中國計量大學理學院導師：曹飛龍 正文

　　基本信息
　　姓名：曹飛龍
　　性別：男
　　學位：博士
　　職稱：教授
　　一級學科：數學
　　二級學科：應用數學
　　二級學院：理學院
　　一級學科2：數學
　　二級學科2：計算數學
　　研究方向：智能計算、可信軟件、圖形圖像處理、函數逼近論及其應用
　　Email：flcao@cjlu.edu.cn

　　在研課題
　　基于球調和分析理論的信號稀疏表示與重構算法”，性質：國家自然科學基金面上項目，排名：1/9，編號：61272023，執(zhí)行時時間：2013.1-2016.12
　　
　　近期發(fā)表的主要成果
　　1. 曹飛龍，夏晟。球面混合插值的逼近性質，中國科學（A輯），43（1），pp 45-60，2013
　　2．F. L. Cao*, S. B. Lin, X. Y. Chang, Z. B. Xu. Learning rates of regularized regression on the unit sphere. Science China, Series A, Mathematics, DOI: 10.1007/ s11425-000-0000-0, 2013(SCI)
　　3．F. L. Cao*, X. Xing. An oracle inequality for regularized minimizers with strongly mixing observations. Front. Math. China, DOI: 10.1007/s11464-012-0186-5, 2013(SCI)
　　4．F. L. Cao*, B. Liu, D. S. Park. Image classification based on effective extreme learning machine. Neurocomputing, 102, pp 90–97, 2013 (SCI)
　　5．F. L. Cao, C. M. Wang. The learning rate for regularized least-squares algorithm on the unit sphere. J. Computational Analysis and Applications, 15(2), pp 224-236, 2013 (SCI)
　　6．M. Li, F. L. Cao*, Z. X. Chen. The equivalent theorem for Jackson-type operators on spherical cap. J. Computational Analysis and Applications, 15(4), pp 778-787, 2013(SCI)
　　7．Z. X. Chen, F. L. Cao*. The properties of logistic function and applications to neural network approximation. J. Computational Analysis and Applications, 15(6), pp 1046-1056, 2013(SCI)
　　8．T. F. Xie, F. L. Cao*. The rate of approximation of Gaussian radial basis neural networks in continuous function space. Acta Mathematica Sinica, English Series, 29(2), pp 295-302, 2013 (SCI)
　　9．Z. H. Zhou, J. W. Zhao, F. L. Cao*. Surface reconstruction based on extreme learning machine. Neural Computing and Applications, doi: 10.1007/s00521-012-0891-8, 2013(SCI)
　　10．J. W. Zhao, Z. H. Zhou, F. L. Cao*. Human face recognition based on ensemble of polyharmonic classifiers. Neural Computing and Applications, DOI: 10.1007/ s00521 -013- 1356-4, 2013(SCI)
　　11．F. L. Cao*, S. B. Lin. Multivariate weighted Bernstein-type inequality and its applications. Acta Mathematica Scientia, 32B(2), pp471–482, 2012(SCI)
　　12．F. L. Cao*, X. Xing, J. W. Zhao. Learning rates of support vector machine classification for density level detection. Neurocomputing, 82, pp 84–90, 2012 (SCI)
　　13．F. L. Cao*, Z. H. Lee, Y. Q. Zhang. Estimates of learning rates of regularized regression via polyline functions. Math. Methods in Applied Sciences, 35, pp 174–181, 2012(SCI)
　　14．F. L. Cao*, D. Wu, Z. H. Lee, Learning rates for regularized classifiers using trigonometric polynomial kernels, Neural Process. Lett, 35, pp265-281, 2012(SCI)
　　15．Z. X. Chen, F. L. Cao*. The construction and approximation of a class of neural networks operators with ramp functions. J. Comput. Anal. Appli, 14(1), pp 101-112, 2012(SCI)
　　16．Z. X. Chen, F. L. Cao*, Jinjie Hu. Error estimates of quasi-interpolation and its derivatives. J. Comput. Applied Math, 236, pp 3137-3146, 2012(SCI)
　　17．Z. X. Chen, F. L. Cao*, J. W. Zhao. The construction and approximation of some neural networks operators. Applied Math. J. Chinese Univ, 27(1), pp 69-77, 2012(SCI)
　　18．Z. B. Xu, Y. Q. Zhang, F. L. Cao*. Estimation of convergence rate for multi-regression learning algorithm, Sciences in China, Series F: Information Science, 55(3), pp 701-713, 2012(SCI)
　　　　徐宗本，張永全，曹飛龍*．多元回歸學習算法收斂速度的估計，中國科學F輯：信息科學，41（2），pp 144-156，2011
　　19．Y. Q. Zhang, F. L. Cao*. Analysis of convergence performance of neural networks ranking algorithm, Neural Networks, 34, pp 65-71, 2012(SCI)
　　20．Y. B. Yuan, H. Y. Zhu, B. Liu, F. L. Cao*.Software reliability modeling with removed errors and compounded-decreased-rate. Mathematical and Computer Modelling, 55, pp 697–709, 2012 (SCI)
　　21．S. B. Lin, F. L. Cao, X. Y. Chang, Z. B. Xu. A general radial quasi-interpolation operator on the sphere. J. Approx. Theory, 164, pp1402-1414, 2012 (SCI)
　　22．S. B. Lin, F. L. Cao, Z. B. Xu. A convergence rate for approximate solutions of Fredholm integral equations of the first kind. Positivity, 16(4), pp 641-652, 2012 (SCI)
　　23．S. B. Lin, F. L. Cao, Z. B. Xu, X. F. Guo. Cubature formula for spherical basis function networks. Chinese Annals of Mathematics-Series B, 33(6), pp 807-814, 2012(SCI)
　　24．J. W. Zhao, Dong Sun Park, Joonwhoan Lee, F. L. Cao*. Generlized extreme learning machine on a metric space, Soft Computing, 16, pp1503–1514, 2012 (SCI)
　　25．S. B. Lin, F. L. Cao, Z. B. Xu, Essential rate for approximation by spherical neural networks, Neural Networks, 24, pp 752–758, 2011(SCI: 813VB)
　　26．Y. Q. Zhang, F. L. Cao*, Z. B. Xu. Estimation of learning rate of least square algorithm via Jackson operators. Neurocomputing, 74, pp 516–521, 2011 (SCI: 712WU)
　　27．Y. Q. Zhang, F. L. Cao*, Z. B. Xu. Optimal rate of the regularized regression learning algorithm, Inter. J. Computer Math, 88(7), pp 1471 -1483, 2011(SCI: 749YA)
　　28．F. L. Cao*, X. Xing. Learning rates for multi-kernel linear programming classifiers, Frontiers of Mathematics in China, 6(2), pp 203-219, 2011 (SCI: 746YG)
　　29．Y. B. Yuan, Y. G. Wang, F. L. Cao*, Optimization approximation solution for regression problem based on extreme learning machine, Neurocomputing, 74, pp 2475–2482, 2011 (SCI: 823ET)
　　30．Y. G. Wang, F. L. Cao*, Y. B. Yuan, A study on effectiveness of extreme learning machine, Neurocomputing, 74, pp 2483–2490, 2011 (SCI: 823ET)
　　31．F. L. Cao*, S. B. Lin, Z. B. Xu. Constructive approximate interpolation by neural networks in the metric space, Math. Computer Model, 52, pp 1674-1681, 2011 (SCI: 644DZ)
　　32. T. F. Xie, F. L. Cao*. The errors of simultaneous approximation of multivariate functions by neural networks, Computers and Mathematics with Applications, 61, pp 3146– 3152, 2011, (SCI: 775IQ)
　　33．S. B. Lin, F. L. Cao*, Z. B. Xu, The essential rate of approximation for radial function manifold, Science in China Ser. A: Mathematics, 54(9), pp 1985-1994, 2011 (SCI: 811OY)
　　34．F. L. Cao*, H. Z. Wang, S. B. Lin. The estimate for approximation error of spherical neural networks, Math. Methods Applied Sciences, 34(15), pp 1888-1895, 2011 (SCI: 831FW)
　　35．Y. G. Wang, F. L. Cao*. Approximation by Boolean sums of Jackson operators on the sphere. J. Computational Analysis and Applications, 13(5), pp 830-842, 2011 (SCI:736XB)
　　36．F. L. Cao*, X. F. Guo, S. B. Lin. Lp error estimations for scattered data interpolation on the sphere. Numerical Functional Analysis and Optimization, 32(12), pp 1205– 1218, 2011 (SCI: )
　　37．F. L. Cao*, S. B. Lin. The capabilities of approximation for interpolation neural networks on the sphere. Math. Methods Applied Sciences, 34, pp 469-478, 2011 (SCI: 731FJ)
　　38．S. B. Lin, F. L. Cao*. Strong Converse Inequality for a Spherical Operator. J. Ineq. Appli, 2011, 1-7, 2011 (SCI: 60QQ)
　　39．F. L. Cao*, S. B. Lin. Nikolskii-type inequality with doubling weights. Journal of Computational Analysis and Applications, 13(5), pp 822-829, 2011 (SCI:736XB)
　　40．F. L. Cao*, Y. F. Liu. Approximation theorems by positive linear operators in weighted spaces, Positivity, 15, 87–103, 2011 (SCI:723JZ)
　　41．T. F. Xie, F. L. Cao*. The ridge function representation of polynomials and an application to neural networks, Acta Math. Sinica (English Series), 27(11), pp 2169– 217, 2011 (SCI: 837CP)
　　42．F. L. Cao*, Y. F. An. Lp Approximation by Multivariate Baskakov-Durrmeyer Operator. J. Ineq. Appli, 2011, 1-7, 2011 (SCI: 760PY)
　　43．T. F. Xie, F. L. Cao*, The errors in simultaneous approximation by feed-forward neural networks, Neurocomputing, 73, pp 903–907, 2010 (SCI: 570AC )
　　44．F. L. Cao*,S. B. Lin, Z. B. Xu. The capabilities of approximation for interpolation neural networks. Neurocomputing, 73, pp 457-460, 2010 (SCI: 701GG)
　　45．F. L. Cao*, Y. B. Yuan. Learning errors of linear programming support vector regression. Applied Math. Modeling, 35, pp1820-1828, 2010 (SCI: 717QR)
　　46．F. L. Cao*, X. F. Guo. Approximation by Jackson-type operator on the sphere. Mathematical Communications, 15, pp 331-346, 2010 (SCI: 691ME)
　　47．Z. X. Chen, F. L. Cao*. Global errors for approximate approximations with Gaussian kernels on compact intervals. Applied Math. Computation, 217: 725–734, 2010 (SCI: 640PG)
　　48．F. L. Cao, S. B. Lin, B. L. Zhang. On general Bernstein and Nikol’ski? type inequalities. Appl. Math. J. Chinese Univ, 25(1), pp 35-42, 2010 (SCI: 568MM)

　　主持完成的科研項目
　　項目名稱：基于逼近理論的誤差可控計算與可信算法研究，
　　性質：國家自然科學基金可信軟件重大研究計劃項目，
　　排名：1/10，批準號：90818020，執(zhí)行時間：2009.1-2011.12
　　1．項目名稱：球面學習理論研究，性質：國家自然基金面上項目，排名：1/9，批準號：60873206，執(zhí)行時間：2009.1-2011.12。
　　2．項目名稱：超強學習機國際研討會，性質：國家自然科學基金國際合作與交流項目，排名：1/1，編號：61110306122，執(zhí)行時時間：2011.9-2012.12。
　　3．項目名稱：奇異攝動時滯系統(tǒng)最優(yōu)控制近似方法研究，性質：國家自然科學基金面上項目，排名：2/9，批準號60874029，執(zhí)行時間：2009.1-2011.12。
　　4．項目名稱：神經網絡逼近與插值的下界估計，性質：省自然科學基金項目，排名：1/6，批準號：Y7080235，執(zhí)行時間：2009.1-2011.12

　　個人簡歷
　　曹飛龍，教授，博士后?，F任理學院院長，浙江省重點學科“應用數學”學科負責人，計量與計算科學研究所所長。
　　（1）浙江省高校中青年學科帶頭人（2004---）
　?。?）浙江省“新世紀151優(yōu)秀人才工程第二層次培養(yǎng)人員”（2006—）
　?。?）西安交通大學兼職博士生導師（2007--）
　　（4）河北師范大學兼職碩士生導師（2003—）
　?。?）浙江省數學教學指導委員會委員（2008—）

　　*如果發(fā)現導師信息存在錯誤或者偏差，歡迎隨時與我們聯系，以便進行更新完善。

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