We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold ( _0 ). We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ( R ). For all (| | ) sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold ( _ ). For ( =0 ), ( _0= _0 R ). We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of ( _0 ) under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of ( _ ), (W^ s ( _ ) ) and (W^ u ( _ ) ), respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of (W^ s ( _ ) ) and (W^ u ( _ ) ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order (O( ) ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in ( _0 ), and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on the Melnikov potential are generic.
Some other related papers are @cite_30 @cite_22 @cite_14 @cite_10 @cite_31 @cite_23 @cite_3 @cite_9 @cite_27 .
@cite_30 @cite_14 @cite_22 @cite_9 @cite_3 @cite_27 @cite_23 @cite_31 @cite_10
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When we write or prepare to write a research paper, we always have appropriate references in mind. However, there are most likely references we have missed and should have been read and cited. As such a good citation recommendation system would not only improve our paper but, overall, the efficiency and quality of literature search. Usually, a citation's context contains explicit words explaining the citation. Using this, we propose a method that "translates" research papers into references. By considering the citations and their contexts from existing papers as parallel data written in two different "languages", we adopt the translation model to create a relationship between these two "vocabularies". Experiments on both CiteSeer and CiteULike dataset show that our approach outperforms other baseline methods and increase the precision, recall and f-measure by at least 5 to 10 , respectively. In addition, our approach runs much faster in the both training and recommending stage, which proves the effectiveness and the scalability of our work. Resume Dans cet article qui developpe une Note ( Giraud, G., C. R. Acad. Sci. Paris Ser. A , 276 (1973) 1173–1175), nous prouvons que, pour n assez grand, tout bicoloriage des aretes de K n contient une proportion de K 4 dont les six aretes sont de meme couleur au moins egale a 1 46 , et que si le nombre de triangles unicolores est minimal, cette proportion passe au moins a (5 − 10 1 2 ) 64 a O(n 7 2 ) pres. Nous exposons aussi une methode de majoration des nombres de Ramsey binaires-bicolores qui fournit ϱ(6, 6) ≤ 169. Document authors commonly use tables to support arguments presented in the text. But, because tables are usually separate from the main body text, readers must split their attention between different parts of the document. We present an interactive document reader that automatically links document text with corresponding table cells. Readers can select a sentence (or tables cells) and our reader highlights the relevant table cells (or sentences). We provide an automatic pipeline for extracting such references between sentence text and table cells for existing PDF documents that combines structural analysis of tables with natural language processing and rule-based matching. On a test corpus of 330 (sentence, table) pairs, our pipeline correctly extracts 48.8 of the references. An additional 30.5 contain only false negatives (FN) errors -- the reference is missing table cells. The remaining 20.7 contain false positives (FP) errors -- the reference includes extraneous table cells and could therefore mislead readers. A user study finds that despite such errors, our interactive document reader helps readers match sentences with corresponding table cells more accurately and quickly than a baseline document reader. Citations play an essential role in navigating academic literature and following chains of evidence in research. With the growing availability of large digital archives of scientific papers, the automated extraction and analysis of citations is becoming increasingly relevant. However, existing approaches to citation extraction still fall short of the high accuracy required to build more sophisticated and reliable tools for citation analysis and corpus navigation. In this paper, we present techniques for high accuracy extraction of citations and references from academic papers. By collecting multiple sources of evidence about entities from documents, and integrating citation extraction, reference segmentation, and citation-reference matching, we are able to significantly improve performance in subtasks including citation identification, author named entity recognition, and citation-reference matching. Applying our algorithm to previously-unseen documents, we demonstrate high F-measure performance of 0.980 for citation extraction, 0.983 for author named entity recognition, and 0.948 for citation-reference matching.