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CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal's highest standard and closest link to the scientific communities.


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Preface to the special issue on analysis in machine learning and data science
Andreas Chirstmann, Qiang Wu and Ding-Xuan Zhou
2020, 19(8) : i-iii doi: 10.3934/cpaa.2020171 +[Abstract](124) +[HTML](50) +[PDF](95.35KB)
Learning rates for partially linear functional models with high dimensional scalar covariates
Yifan Xia, Yongchao Hou, Xin He and Shaogao Lv
2020, 19(8) : 3917-3932 doi: 10.3934/cpaa.2020172 +[Abstract](81) +[HTML](31) +[PDF](434.57KB)
Sparse generalized canonical correlation analysis via linearized Bregman method
Jia Cai and Junyi Huo
2020, 19(8) : 3933-3945 doi: 10.3934/cpaa.2020173 +[Abstract](77) +[HTML](31) +[PDF](691.54KB)
Quantitative robustness of localized support vector machines
Florian Dumpert
2020, 19(8) : 3947-3956 doi: 10.3934/cpaa.2020174 +[Abstract](96) +[HTML](34) +[PDF](374.28KB)
Exact asymptotic orders of various randomized widths on Besov classes
Liqin Duan and Peixin Ye
2020, 19(8) : 3957-3971 doi: 10.3934/cpaa.2020175 +[Abstract](65) +[HTML](38) +[PDF](448.05KB)
Learning rates for the kernel regularized regression with a differentiable strongly convex loss
Baohuai Sheng, Huanxiang Liu and Huimin Wang
2020, 19(8) : 3973-4005 doi: 10.3934/cpaa.2020176 +[Abstract](89) +[HTML](75) +[PDF](617.25KB)
Uncompactly supported density estimation with $ L^{1} $ risk
Kaikai Cao and Youming Liu
2020, 19(8) : 4007-4022 doi: 10.3934/cpaa.2020177 +[Abstract](64) +[HTML](29) +[PDF](440.46KB)
Convergence of online pairwise regression learning with quadratic loss
Shuhua Wang, Zhenlong Chen and Baohuai Sheng
2020, 19(8) : 4023-4054 doi: 10.3934/cpaa.2020178 +[Abstract](105) +[HTML](38) +[PDF](570.92KB)
Analysis non-sparse recovery for relaxed ALASSO
Hang Xu and Song Li
2020, 19(8) : 4055-4068 doi: 10.3934/cpaa.2020179 +[Abstract](69) +[HTML](32) +[PDF](397.53KB)
Quantitative convergence analysis of kernel based large-margin unified machines
Jun Fan and Dao-Hong Xiang
2020, 19(8) : 4069-4083 doi: 10.3934/cpaa.2020180 +[Abstract](73) +[HTML](43) +[PDF](422.51KB)
Function approximation by deep networks
H. N. Mhaskar and T. Poggio
2020, 19(8) : 4085-4095 doi: 10.3934/cpaa.2020181 +[Abstract](71) +[HTML](36) +[PDF](514.57KB)
Representations for the inverses of certain operators
Ana-Maria Acu, Madalina Dancs and Voichiţa Adriana Radu
2020, 19(8) : 4097-4109 doi: 10.3934/cpaa.2020182 +[Abstract](82) +[HTML](33) +[PDF](379.71KB)
Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
Abhishake Rastogi
2020, 19(8) : 4111-4126 doi: 10.3934/cpaa.2020183 +[Abstract](83) +[HTML](38) +[PDF](452.44KB)
First jump time in simulation of sampling trajectories of affine jump-diffusions driven by $ \alpha $-stable white noise
Jiao Song, Jiang-Lun Wu and Fangzhou Huang
2020, 19(8) : 4127-4142 doi: 10.3934/cpaa.2020184 +[Abstract](77) +[HTML](30) +[PDF](5820.91KB)
Computing eigenpairs of two-parameter Sturm-Liouville systems using the bivariate sinc-Gauss formula
Rashad M. Asharabi and Jürgen Prestin
2020, 19(8) : 4143-4158 doi: 10.3934/cpaa.2020185 +[Abstract](75) +[HTML](48) +[PDF](617.52KB)
Kernel-based maximum correntropy criterion with gradient descent method
Ting Hu
2020, 19(8) : 4159-4177 doi: 10.3934/cpaa.2020186 +[Abstract](72) +[HTML](35) +[PDF](442.3KB)
A numerical method to compute Fisher information for a special case of heterogeneous negative binomial regression
Xin Guo, Qiang Fu, Yue Wang and Kenneth C. Land
2020, 19(8) : 4179-4189 doi: 10.3934/cpaa.2020187 +[Abstract](78) +[HTML](38) +[PDF](486.69KB)
Stochastic AUC optimization with general loss
Zhenhuan Yang, Wei Shen, Yiming Ying and Xiaoming Yuan
2020, 19(8) : 4191-4212 doi: 10.3934/cpaa.2020188 +[Abstract](81) +[HTML](50) +[PDF](1392.43KB)
Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression
Lucian Coroianu, Danilo Costarelli, Sorin G. Gal and Gianluca Vinti
2020, 19(8) : 4213-4225 doi: 10.3934/cpaa.2020189 +[Abstract](89) +[HTML](34) +[PDF](414.25KB)
A general multipurpose interpolation procedure: the magic points
Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera and S. H. Pau
2009, 8(1) : 383-404 doi: 10.3934/cpaa.2009.8.383 +[Abstract](4033) +[PDF](826.7KB) Cited By(58)
A Brezis-Nirenberg result for non-local critical equations in low dimension
Raffaella Servadei and Enrico Valdinoci
2013, 12(6) : 2445-2464 doi: 10.3934/cpaa.2013.12.2445 +[Abstract](3731) +[PDF](509.5KB) Cited By(57)
A Liouville type Theorem for an integral system
Dezhong Chen and Li Ma
2006, 5(4) : 855-859 doi: 10.3934/cpaa.2006.5.855 +[Abstract](3003) +[PDF](102.3KB) Cited By(57)
Convergence of generalized proximal point algorithms
Giuseppe Marino and Hong-Kun Xu
2004, 3(4) : 791-808 doi: 10.3934/cpaa.2004.3.791 +[Abstract](3135) +[PDF](181.7KB) Cited By(56)
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
Gianni Gilardi, A. Miranville and Giulio Schimperna
2009, 8(3) : 881-912 doi: 10.3934/cpaa.2009.8.881 +[Abstract](2787) +[PDF](395.6KB) Cited By(46)
The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$
Lihui Guo, Wancheng Sheng and Tong Zhang
2010, 9(2) : 431-458 doi: 10.3934/cpaa.2010.9.431 +[Abstract](3457) +[PDF](1276.3KB) Cited By(42)
Global weak solutions for a viscous liquid-gas model with singular pressure law
Steinar Evje and Kenneth Hvistendahl Karlsen
2009, 8(6) : 1867-1894 doi: 10.3934/cpaa.2009.8.1867 +[Abstract](2820) +[PDF](318.8KB) Cited By(42)
A result on the existence of global attractors for semigroups of closed operators
V. Pata and Sergey Zelik
2007, 6(2) : 481-486 doi: 10.3934/cpaa.2007.6.481 +[Abstract](2672) +[PDF](113.6KB) Cited By(42)
Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent
Sergey Zelik
2004, 3(4) : 921-934 doi: 10.3934/cpaa.2004.3.921 +[Abstract](3018) +[PDF](176.4KB) Cited By(39)
Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights
M. Chuaqui, C. Cortázar, M. Elgueta and J. García-Melián
2004, 3(4) : 653-662 doi: 10.3934/cpaa.2004.3.653 +[Abstract](2726) +[PDF](152.5KB) Cited By(39)
Random attractors for stochastic parabolic equations with additive noise in weighted spaces
Xiaojun Li, Xiliang Li and Kening Lu
2018, 17(3) : 729-749 doi: 10.3934/cpaa.2018038 +[Abstract](4863) +[HTML](492) +[PDF](462.14KB) PDF Downloads(273)
Semi-exact solutions and pulsating fronts for Lotka-Volterra systems of two competing species in spatially periodic habitats
Chiun-Chuan Chen, Yin-Liang Huang, Li-Chang Hung and Chang-Hong Wu
2020, 19(1) : 1-18 doi: 10.3934/cpaa.2020001 +[Abstract](1311) +[HTML](247) +[PDF](460.49KB) PDF Downloads(271)
Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis
Norikazu Saito
2012, 11(1) : 339-364 doi: 10.3934/cpaa.2012.11.339 +[Abstract](2859) +[PDF](486.1KB) PDF Downloads(257)
Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up
Yanbing Yang and Runzhang Xu
2019, 18(3) : 1351-1358 doi: 10.3934/cpaa.2019065 +[Abstract](3175) +[HTML](348) +[PDF](342.33KB) PDF Downloads(249)
Coupled systems of Hilfer fractional differential inclusions in banach spaces
Saïd Abbas, Mouffak Benchohra and John R. Graef
2018, 17(6) : 2479-2493 doi: 10.3934/cpaa.2018118 +[Abstract](3705) +[HTML](212) +[PDF](328.43KB) PDF Downloads(249)
Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity
Mohammad M. Al-Gharabli, Aissa Guesmia and Salim A. Messaoudi
2019, 18(1) : 159-180 doi: 10.3934/cpaa.2019009 +[Abstract](3969) +[HTML](245) +[PDF](367.7KB) PDF Downloads(248)
The properties of positive solutions to semilinear equations involving the fractional Laplacian
Rongrong Yang and Zhongxue Lü
2019, 18(3) : 1073-1089 doi: 10.3934/cpaa.2019052 +[Abstract](3466) +[HTML](314) +[PDF](382.99KB) PDF Downloads(243)
The Nehari manifold for a fractional Laplacian equation involving critical nonlinearities
Qingfang Wang
2018, 17(6) : 2261-2281 doi: 10.3934/cpaa.2018108 +[Abstract](4561) +[HTML](258) +[PDF](409.64KB) PDF Downloads(224)
Spreading speeds and traveling waves for space-time periodic nonlocal dispersal cooperative systems
Xiongxiong Bao, Wenxian Shen and Zhongwei Shen
2019, 18(1) : 361-396 doi: 10.3934/cpaa.2019019 +[Abstract](3876) +[HTML](225) +[PDF](502.44KB) PDF Downloads(218)
Homoclinic solutions of discrete $ \phi $-Laplacian equations with mixed nonlinearities
Genghong Lin and Zhan Zhou
2018, 17(5) : 1723-1747 doi: 10.3934/cpaa.2018082 +[Abstract](3980) +[HTML](296) +[PDF](490.86KB) PDF Downloads(215)

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