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Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, publishes original and expository full-length research articles of significant advances in all branches of mathematics, applied mathematics and related fields. All articles should be written to communicate their contents to a broad scientific audience and must meet high standards for scientific content and clarity. After review and acceptance, articles enter production for immediate publication.

ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007, details at AMS.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 6 issues a year in March, June, August, September, November and December.
  • ERA is a free access publication.
  • Archived in Portico and CLOCKSS.
  • ERA is a publication of the American Institute of Mathematical Sciences. All rights reserved.

Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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Note on coisotropic Floer homology and leafwise fixed points
Fabian Ziltener
2021, 29(4) : 2553-2560 doi: 10.3934/era.2021001 +[Abstract](384) +[HTML](190) +[PDF](313.5KB)
Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system
Riadh Chteoui, Abdulrahman F. Aljohani and Anouar Ben Mabrouk
2021, 29(4) : 2561-2597 doi: 10.3934/era.2021002 +[Abstract](547) +[HTML](240) +[PDF](1477.82KB)
Global stability of traveling waves for a spatially discrete diffusion system with time delay
Ting Liu and Guo-Bao Zhang
2021, 29(4) : 2599-2618 doi: 10.3934/era.2021003 +[Abstract](425) +[HTML](203) +[PDF](386.34KB)
On the universal $ \alpha $-central extensions of the semi-direct product of Hom-preLie algebras
Bing Sun, Liangyun Chen and Yan Cao
2021, 29(4) : 2619-2636 doi: 10.3934/era.2021004 +[Abstract](364) +[HTML](208) +[PDF](406.05KB)
Tori can't collapse to an interval
Sergio Zamora
2021, 29(4) : 2637-2644 doi: 10.3934/era.2021005 +[Abstract](352) +[HTML](190) +[PDF](394.75KB)
$ C^* $-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms
Kengo Matsumoto
2021, 29(4) : 2645-2656 doi: 10.3934/era.2021006 +[Abstract](341) +[HTML](187) +[PDF](316.12KB)
Telescoping method, summation formulas, and inversion pairs
Qing-Hu Hou and Yarong Wei
2021, 29(4) : 2657-2671 doi: 10.3934/era.2021007 +[Abstract](396) +[HTML](222) +[PDF](346.35KB)
Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra
Hongyan Guo
2021, 29(4) : 2673-2685 doi: 10.3934/era.2021008 +[Abstract](417) +[HTML](194) +[PDF](337.68KB)
On $ n $-slice algebras and related algebras
Jin-Yun Guo, Cong Xiao and Xiaojian Lu
2021, 29(4) : 2687-2718 doi: 10.3934/era.2021009 +[Abstract](287) +[HTML](210) +[PDF](541.55KB)
Local well-posedness of perturbed Navier-Stokes system around Landau solutions
Jingjing Zhang and Ting Zhang
2021, 29(4) : 2719-2739 doi: 10.3934/era.2021010 +[Abstract](290) +[HTML](156) +[PDF](413.85KB)
A multiscale stochastic criminal behavior model under a hybrid scheme
Chuntian Wang and Yuan Zhang
2021, 29(4) : 2741-2753 doi: 10.3934/era.2021011 +[Abstract](264) +[HTML](169) +[PDF](1163.89KB)
An a posteriori error estimator based on least-squares finite element solutions for viscoelastic fluid flows
Hsueh-Chen Lee and Hyesuk Lee
2021, 29(4) : 2755-2770 doi: 10.3934/era.2021012 +[Abstract](441) +[HTML](185) +[PDF](4771.42KB)
Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra
Pengliang Xu and Xiaomin Tang
2021, 29(4) : 2771-2789 doi: 10.3934/era.2021013 +[Abstract](301) +[HTML](183) +[PDF](346.41KB)
Averaging principle on infinite intervals for stochastic ordinary differential equations
David Cheban and Zhenxin Liu
2021, 29(4) : 2791-2817 doi: 10.3934/era.2021014 +[Abstract](335) +[HTML](152) +[PDF](410.94KB)
Ergodic measures of intermediate entropy for affine transformations of nilmanifolds
Wen Huang, Leiye Xu and Shengnan Xu
2021, 29(4) : 2819-2827 doi: 10.3934/era.2021015 +[Abstract](289) +[HTML](161) +[PDF](330.89KB)
A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
Christos Sourdis
2021doi: 10.3934/era.2021016 +[Abstract](288) +[HTML](126) +[PDF](341.7KB)
On a general homogeneous three-dimensional system of difference equations
Nouressadat Touafek, Durhasan Turgut Tollu and Youssouf Akrour
2021doi: 10.3934/era.2021017 +[Abstract](294) +[HTML](144) +[PDF](492.41KB)
Refined Wilf-equivalences by Comtet statistics Special Issues
Shishuo Fu, Zhicong Lin and Yaling Wang
2021doi: 10.3934/era.2021018 +[Abstract](263) +[HTML](124) +[PDF](534.03KB)
Convergence analysis of Fourier pseudo-spectral schemes for three-dimensional incompressible Navier-Stokes equations Special Issues
Cheng Wang
2021doi: 10.3934/era.2021019 +[Abstract](320) +[HTML](131) +[PDF](495.86KB)
Structure of sympathetic Lie superalgebras Special Issues
Yusi Fan, Chenrui Yao and Liangyun Chen
2021doi: 10.3934/era.2021020 +[Abstract](261) +[HTML](138) +[PDF](303.23KB)
On inner Poisson structures of a quantum cluster algebra without coefficients Special Issues
Fang Li and Jie Pan
2021doi: 10.3934/era.2021021 +[Abstract](275) +[HTML](123) +[PDF](308.09KB)
Complexity in time-delay networks of multiple interacting neural groups Special Issues
Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang and Xingyong Li
2021doi: 10.3934/era.2021022 +[Abstract](285) +[HTML](138) +[PDF](3695.69KB)
Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron Special Issues
Xianjun Wang, Huaguang Gu and Bo Lu
2021doi: 10.3934/era.2021023 +[Abstract](302) +[HTML](179) +[PDF](2461.63KB)
Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect
Meng-Xue Chang, Bang-Sheng Han and Xiao-Ming Fan
2021doi: 10.3934/era.2021024 +[Abstract](284) +[HTML](125) +[PDF](405.63KB)
Picture groups and maximal green sequences Special Issues
Kiyoshi Igusa and Gordana Todorov
2021doi: 10.3934/era.2021025 +[Abstract](285) +[HTML](150) +[PDF](534.52KB)
Instability and bifurcation of a cooperative system with periodic coefficients Special Issues
Tian Hou, Yi Wang and Xizhuang Xie
2021doi: 10.3934/era.2021026 +[Abstract](325) +[HTML](126) +[PDF](807.77KB)
Simultaneous recovery of surface heat flux and thickness of a solid structure by ultrasonic measurements Special Issues
Youjun Deng, Hongyu Liu, Xianchao Wang, Dong Wei and Liyan Zhu
2021doi: 10.3934/era.2021027 +[Abstract](275) +[HTML](136) +[PDF](525.34KB)
Three types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise
Lianbing She, Nan Liu, Xin Li and Renhai Wang
2021doi: 10.3934/era.2021028 +[Abstract](191) +[HTML](117) +[PDF](624.31KB)
Global behavior of P-dimensional difference equations system
Amira Khelifa and Yacine Halim
2021doi: 10.3934/era.2021029 +[Abstract](233) +[HTML](100) +[PDF](397.48KB)
A multigrid based finite difference method for solving parabolic interface problem Special Issues
Hongsong Feng and Shan Zhao
2021doi: 10.3934/era.2021031 +[Abstract](203) +[HTML](138) +[PDF](18671.43KB)
A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces Special Issues
Derrick Jones and Xu Zhang
2021doi: 10.3934/era.2021032 +[Abstract](246) +[HTML](109) +[PDF](1840.69KB)
Relative mmp without $ \mathbb{Q} $-factoriality Special Issues
János Kollár
2021doi: 10.3934/era.2021033 +[Abstract](198) +[HTML](113) +[PDF](300.75KB)
Firing patterns and bifurcation analysis of neurons under electromagnetic induction Special Issues
Qixiang Wen, Shenquan Liu and Bo Lu
2021doi: 10.3934/era.2021034 +[Abstract](252) +[HTML](138) +[PDF](6539.09KB)
Enhancement of gamma oscillations in E/I neural networks by increase of difference between external inputs Special Issues
Xiaochun Gu, Fang Han, Zhijie Wang, Kaleem Kashif and Wenlian Lu
2021doi: 10.3934/era.2021035 +[Abstract](290) +[HTML](124) +[PDF](1044.39KB)
Fractional $ p $-sub-Laplacian operator problem with concave-convex nonlinearities on homogeneous groups
Jinguo Zhang and Dengyun Yang
2021doi: 10.3934/era.2021036 +[Abstract](116) +[HTML](48) +[PDF](1940.13KB)
Global boundedness for a chemotaxis-competition system with signal dependent sensitivity and loop
Chun Huang
2021doi: 10.3934/era.2021037 +[Abstract](114) +[HTML](62) +[PDF](350.79KB)
Ground state and nodal solutions for fractional Kirchhoff equation with pure critical growth nonlinearity
Chungen Liu and Huabo Zhang
2021doi: 10.3934/era.2021038 +[Abstract](112) +[HTML](51) +[PDF](353.04KB)
On Nonvanishing for uniruled log canonical pairs
Vladimir Lazić and Fanjun Meng
2021doi: 10.3934/era.2021039 +[Abstract](99) +[HTML](45) +[PDF](333.12KB)
On minimal 4-folds of general type with $ p_g \geq 2 $
Jianshi Yan
2021doi: 10.3934/era.2021040 +[Abstract](112) +[HTML](60) +[PDF](322.56KB)
Synchronization for a class of complex-valued memristor-based competitive neural networks(CMCNNs) with different time scales
Yong Zhao and Shanshan Ren
2021doi: 10.3934/era.2021041 +[Abstract](121) +[HTML](53) +[PDF](308.67KB)
Balance of complete cohomology in extriangulated categories
Jiangsheng Hu, Dongdong Zhang, Tiwei Zhao and Panyue Zhou
2021doi: 10.3934/era.2021042 +[Abstract](7) +[HTML](8) +[PDF](422.39KB)
Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions
Youngmok Jeon and Dongwook Shin
2021doi: 10.3934/era.2021043 +[Abstract](9) +[HTML](6) +[PDF](471.45KB)
Accelerating the Bayesian inference of inverse problems by using data-driven compressive sensing method based on proper orthogonal decomposition
Meixin Xiong, Liuhong Chen, Ju Ming and Jaemin Shin
2021doi: 10.3934/era.2021044 +[Abstract](11) +[HTML](7) +[PDF](827.29KB)
An adjoint-based a posteriori analysis of numerical approximation of Richards equation
Victor Ginting
2021doi: 10.3934/era.2021045 +[Abstract](9) +[HTML](7) +[PDF](453.31KB)
A feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation
Zhen-Zhen Tao and Bing Sun
2021doi: 10.3934/era.2021046 +[Abstract](9) +[HTML](8) +[PDF](977.28KB)
On a fractional schrödinger equation in the presence of harmonic potential
Zhiyan Ding and Hichem Hajaiej
2021doi: 10.3934/era.2021047 +[Abstract](10) +[HTML](7) +[PDF](5033.89KB)
Non-existence of solutions to some degenerate coercivity elliptic equations involving measures data
Maoji Ri, Shuibo Huang and Canyun Huang
2020, 28: 165-182 doi: 10.3934/era.2020011 +[Abstract](1040) +[HTML](491) +[PDF](392.76KB) Cited By(4)
Strong $ (L^2,L^\gamma\cap H_0^1) $-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension
Hongyong Cui, Peter E. Kloeden and Wenqiang Zhao
2020, 28: 1357-1374 doi: 10.3934/era.2020072 +[Abstract](786) +[HTML](401) +[PDF](384.95KB) Cited By(3)
On the mutual singularity of multifractal measures
Zied Douzi and Bilel Selmi
2020, 28: 423-432 doi: 10.3934/era.2020024 +[Abstract](955) +[HTML](356) +[PDF](324.42KB) Cited By(3)
On the time decay in phase–lag thermoelasticity with two temperatures
Antonio Magaña, Alain Miranville and Ramón Quintanilla
2019, 27: 7-19 doi: 10.3934/era.2019007 +[Abstract](1759) +[HTML](835) +[PDF](365.4KB) Cited By(3)
Rough semi-uniform spaces and its image proximities
Surabhi Tiwari and Pankaj Kumar Singh
2020, 28: 1095-1106 doi: 10.3934/era.2020060 +[Abstract](747) +[HTML](452) +[PDF](3941.13KB) Cited By(2)
Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights
Vanessa Barros, Carlos Nonato and Carlos Raposo
2020, 28: 205-220 doi: 10.3934/era.2020014 +[Abstract](1053) +[HTML](375) +[PDF](347.49KB) Cited By(2)
A multiple-relaxation-time lattice Boltzmann method with Beam-Warming scheme for a coupled chemotaxis-fluid model
Zhonghua Qiao and Xuguang Yang
2020, 28: 1207-1225 doi: 10.3934/era.2020066 +[Abstract](824) +[HTML](391) +[PDF](1610.81KB) Cited By(2)
Well-posed final value problems and Duhamel's formula for coercive Lax–Milgram operators
Jon Johnsen
2019, 27: 20-36 doi: 10.3934/era.2019008 +[Abstract](1536) +[HTML](738) +[PDF](448.4KB) Cited By(2)
Some multivariate polynomials for doubled permutations
Bin Han
2021, 29: 1925-1944 doi: 10.3934/era.2020098 +[Abstract](758) +[HTML](365) +[PDF](398.24KB) Cited By(2)
Some recent progress on inverse scattering problems within general polyhedral geometry
Xinlin Cao, Huaian Diao and Jinhong Li
2021, 29: 1753-1782 doi: 10.3934/era.2020090 +[Abstract](782) +[HTML](416) +[PDF](492.02KB) Cited By(2)
A conjecture on cluster automorphisms of cluster algebras
Peigen Cao, Fang Li, Siyang Liu and Jie Pan
2019, 27: 1-6 doi: 10.3934/era.2019006 +[Abstract](2055) +[HTML](888) +[PDF](313.13KB) PDF Downloads(379)
On a final value problem for a nonlinear fractional pseudo-parabolic equation
Vo Van Au, Hossein Jafari, Zakia Hammouch and Nguyen Huy Tuan
2021, 29: 1709-1734 doi: 10.3934/era.2020088 +[Abstract](1240) +[HTML](332) +[PDF](484.76KB) PDF Downloads(309)
$ H^2 $ blowup result for a Schrödinger equation with nonlinear source term
Xuan Liu and Ting Zhang
2020, 28: 777-794 doi: 10.3934/era.2020039 +[Abstract](925) +[HTML](638) +[PDF](392.34KB) PDF Downloads(304)
Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence
Yang Yang, Yun-Rui Yang and Xin-Jun Jiao
2020, 28: 1-13 doi: 10.3934/era.2020001 +[Abstract](1441) +[HTML](672) +[PDF](369.78KB) PDF Downloads(303)
The global conservative solutions for the generalized camassa-holm equation
Li Yang, Chunlai Mu, Shouming Zhou and Xinyu Tu
2019, 27: 37-67 doi: 10.3934/era.2019009 +[Abstract](1471) +[HTML](694) +[PDF](562.79KB) PDF Downloads(292)
A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction
Zexuan Liu, Zhiyuan Sun and Jerry Zhijian Yang
2020, 28: 1487-1501 doi: 10.3934/era.2020078 +[Abstract](894) +[HTML](401) +[PDF](5508.22KB) PDF Downloads(292)
The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term
Gongwei Liu
2020, 28: 263-289 doi: 10.3934/era.2020016 +[Abstract](1107) +[HTML](460) +[PDF](383.54KB) PDF Downloads(288)
Non-existence of solutions to some degenerate coercivity elliptic equations involving measures data
Maoji Ri, Shuibo Huang and Canyun Huang
2020, 28: 165-182 doi: 10.3934/era.2020011 +[Abstract](1040) +[HTML](491) +[PDF](392.76KB) PDF Downloads(282)
Finite time blow-up for a wave equation with dynamic boundary condition at critical and high energy levels in control systems
Xiaoqiang Dai, Chao Yang, Shaobin Huang, Tao Yu and Yuanran Zhu
2020, 28: 91-102 doi: 10.3934/era.2020006 +[Abstract](1456) +[HTML](715) +[PDF](299.33KB) PDF Downloads(268)
Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces
Muwafaq Salih and Árpád Száz
2020, 28: 471-548 doi: 10.3934/era.2020027 +[Abstract](1091) +[HTML](649) +[PDF](771.11KB) PDF Downloads(264)

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