 | j | n, is a Hermitian and positive definite N X N matrix. If n = 2, the iterative methods of Peaceman-Rachford [1, Chapter 7], or D'yakonov [2] and Kellogg [3], may be used to solve (1). In this paper these methods ...

Two-dimensional hypersingular equations over a disc are considered. A spectral method is developed, using Fourier series in the azimuthal direction and orthogonal polynomials in the radial direction. The method is proved to be convergent. Then, Tranter’s method is discussed. This method was devised in the 1950s to solve certain pairs of dual integral equations. It is shown that this method is a...

In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order semilinear elliptic equations. We first introduce several approximate dual problems, and briefly discuss the target problem class. We then review some standard facts concerning conforming finite element discretization and error-estimate-driven adaptive finite element me...