We propose a discretization scheme for a numerical solution of elliptic PDE’s, based on local representation of functions, by their Taylor polynomials (jets). This scheme utilizes jet calculus to provide a very high order of accuracy for a relatively small number of unknowns involved.

Residual distribution schemes are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution is globally continuous, defined by a Finite Element space based on triangular Lagrangian Pk elements. A natural subtriangulation of these elements allows the reuse of simple distribution formula previously developed for linear P1 triangles. Th...

Given an ordinary differential equation on a homogeneous manifold, one can construct a “geometric integrator” by determining a compatible ordinary differential equation on the associated Lie group, using a Lie group integration scheme to construct a discrete time approximation of the solution curves in the group, and then mapping the discrete trajectories onto the homogeneous manifold using the...

Due to their linguistic and extra-linguistic nature toponyms deserve a special treatment when they are translated. The paper deals with issues related to automated translation of toponyms from English into Latvian. Translation process allows us to translate not only toponyms from a dictionary, but out-of-vocabulary toponyms as well. Translation of out-of-vocabulary toponyms is divided into thre...

Statistical Machine Translation (SMT) is a new paradigm in machine translation, which enables highquality translation. However, many translation errors occur in the translation of complex and compound sentences because of the lack of grammatical knowledge about the global structure of a sentence. We adopt the pre-editing method, which divides sentences into clauses, and translate these clauses ...

In this paper we solve the elasticity problem of two elastic half spaces that are joined together over a region that does not differ much from a circle, i.e., the problem of an external planar crack leaving a nearly circular uncracked connection. The method we use is based on the perturbation technique developed by Rice (1985) for solving the elastic field of a crack whose front deviates slight...

Abstract. We are concerned with the detection of edges – the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our...

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on gener...

Predicate-argument structure contains rich semantic information of which statistical machine translation hasn’t taken full advantage. In this paper, we propose two discriminative, feature-based models to exploit predicateargument structures for statistical machine translation: 1) a predicate translation model and 2) an argument reordering model. The predicate translation model explores lexical ...