Most Down Articles

Published in last 1 year | In last 2 years| In last 3 years| All| Most Downloaded in Recent Month | Most Downloaded in Recent Year|

All

Please wait a minute...


For Selected: Download Citations EndNote Ris BibTeX Toggle Thumbnails

Select

On the Distribution of the Values of a Class of Arithmetical Functions SHAO Pin-tsung Chinese Quarterly Journal of Mathematics    1987, 2 (2): 27-43.   Abstract （175）      PDF（pc） （895KB）（398）       Knowledge map    Save 对于数义在自然数集 N 上的数论函数（Arithmetical function）f（n）, n\inN,取值可以是实数, 也可以是复数（一般为实数）, 例如著名的 Euler 函数 \varphi(n)=\Sigma_{(a,n)=1,a<n}1,  除数函数τ（n）=\Sigma_{d/n}1,以及除数和函数σ（n）=\Sigma_{d/n}d  Related Articles | Metrics

Select

Nested Alternating Direction Method of Multipliers to Low-Rank and Sparse-Column Matrices Recovery SHEN Nan , JIN Zheng-fen , WANG Qiu-yu Chinese Quarterly Journal of Mathematics    2021, 36 (1): 90-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.007 Abstract （143）      PDF（pc） （427KB）（380）       Knowledge map    Save The task of dividing corrupted-data into their respective subspaces can be well illustrated, both theoretically and numerically, by recovering low-rank and sparse-column components of a given matrix. Generally, it can be characterized as a matrix and a `2,1-norm involved convex minimization problem. However, solving the resulting problem is full of challenges due to the non-smoothness of the objective function. One of the earliest solvers is an 3-block alternating direction method of multipliers (ADMM) which updates each variable in a Gauss-Seidel manner. In this paper, we present three variants of ADMM for the 3-block separable minimization problem. More preciously, whenever one variable is derived, the resulting problems can be regarded as a convex minimization with 2 blocks, and can be solved immediately using the standard ADMM. If the inner iteration loops only once, the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner. If the solution from the inner iteration is assumed to be exact, the convergence can be deduced easily in the literature. The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive. Related Articles | Metrics

Select

On Some Recent Progress in Complex Geometry|the Area Related to Homogeneous Manifolds GUAN Daniel Chinese Quarterly Journal of Mathematics    2020, 35 (2): 111-144.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.001 Abstract （440）      PDF（pc） （1154KB）（367）       Knowledge map    Save In this article, we give a survey of some progress of the complex geometry, mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years. In particular, we explore some works in the special area in Dierential Geometry, Lie Group and Complex Homogeneous Space. Together with the special area in nonlinear analysis on complex manifolds, they are the two major aspects of my research interests. Related Articles | Metrics

Select

Buildings and Groups III LAI King-fai Chinese Quarterly Journal of Mathematics    2021, 36 (1): 1-31.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.001 Abstract （269）      PDF（pc） （533KB）（364）       Knowledge map    Save This is the third part of a pedagogical introduction to the theory of buildings of Jacques Tits. We describe the construction and properties of the Bruhat-Tits building of a reductive group over a local field. Related Articles | Metrics

Select

Well-Posedness for Timoshenko System with Thermodiffusion Effects and Delay QIN Yu-ming, HAN Ning Chinese Quarterly Journal of Mathematics    2022, 37 (1): 1-9.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.001 Abstract （141）      PDF（pc） （293KB）（349）       Knowledge map    Save  In this paper, we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects. Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam. The C 0 -semigroup theory will be used to prove the well-posedness of the considered problem. Related Articles | Metrics

Select

Dyons of Unit Topological Charges in Gauged Skyrme Model WU Zhong-lin, LI Dong-ya Chinese Quarterly Journal of Mathematics    2019, 34 (2): 152-170.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.02.004 Abstract （58）      PDF（pc） （609KB）（328）       Knowledge map    Save Dyons are an important family of topological solitons carrying both electric and magnetic charges and the presence of a nontrivial temporal component of the gauge field essential for the existence of electricity often makes the analysis of the underlying nonlinear equations rather challenging since the governing action functional assumes an indefinite form. In this work, developing a constrained variational technique, We establish an existence theorem for the dyon solitons in a Skyrme model coupled with SO(3)-gauge fields, formulated by Brihaye, Kleihaus, and Tchrakian. These solutions carry unit monopole and Skyrme charges.  Related Articles | Metrics

Select

A Posterior Estimates in the Finite Element Methods E Wei-nan, MU Mo, HUANG Hong-ci Chinese Quarterly Journal of Mathematics    1988, 3 (1): 97-107.   Abstract （432）      PDF（pc） （588KB）（326）       Knowledge map    Save Related Articles | Metrics

Select

General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms ZHANG Hong-wei, LI Dong-hao, HU Qing-ying Chinese Quarterly Journal of Mathematics    2020, 35 (3): 302-310.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.005 Abstract （144）      PDF（pc） （473KB）（317）       Knowledge map    Save We consider a wave equation with nonlocal nonlinear damping and source terms. We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique. The main difficult is how to handle with the nonlocal nonlinear damping term. Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso（Evolution Equation and Control Theory, 2017（6）:437-470） and Narciso（Evolution Equations and Control Theory, 2020, 9（2）: 487-508）. Related Articles | Metrics

Select

EEG Feature Learning Model Based on Intrinsic Time-Scale Decomposition and Adaptive Huber Loss YANG Li-jun, JIANG Shu-yue, WEI Xiao-ge , XIAO Yun-hai Chinese Quarterly Journal of Mathematics    2022, 37 (3): 281-300.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.006 Abstract （121）      PDF（pc） （538KB）（316）       Knowledge map    Save According to the World Health Organization, about 50 million people world- wide suffer from epilepsy. The detection and treatment of epilepsy face great challenges. Electroencephalogram (EEG) is a significant research object widely used in diagnosis and treatment of epilepsy. In this paper, an adaptive feature learning model for EEG signals is proposed, which combines Huber loss function with adaptive weight penalty term. Firstly, each EEG signal is decomposed by intrinsic time-scale decomposition. Secondly, the statistical index values are calculated from the instantaneous amplitude and frequency of every component and fed into the proposed model. Finally, the discriminative features learned by the proposed model are used to detect seizures. Our main innovation is to consider a highly flexible penalization based on Huber loss function, which can set different weights according to the influence of different features on epilepsy detection. Besides, the new model can be solved by proximal alternating direction multiplier method, which can effectively ensure the convergence of the algorithm. The performance of the proposed method is evaluated on three public EEG datasets provided by the Bonn University, Childrens Hospital Boston-Massachusetts Institute of Technology, and Neurological and Sleep Center at Hauz Khas, New Delhi(New Delhi Epilepsy data). The recognition accuracy on these two datasets is 98% and 99.05%, respectively, indicating the application value of the new model. Related Articles | Metrics

Select

Finite Difference Methods for the Time Fractional Advection-diffusion Equation MA Yan, MUSBAH F.S. Chinese Quarterly Journal of Mathematics    2019, 34 (3): 259-273.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.004 Abstract （98）      PDF（pc） （559KB）（302）       Knowledge map    Save In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Gr¨unwald-Letnikov formula of order α∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper. Related Articles | Metrics

Select

Buildings and Groups II CHAO Kuok Fai, LAI King Fai Chinese Quarterly Journal of Mathematics    2020, 35 (3): 221-254.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.001 Abstract （276）      PDF（pc） （1238KB）（285）       Knowledge map    Save This is the second part of a pedagogical introduction to the theory of buildings of Jacques Tits. We define a(B,N) pair and construct a building out of it. Then we give a description of Chevalley groups, their(B,N) pair and the associated buildings. We illustrates this theory with many examples from classical groups.  Related Articles | Metrics

Select

Strongly α-Refexive Rings Relative to a Monoid PENG Zhai-ming, GU Qin-qin, ZHANG Rui-rui Chinese Quarterly Journal of Mathematics    2018, 33 (3): 260-271.   DOI: 10.13371/j.cnki.chin.q.j.m.2018.03.004 Abstract （69）      PDF（pc） （445KB）（264）       Knowledge map    Save For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.  Related Articles | Metrics

Select

Vacuum Problem for The System of One Dimensional Isentropic Flow Li Da-qian, Zhao Yan-chun Chinese Quarterly Journal of Mathematics    1986, 1 (1): 41-46.   Abstract （88）      PDF（pc） （373KB）（259）       Knowledge map    Save Related Articles | Metrics

Select

Building and Groups I LAI King-fai, LIANG Zhi-bin Chinese Quarterly Journal of Mathematics    2020, 35 (1): 1-28.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.01.001 Abstract （152）      PDF（pc） （913KB）（259）       Knowledge map    Save This is a pedagogical introduction to the theory of buildings 〇£ Jacques Tits and to some applications of this theory. This paper has 4 parts. In the first part we discuss incidence geometry, Coxeter systems and give two definitions of buildings. We study in the second part the spherical and affine buildings of Chevalley groups. In the third part we deal with Bruhat-Tits theory of reductive groups over local fields. Finally we discuss the construction of the p-adic flag manifolds. Related Articles | Metrics

Select

Sparse Reduced-Rank Regression with Outlier Detection LIANG Bing-jie Chinese Quarterly Journal of Mathematics    2021, 36 (3): 275-287.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.006 Abstract （85）      PDF（pc） （622KB）（257）       Knowledge map    Save  Based on the multivariate mean-shift regression model, we propose a new sparse reduced-rank regression approach to achieve low-rank sparse estimation and outlier detection simultaneously. A sparse mean-shift matrix is introduced in the model to indicate outliers. The rank constraint and the group-lasso type penalty for the coefficient matrix encourage the low-rank row sparse structure of coefficient matrix and help to achieve dimension reduction and variable selection. An algorithm is developed for solving our problem. In our simulation and real-data application, our new method shows competitive performance compared to other methods. Related Articles | Metrics

Select

Finite Dierence Method for Riesz Space Fractional Advection-dispersion Equation with Fractional Robin Boundary Condition LIN Hai-xin, FANG Shao-mei, Chinese Quarterly Journal of Mathematics    2020, 35 (3): 278-289.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.003 Abstract （151）      PDF（pc） （611KB）（252）       Knowledge map    Save In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Gru¨nwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy O（?t2+ h2）. The solvability,stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme.  Related Articles | Metrics

Select

A Finite Volume Unstructured Mesh Method for Fractional-in-space Allen-Cahn Equation CHEN Ai-min, , LIU Fa-wang Chinese Quarterly Journal of Mathematics    2017, 32 (4): 345-354.   DOI: 10.13371/j.cnki.chin.q.j.m.2017.04.002 Abstract （79）      PDF（pc） （761KB）（250）       Knowledge map    Save Fractional-in-space Allen-Cahn equation containing a very strong nonlinear source term and small perturbation shows metastability and a quartic double well potential.Using a finite volume unstructured triangular mesh method, the present paper solves the twodimensional fractional-in-space Allen-Cahn equation with homogeneous Neumann boundary condition on different irregular domains. The efficiency of the method is presented through numerical computation of the two-dimensional fractional-in-space Allen-Cahn equation on different domains.  Related Articles | Metrics

Select

On Intersection Multiplicity of Algebraic Curves LIANG Hong-Chang Chinese Quarterly Journal of Mathematics    2019, 34 (1): 14-20.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.01.002 Abstract （101）      PDF（pc） （306KB）（250）       Knowledge map    Save In this paper, we study the intersection multiplicity of algebraic curves at a point both in R~2 and in real projective plane P~2. We introduce the fold point of curves and provide conditions for the relations between the intersection multiplicity of curves at a point and the folds of the point.  Related Articles | Metrics

Select

On One-Dimensionsl Dynamics ZHOU Zuo-ling Chinese Quarterly Journal of Mathematics    1988, 3 (1): 42-65.   Abstract （119）      PDF（pc） （1556KB）（246）       Knowledge map    Save Related Articles | Metrics

Select

Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type OUYANG Bai-ping, XIAO Sheng-zhong Chinese Quarterly Journal of Mathematics    2021, 36 (3): 235-243.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.002 Abstract （130）      PDF（pc） （330KB）（241）       Knowledge map    Save In this paper, we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type. By using methods of an iteration argument and differential inequalities, we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions. Meanwhile, we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation. Related Articles | Metrics