Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized Kerr-Schild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied...

The IDR method of Sonneveld and van Gijzen [SIAM J. Sci. Comput., 31:1035–1062, 2008] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petro...

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouville operator in the sense of the norm. Spectral Galerkin and Petrov-Galerkin methods for tempered fractional advection problems and tempered ...

A new family of Petrov-Galerkin nite element methods on triangular grids is constructed for singularly perturbed elliptic problems in two dimensions. It uses divergence-free trial functions that form a natural generalization of one-dimensional exponential trial functions. This family includes an improved version of the divergence-free nite element method used in the PLTMG code. Numerical result...

PTB 23 Model F1 Sent./s. Charniak (2000) 89.5 Stanford PCFG (2003) 85.5 5.3 Petrov (2007) 90.1 8.6 Zhu (2013) 90.3 39.0 Carreras (008) 91.1 CJ Reranking (2005) 91.5 4.3 Stanford RNN (2013) 90.0 2.8 PAD 90.6 34.3 PAD (Pruned) 90.5 58.6 CTB 5 Model F1 Charniak (2000) 80.8 Bikel (2004) 80.6 Petrov (2007) 83.3 Zhu (2013) 83.2 PAD 82.4 Experiments Contributions • A phrase-structure parser (PAD) achi...

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...

We present an unsupervised approach to part-of-speech tagging based on projections of tags in a word-aligned bilingual parallel corpus. In contrast to the existing state-of-the-art approach of Das and Petrov, we have developed a substantially simpler method by automatically identifying “good” training sentences from the parallel corpus and applying self-training. In experimental results on eigh...

The minimal prolongation structure for the Robinson-Trautman equations of Petrov type III is shown to always include the infinite-dimensional, contragredient algebra, K 2 , which is of infinite growth. Knowledge of faithful representations of this algebra would allow the determination of Bäcklund transformations to evolve new solutions. The general class of Robinson-Trautman solutions [1] to th...