中国计量大学理学院导师：曹飞龙 正文

　　基本信息
　　姓名：曹飞龙
　　性别：男
　　学位：博士
　　职称：教授
　　一级学科：数学
　　二级学科：应用数学
　　二级学院：理学院
　　一级学科2：数学
　　二级学科2：计算数学
　　研究方向：智能计算、可信软件、图形图像处理、函数逼近论及其应用
　　Email：flcao@cjlu.edu.cn

　　在研课题
　　基于球调和分析理论的信号稀疏表示与重构算法”，性质：国家自然科学基金面上项目，排名：1/9，编号：61272023，执行时时间：2013.1-2016.12
　　
　　近期发表的主要成果
　　1. 曹飞龙，夏晟。球面混合插值的逼近性质，中国科学（A辑），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，张永全，曹飞龙*．多元回归学习算法收敛速度的估计，中国科学F辑：信息科学，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)

　　主持完成的科研项目
　　项目名称：基于逼近理论的误差可控计算与可信算法研究，
　　性质：国家自然科学基金可信软件重大研究计划项目，
　　排名：1/10，批准号：90818020，执行时间：2009.1-2011.12
　　1．项目名称：球面学习理论研究，性质：国家自然基金面上项目，排名：1/9，批准号：60873206，执行时间：2009.1-2011.12。
　　2．项目名称：超强学习机国际研讨会，性质：国家自然科学基金国际合作与交流项目，排名：1/1，编号：61110306122，执行时时间：2011.9-2012.12。
　　3．项目名称：奇异摄动时滞系统最优控制近似方法研究，性质：国家自然科学基金面上项目，排名：2/9，批准号60874029，执行时间：2009.1-2011.12。
　　4．项目名称：神经网络逼近与插值的下界估计，性质：省自然科学基金项目，排名：1/6，批准号：Y7080235，执行时间：2009.1-2011.12

　　个人简历
　　曹飞龙，教授，博士后。现任理学院院长，浙江省重点学科“应用数学”学科负责人，计量与计算科学研究所所长。
　　（1）浙江省高校中青年学科带头人（2004---）
　　（2）浙江省“新世纪151优秀人才工程第二层次培养人员”（2006—）
　　（3）西安交通大学兼职博士生导师（2007--）
　　（4）河北师范大学兼职硕士生导师（2003—）
　　（5）浙江省数学教学指导委员会委员（2008—）

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