The factored translation model in Moses (Koehn et al. 2007; Avramidis and Koehn 2008; Koehn 2010), which consists of translation processes followed by a generation process, intends to handle morphologically rich languages by integrating additional linguistic markup at the word level, where each type of additional word-level information is called a factor with the independent assumptions shown i...

Using the integrating factor method, this paper deals with the Hyers-Ulam stability of a class of exact differential equations of second order. As a direct application of the main result, we also obtain the HyersUlam stability of a special class of Cauchy-Euler equations of second order. c ©2016 All rights reserved.

New idea and algorithm are proposed to compute asymptotic expression of limit cycles bifurcated from the isochronous center. Compared with known inverse integrating factor method, new algorithm to analytically computing shape of limit cycle proposed in this paper is simple and easy to apply. The applications of new algorithm to some examples are also given.

We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields which are volume preserving and possess nontrivial normalizers. Our approach is geometric and coordinate-free and hence it works on any smooth orientable manif...