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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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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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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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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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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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Characterization and Applications of Semi-E-preinvex Functions  QUAN Jing, LONG Xian-jun, PENG Zai-yun, TAN Ying-shuang Chinese Quarterly Journal of Mathematics    2010, 25 (3): 436-443.   Abstract （24）      PDF（pc） （324KB）（193）       Knowledge map    Save A class of sets called E-invex sets and a class of functions called E-preinvex functions, semi-E-preinvex functions and generalized semi-E-preinvex functions are introduced. They are the generalizations of E-convex sets, E-convex functions and semi-E-convex functions respectively, also the generalizations of invex sets and preinvex functions. Furthermore some optimality results of mathematical programming problems involved semi-E-preinvex functions and generalized semi-E-preinvex functions are obtained.  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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The Upper Bound of the Moebius Scalar Curvature of Submanifolds in Sn+p ZHONG Ding-xing, SUN Hong-an, MO Xiao-kai Chinese Quarterly Journal of Mathematics    2010, 25 (1): 65-73.   Abstract （31）      PDF（pc） （386KB）（176）       Knowledge map    Save The most important Moebius invariants in the Moebius differential geometry of submanifolds in Sn+p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form Φ and the Blaschke tensor A. In this paper, we obtain the upper bound of the Moebius scalar curvature of submanifolds with parallel Moebius form in Sn+p. Related Articles | Metrics

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Parameter Estimations of the TFR Model Under Exponential Distribution at a Normal Stress WANG Yu Chinese Quarterly Journal of Mathematics    2009, 24 (2): 234-238.   Abstract （23）      PDF（pc） （247KB）（167）       Knowledge map    Save The TFR(Tampered Failure Rate) model was proposed by Bhattacharyya and Soejoeti(1989) for step-stress accelerated life tests. On step-stress completely accelerated test occasions, the paper gives a method of estimating parameters under a normal stress. Related Articles | Metrics

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Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity PAN Jia-hui, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2023, 38 (4): 360-369.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.003 Abstract （56）      PDF（pc） （358KB）（137）       Knowledge map    Save  In this paper, we study the initial boundary value problem of pseudo-parabolic p-Laplacian type equation, which be use to model some important physical and biological phenomena. By using the potential well method, we obtain the global existence, asymptotic behavior and blow up results of weak solution with subcritical initial energy. Then we also extend these results to the critical initial energy. 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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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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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 （715）      PDF（pc） （588KB）（381）       Knowledge map    Save Related Articles | Metrics

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A Remark on Double Ore Extensions LI Qi-Ning Chinese Quarterly Journal of Mathematics    2019, 34 (1): 99-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.01.011 Abstract （141）      PDF（pc） （439KB）（276）       Knowledge map    Save The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.  Related Articles | Metrics

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Finite Time Blowup with Upper Bound of Blowup Time of Solutions to Semilinear Parabolic Equations with General Nonlinearity LI Na, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2022, 37 (1): 103-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.011 Abstract （129）      PDF（pc） （315KB）（206）       Knowledge map    Save In this paper, we consider a semilinear parabolic equation with a general nonlinearity. We establish a new finite time blow-up criterion and also derive the upper bound for the blow-up time. The results partially generalize some recent ones obtained by He Ma et al. Related Articles | Metrics

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Dynamic Analysis of a Predator-Prey Model with State-Dependent Impulsive Effects LI Yong-feng, ZHU Cheng-zhi, LIU Yan-wei Chinese Quarterly Journal of Mathematics    2023, 38 (1): 1-19.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.001 Abstract （121）      PDF（pc） （2367KB）（255）       Knowledge map    Save  In this paper, a pest-dependent model and integrated pest management strategy is proposed, that is, when pest populations reach levels that impair economic development, we will use a combination of strategies, such as biological, cultural and chemical control strategies reduce pests to a reasonable level. First, we investigated the system without control measures, and discussed the existence and stability of equilibria, we also proved the system has no limit cycle. Then, a state feedback impulsive model is constructed, the existence and uniqueness of the order-one periodic solution are proved by means of the successor function method to confirm the feasibility of the biological and chemical control strategy of pest management. Secondly, the stability of system is proved by the analogue of the Poincar ´ e criterion. Finally, we give an example and numerical simulations to explain the mathematical conclusions. Related Articles | Metrics

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Complexity on Proximal Quasi-Newton Methods for a Class of Nonconvex Composite Optimization JIN Ling-Zi Chinese Quarterly Journal of Mathematics    2023, 38 (1): 62-84.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.005 Abstract （105）      PDF（pc） （404KB）（221）       Knowledge map    Save This paper studies a class of nonconvex composite optimization, whose objective is a summation of an average of nonconvex (weakly) smooth functions and a convex nonsmooth function, where the gradient of the former function has the Hölder continuity. By exploring the structure of such kind of problems, we first propose a proximal (quasi-)Newton algorithm wPQN (Proximal quasi-Newton algorithm for weakly smooth optimization) and investigate its theoretical complexities to find an approximate solution. Then we propose a stochastic variant algorithm wPSQN (Proximal stochastic quasi-Newton algorithm for weakly smooth optimization), which allows a random subset of component functions to be used at each iteration. Moreover, motivated by recent success of variance reduction techniques, we propose two variance reduced algorithms, wPSQN-SVRG and wPSQN-SARAH, and investigate their computational complexity separately. Related Articles | Metrics

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The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix ZENG Min, YUAN Yong-xin Chinese Quarterly Journal of Mathematics    2023, 38 (4): 401-409.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.007 Abstract （49）      PDF（pc） （347KB）（86）       Knowledge map    Save The representation for the Moore-Penrose inverse of the matrix A B C D  is derived by using the solvability theory of linear equations, where A∈Cm×n, B∈Cm×p, C∈Cq×n and D∈Cq×p, with which some special cases are discussed. Related Articles | Metrics