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Calculation Method of Power Law Fluid Equivalent Permeability Considering Capillary Shape YANG Er-long, LI Huan, GAO Hui-juan, GU Ting-ting Chinese Quarterly Journal of Mathematics    2015, 30 (3): 420-428.   DOI: 10.13371/j.cnki.chin.q.j.m.2015.03.013 Abstract （42）      PDF（pc） （534KB）（539）       Knowledge map    Save While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections. Related Articles | Metrics

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The Growth of the Entire Function Represented by the Laplace-Stieltjes Transform in the Whole Plane NING Ju-hong , SONG Wen-pei , HUANG Wen-ping Chinese Quarterly Journal of Mathematics    2020, 35 (4): 363-369.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.004 Abstract （62）      PDF（pc） （315KB）（488）       Knowledge map    Save  In the paper, the α-order of the Laplace-Stieltjes Transform is introduced firstly, then we get the relationship between  α-order represented by the maximum modulus and α-order represented by A∗n, λn. Lastly, we obtain the relationship between type τ represented by the maximum modulus and type τ represented by A∗n, λn. Related Articles | Metrics

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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 （127）      PDF（pc） （306KB）（476）       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

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The Proof of Structural Stability of Hyperbolic Fixed Points in Ordinary Di®erential Equations WANG Qi, ZHANG Shuo Chinese Quarterly Journal of Mathematics    2018, 33 (1): 93-97.   DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.011 Abstract （147）      PDF（pc） （254KB）（433）       Knowledge map    Save In ordinary differential equations, structural stability of hyperbolic fixed points is a classical result, but the proof of this result in [2] has same small mistake. In this paper,we will correct the above mistake by using the Hartman theorem and its idea.  Related Articles | Metrics

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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 （240）      PDF（pc） （895KB）（420）       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

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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 （367）      PDF（pc） （427KB）（401）       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

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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 （385）      PDF（pc） （533KB）（396）       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

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n-tilting Torsion Classes and n-cotilting Torsion-free Classes HE Dong-lin, LI Yu-yan Chinese Quarterly Journal of Mathematics    2019, 34 (2): 196-203.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.02.007 Abstract （91）      PDF（pc） （326KB）（394）       Knowledge map    Save In this paper, we consider some generalizations of tilting torsion classes and cotilting torsion-free classes, give the definition and characterizations of n-tilting torsion classes and n-cotilting torsion-free classes, and study n-tilting preenvelopes and n-cotilting precovers.  Related Articles | Metrics

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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 （198）      PDF（pc） （293KB）（387）       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

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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 （546）      PDF（pc） （1154KB）（386）       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

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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 （714）      PDF（pc） （588KB）（381）       Knowledge map    Save Related Articles | Metrics

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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 （142）      PDF（pc） （538KB）（368）       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

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Majority Coloring of r-Regular Digraph XIA Wei-hao, SHI Mei, XIAO Ming-yue, CAI Jian-sheng, WANG Ji-hui Chinese Quarterly Journal of Mathematics    2022, 37 (2): 142-146.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.004 Abstract （218）      PDF（pc） （330KB）（357）       Knowledge map    Save  A majority k-coloring of a digraph D with k colors is an assignment c: V ( D ) →{ 1,2,···,k} , such that for every v∈V (D), we have c(w)=c(v) for at most half of all out-neighbors w∈N+( v ). For a natural number k≥2, a 1/k-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a 1/k proportion of its out-neighbours. Kreutzer, Oum, Seymour, van der Zypen and Wood proved that every digraph has a majority 4-coloring and conjectured that every digraph admits a majority 3-coloring. Gir$\widetilde{a}$o, Kittipassorn and Popielarz proved that every digraph has a 1/k-majority 2k-coloring and conjectured that every digraph admits a 1\k-majority (2k−1)-coloring. We showed that every r -regular digraph D with r>36ln(2n) has a majority 3-coloring and proved that every digraph D with minimum outdegree $\delta^+>\frac{2k^2(2k-1)^2}{(k-1)^2}\ln{[(2k-1)n]}$ has a 1/k-majority (2k−1)-coloring. And we also proved that every r-regular digraph D with  $r>\frac{3k^2(2k-1)}{(k-1)^2} \ln(2n)$ has a 1/k-majority (2k−1)-coloring. Related Articles | Metrics

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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 （169）      PDF（pc） （473KB）（353）       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

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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 （76）      PDF（pc） （609KB）（351）       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

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On stability of discrete dynamical system WANG Mu-qiu, WANG Lian Chinese Quarterly Journal of Mathematics    1987, 2 (3): 12-30.   Abstract （53）      PDF（pc） （1147KB）（328）       Knowledge map    Save Related Articles | Metrics

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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 （122）      PDF（pc） （559KB）（327）       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

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Cover a 3-regular Claw-free Graph by Induced Matchings DONG Li, TANG Jing-yong, SONG Xin-yu Chinese Quarterly Journal of Mathematics    2011, 26 (3): 355-359.   Abstract （42）      PDF（pc） （271KB）（323）       Knowledge map    Save The induced matching cover number of a graph G without isolated vertices, denoted by imc(G), is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk} such that, V(M1)∪V(M2)∪···∪V(Mk) covers V(G). This paper shows that, if G is a 3-regular claw-free graph, then imc(G)∈{2,3}. Related Articles | Metrics

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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 （314）      PDF（pc） （1238KB）（309）       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

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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 （138）      PDF（pc） （373KB）（289）       Knowledge map    Save Related Articles | Metrics