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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 （437）      PDF（pc） （1154KB）（366）       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 （423）      PDF（pc） （588KB）（322）       Knowledge map    Save 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 （273）      PDF（pc） （1238KB）（283）       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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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 （265）      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

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On Relationship between Lower-order of Coefficients and Growth of Solutions of Complex Differential Equations near a Singular Point LIU Yuan-zhu, LONG Jian-ren, ZENG San-gui Chinese Quarterly Journal of Mathematics    2020, 35 (2): 163-170.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.003 Abstract （187）      PDF（pc） （495KB）（239）       Knowledge map    Save We investigate the growth of solutions of the following complex linear differential equation f’’+ A（z）f’+ B（z）f = 0,where A（z） and B（z） are analytic functions in C-{z0}, z0 ∈ C. Some estimations of lower bounded of growth of solutions of the differential equation are obtained by using the concept of lower order.  Related Articles | Metrics

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Existence and Concentration of Solutions for An Indefinite Schrodinger-Kirchhoff System CHEN Yu-song, CHANG He-jie Chinese Quarterly Journal of Mathematics    2020, 35 (1): 37-45.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.01.003 Abstract （186）      PDF（pc） （615KB）（189）       Knowledge map    Save This paper is concerned with the nonlinear Schrodinger-Kirchhoff system $-(a+b \int _{R^{3}}|\nabla u|^{2} dx)  \triangle u+ \lambda V(x)u=f(x,u)$ in R3, where constants a > 0,b ≥ 0 and λ > 0 is a parameter. We require that V (χ) ∈ C(R3) and has a potential well V -1(0). Combining this with other suitable assumptions on K and ƒ, the existence of nontrivisd solutions is obtained via vaxiational methods. Furthermore, the concentration behavior of the nontrivial solution is also explored on the set V -1(0) as λ → + ∞ as well. It is worth noting that the (PS )-condition can not be directly got as done in the literature, which makes the problem more complicated. To overcome this difficulty, we adopt different method. Related Articles | Metrics

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On the Sum of Powers of Natural Numbers CHEN Jing-run, LI Jian-yu Chinese Quarterly Journal of Mathematics    1987, 2 (1): 1-18.   Abstract （180）      PDF（pc） （2527KB）（192）       Knowledge map    Save Related Articles | Metrics

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The Maximal Subgroups of n * n Nonnegative Integral Matrices YANG Lin, REN Miao-miao Chinese Quarterly Journal of Mathematics    2020, 35 (2): 186-193.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.006 Abstract （176）      PDF（pc） （525KB）（128）       Knowledge map    Save In this paper we study the subgroup structure of the semigroup Mn(Z+) of all n * n nonnegative integral matrices under multiplication. We prove that every maximal subgroup of Mn(Z+) containing an idempotent element of rank r is isormorphic to Sr. 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 （175）      PDF（pc） （330KB）（93）       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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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 （172）      PDF（pc） （895KB）（397）       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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Korn’s Inequality and Divergence Equations on Generalize Orlicz Spaces WU Rui-min , WANG Song-bai Chinese Quarterly Journal of Mathematics    2020, 35 (4): 344-353.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.002 Abstract （164）      PDF（pc） （387KB）（148）       Knowledge map    Save  Let ϕ be a generalized Orlicz function satisfying (A0), (A1), (A2), (aInc) and (aDec). We prove that the mapping  f →f #:=supB 1/\int|B||f(x)-fB|dx is continuous on Lϕ(·)(Rn) by extrapolation. Based on this result we generalize Korn’s inequality to the setting of generalized Orlicz spaces, i.e., ||\triangledown f||L^{ϕ(·)}(Ω)  \lesssim||DF|||L^{ϕ}(Ω) . Using the Calder´on–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu=f has a solution u∈(W01,ϕ(·)(Ω))n such that ||\triangledown u||L^{ϕ(·)}(Ω) \lesssim ||f||L^{ϕ}(Ω). Related Articles | Metrics

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Rainbow Vertex-connection Number of Ladder and MÄobius Ladder LIU Hui-min, MAO Ya-ping Chinese Quarterly Journal of Mathematics    2016, 31 (4): 399-405.   DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.008 Abstract （162）      PDF（pc） （352KB）（203）       Knowledge map    Save A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc（G）, is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc（G）. Observe that rvc（G） ≤ srvc（G） for any nontrivial connected graph G. In this paper, for a Ladder Ln,we determine the exact value of srvc（Ln） for n even. For n odd, upper and lower bounds of srvc（Ln） are obtained. We also give upper and lower bounds of the（strong） rainbow vertex-connection number of Mbius Ladder.  Related Articles | Metrics

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Majorization and Fekete-Szegö Problems for Multivalent Meromorphic Functions Associated with the Mittag-Leffler Function LONG Pin-hong, GANGADHARAN Murugusundaramoorthy, HAN Hui-li, WANG Wen-shuai Chinese Quarterly Journal of Mathematics    2022, 37 (2): 111-123.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.001 Abstract （161）      PDF（pc） （356KB）（230）       Knowledge map    Save The main object of this present paper is to investigate the problem of majorization of certain class of multivalent meromorphic functions of complex order involving Mittag-Leffler function. Meanwhile, for this subclass the corresponding coefficient estimates and some Fekete-Szeg¨ o type inequalities are obtained. Moreover we point out some new or known consequences of our main results. Related Articles | Metrics

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A Non-Archimedean Version of the Classical Hilbert Inequality JIN Jian-jun, LI Chun-hua Chinese Quarterly Journal of Mathematics    2020, 35 (4): 431-440.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.012 Abstract （157）      PDF（pc） （315KB）（133）       Knowledge map    Save In this note, we introduce and study a p-adic Hilbert-type integral operator and obtain its sharp norm estimate. As applications, we establish a p-adic Hilbert-type inequality with the best constant and its equivalent form. Related Articles | Metrics

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A New Filled Function for Global Optimization Problems with Box Constraints QU De-qiang, WU Dan, SHANG You-lin Chinese Quarterly Journal of Mathematics    2020, 35 (4): 354-362.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.003 Abstract （153）      PDF（pc） （286KB）（168）       Knowledge map    Save  In this paper, auxiliary function method for global optimization with box constraints is considered. First, a new non-parameter filled function which has the same local minimizers of the objective function is proposed. By the character that having same local minimizers, and these minimizers are all better than the current minimizer of the objective function, it does not need to minimize the objective function except for the first iteration in the filled function method. It changes the frame of conventional filled function methods that objective function and filled function are minimized alternately, and can effectively reduce the iterations of the algorithm and accelerate the speed of global optimization. And then the theoretical properties of the filled function are discussed and the corresponding algorithm is established. Finally, numerical experiments are made and comparisons on several test problems are shown which exhibit the feasibility and effectiveness of the algorithm. Related Articles | Metrics

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Singularities of the Moduli Space of n Unordered Points on the Riemann Sphere WU Yue, XU Bin Chinese Quarterly Journal of Mathematics    2020, 35 (2): 145-162.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.002 Abstract （151）      PDF（pc） （855KB）（125）       Knowledge map    Save We classify the nite groups associated to the orbifold singularities of the moduli space of n5 unordered points on the Riemann sphere. Related Articles | Metrics

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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 （150）      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

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Existence and Multiplicity of Positive Solutions for a Coupled Fourth-Order System of Kirchhoff Type LI Zhen-hui, XU Li-ping Chinese Quarterly Journal of Mathematics    2021, 36 (1): 49-66.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.004 Abstract （149）      PDF（pc） （377KB）（183）       Knowledge map    Save In this paper, we study a coupled fourth-order system of Kirchhoff type. Under appropriate hypotheses of Vi(x) for i=1,2, f and g, we obtained two main existence theorems of weak solutions for the problem by variational methods. Some recent results are extended. Related Articles | Metrics

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The Conjugate Gradient Method in Random Variables HSU Ming-hsiu, LAI King-fai Chinese Quarterly Journal of Mathematics    2021, 36 (2): 111-121.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.001 Abstract （149）      PDF（pc） （322KB）（194）       Knowledge map    Save We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method. Related Articles | Metrics

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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 （148）      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