a class of submodular functions for document summarization

... 1. 3.3 Automatic summarization evaluation Automatic evaluation of summary quality is impor- tant for the research of document summarization as it avoids the labor-intensive and potentially inconsis- tent ... summarization can be viewed as a problem of submodular function maximization. We also in this section show that many standard methods for summarization are, in fact, al- ready performing submodular function ... constant-factor approximation guarantee does not apply in this case. When scoring a summary at the sub-sentence level, submodularity naturally arises. Concept-based summarization (Filatova and Hatzivassiloglou,...

Ngày tải lên: 23/03/2014, 16:20

... Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. New proofs of Schur-concavity for a class of ... (sftguchun@buu.edu.cn) ISSN 1029-242X Article type Research Submission date 24 May 2011 Acceptance date 17 January 2012 Publication date 17 January 2012 Article URL http://www.journalofinequalitiesandapplications.com/content/2012/1/12 This ... your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information about other SpringerOpen publications go...

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... Albarreal, M.C. Calzada, J.L. Cruz, E. Fern ´ andez-Cara, M. Mari´n, Stability and Convergence of a Parallel Fractional Step Method for the Solution of Linear Parabolic Problems, Applied Mathematics ... Journal of Science, Mathematics - Physics 23 (2007) 201-209 Fully parallel methods for a class of linear partial differential-algebraic equations Vu Tien Dung ∗ Department of Mathematics, Mechanics, ... parallel methods for solving linear partial differential- algebraic equations (PDAEs) of the form: Au t + B∆u = f(x, t) (1) where A is a singular, symmetric and nonnegative matrix, while B is a...

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... USA *Corresponding author: manuel.delasen@ehu.es Email address: RPA: Agarwal@tamuk.edu Abstract This article discusses three weak φ-contractive conditions of rational type for a class of ... via Lemma 2.1 as follows for the case when A and B do not intersect, in general: Theorem 3.1. Assume that BABAT ∪ → ∪ : is a modified weak φ-contraction, that is, a cyclic self-map satisfying ... self-mappings under three general weak contractive conditions of rational type Manuel De la Sen *1 and Ravi P Agarwal 2 1 Instituto de Investigacion y Desarrollo de Procesos, Universidad del Pais...

Ngày tải lên: 18/06/2014, 22:20

... equations Huantao Zhu 1 and Weibing Wang ∗2 1 Hunan College of Information, Changsha, Hunan 410200, P.R. China 2 Department of Mathematics, Hunan University of Science and Technology, Xiangtan, ... Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Periodic solutions for a class of higher ... study was supported by the NNSF of China (10871063) and Scientific Research Fund of Hunan Provincial Education Department (10B017). References [1] Agarwal, RP: Difference Equations and Inequalities,...

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... the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Lyapunov-type inequalities for a class of even-order differential equations Journal ... Lyapunov-typ e inequalities for certain higher order differential equations. J. Math. Anal. Appl. 195 , 527–536 (1995) [9] Tang, XH, Zhang, M: Lyapunov inequalities and stability for linear Hamiltonian ... Research Submission date 19 October 2011 Acceptance date 12 January 2012 Publication date 12 January 2012 Article URL http://www.journalofinequalitiesandapplications.com/content/2012/1/5 This peer-reviewed article...

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... Boundary Value Problems. Chapman and hall/CRC Press, Boca Raton (2005) 10. Gasiński, L, Papageorgiou, NS: Nontrivial solutions for a class of resonant p-Laplacian Neumann problems. Nonlinear Anal. ... u t (x,0)=u 1 (x) . P-Kirchhoff problem began to attract the attention of several researchers mainly after the work of Lions [1], where a funct ional analysis approach was proposed to attack it. The reader may consult ... (1986) doi:10.1186/1687-2770-2011-32 Cite this article as: Yang and Zhang: Existence results for a class of nonlocal problems involving p-Laplacian. Boundary Value Problems 2011 2011:32. Yang and Zhang Boundary Value Problems...

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... Math Anal Appl. 352, 99–111 (2009). doi:10.1016/j.jmaa.2008.06.021 16. Kang, D: Solution of the quasilinear elliptic problem with a critical Sobolev-Hardy exponent and a Hardy term. J Math Anal ... 2011:37 http://www.boundaryvalueproblems.com/content/2011/1/37 Page 11 of 15 11. Wang, L, Wei, Q, Kang, D: Multiple positive solutions for p-Laplace elliptic equations involving concave-convex nonlinearities and a Hardytype term. Nonlinear Anal. 74, ... sign-changing weight functions. Abstr Appl Anal 2009, 24 (2009). Article ID 652109) 20. Kang, D, Huang, Y, Liu, S: Asymptotic estimates on the extremal functions of a quasilinear elliptic problem....

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... Investigacion y Desarrollo de Procesos, Universidad del Pais Vasco, Campus of Leioa (Bizkaia), Aptdo. 644-Bilbao, 48080- Bilbao, Spain Full list of author information is available at the end of the article Abstract This ... theorem for mappings satisfying a contractive condition of rational type of partially ordered metric space. Abstr Appl Anal 2010, 8 (2010). (Article Number 190701) 2. Harjani, J, Sadarangani, K: Fixed ... identical to (3.30) except in the order of its elements. □ An example is given below Example 3.6: Take p = 2 and subsets A 1 ≡ C (a, 0 ,a- a 0 ) and A 2 ≡ C( -a, 0 ,a- a 0 )ofR 2 are circles of centre in (a, ...

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... tree (a particular case of tree-indexed Markov chains field and PPG-invariant random field). Yang [9] has studied the strong law of large numbers for frequency of occurrence of state and Shannon-McMillan ... existence of en tropy rate for some stationary random fields on a homogeneous tree. Pemantle [5] proved a mixing prop erty and a weak law of large numbers for a PPG-invariant and ergodic random field ... Correspondence: shizhiyan1984@126.com 1 Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract In this paper, we are to establish...

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... difference equations can be considered as the discrete analog of classical Volterra-Fredholm type integral equations, which arise in the theory of parabolic boundary value problems , the mathematical modeling ... 2011:30 http://www.advancesindifferenceequations.com/content/2011/1/30 Page 16 of 16 RESEARCH Open Access Qualitative and quantitative analysis for solutions to a class of Volterra-Fredholm type ... and their applications. J Comupt Appl Math. 202, 339–351 (2007). doi:10.1016/j.cam.2006.02.036 12. Pang, PYH, Agarwal, RP: On an integral inequality and discrete analogue. J Math Anal Appl. 194,...

Ngày tải lên: 21/06/2014, 00:20

... estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions Faramarz Tahamtani * and Amir Peyravi * Correspondence: tahamtani@shirazu.ac.ir Department of Mathematics, College ... Nouria, S: Polynomial and analytic boundary feedback stabilization of square plate. Bol Soc Parana Math. 27(2):23–43 (2009) 19. Ammari, K, Tucsnak, M: Stabilization of second order evolution equations ... this article as: Tahamtani and Peyravi: Spatial estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions. Boundary Value Problems 2011 2011:19. Submit your manuscript...

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