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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 （179）      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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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 （166）      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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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 （153）      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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Global Existence and Uniqueness of Periodic Waves for a Perturbed Combined Double-Dispersive Equation LIAO Xiao-zhao, HUANG Wen-tao, YANG Su-min Chinese Quarterly Journal of Mathematics    2022, 37 (2): 124-131.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.002 Abstract （146）      PDF（pc） （534KB）（80）       Knowledge map    Save In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation (PDE). The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation (ODE). The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle, which corresponds the periodic traveling wave for the PDE model. The main tool is the Abelian integral taken from Poincar´ e bifurcation theory. Simulation is carried out to verify the theoretical result. Related Articles | Metrics

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Painlev\'{e} Analysis of Higher Order Nonlinear Evolution Equations with Variable Coefficients Wang Yuan Chinese Quarterly Journal of Mathematics    2021, 36 (2): 196-203.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.008 Abstract （144）      PDF（pc） （266KB）（190）       Knowledge map    Save There is a close relationship between the Painlev´e integrability and other integrability of nonlinear evolution equation. By using the Weiss-Tabor-Carnevale (WTC) method and the symbolic computation of Maple, the Painlev´e test is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients. Finally the Painlev´e integrability condition of this equation is gotten. Related Articles | Metrics

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Volume Inequalities for Sections and Projections of Asymmetric Convex Bodies CAO Zi-xin, Li Ai-jun Chinese Quarterly Journal of Mathematics    2022, 37 (2): 178-188.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.007 Abstract （142）      PDF（pc） （346KB）（75）       Knowledge map    Save In this paper, we establish volume inequalities for k-dimensional sections and projections of convex bodies (not necessarily symmetric) and their polars in a more general position than John’s position. 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 （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

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Induced Matching-Extendability of Halin Graphs ZHANG Qing-nan, HUI Zhi-hao, YANG Yu, WANG An, Chinese Quarterly Journal of Mathematics    2022, 37 (4): 380-385.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.005 Abstract （131）      PDF（pc） （344KB）（80）       Knowledge map    Save  Let G be a connected graph having a perfect matching. The graph G is said to be induced matching (IM) extendable if every induced matching M of G is contained in a perfect matching of G. In this paper, we show that Halin graph G =T ∪C is IMextendable if and only if its characteristic tree T is isomorphic to K1,3, K1,5, K1,7 or S2,2. Related Articles | Metrics

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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

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Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations with Degenerate Nonlocal Damping and Source Terms LIU Shuo, ZHANG Hong-wei, Hu Qing-ying Chinese Quarterly Journal of Mathematics    2021, 36 (2): 210-220.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.010 Abstract （122）      PDF（pc） （298KB）（192）       Knowledge map    Save This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms. We will prove that the energy associated to the system is unbounded. In fact, it will be proved that the energy will grow up as an exponential function as time goes to infinity, provided that the initial data are positive 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 （122）      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

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The Normal Family of Meromorphic Functions Concerning Shared Analytic Function YANG Qi, YUAN Wen-jun, TIAN Hong-gen Chinese Quarterly Journal of Mathematics    2022, 37 (1): 26-36.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.003 Abstract （122）      PDF（pc） （330KB）（136）       Knowledge map    Save In this paper, we study the normal criterion of meromorphic functions concerning shared analytic function. We get some theorems concerning shared analytic function, which improves some earlier related results. Related Articles | Metrics

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AOR Iterative Method for Coupled Lyapunov Matrix Equations ZHANG Shi-jun , WANG Shi-heng , WANG Ke Chinese Quarterly Journal of Mathematics    2021, 36 (2): 141-148.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.003 Abstract （118）      PDF（pc） （285KB）（225）       Knowledge map    Save  An AOR (Accelerated Over-Relaxation) iterative method is suggested by introducing one more parameter than SOR (Successive Over-Relaxation) method for solving coupled Lyapunov matrix equations (CLMEs) that come from continuous-time Markovian jump linear systems. The proposed algorithm improves the convergence rate, which can be seen from the given illustrative examples. The comprehensive theoretical analysis of convergence and optimal parameter needs further investigation. Related Articles | Metrics

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A Novel Parameter-Free Filled Function and Its Application in Least Square Method LI Shuo, SHANG You-lin, QU De-qiang, Chinese Quarterly Journal of Mathematics    2021, 36 (3): 263-274.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.005 Abstract （117）      PDF（pc） （289KB）（132）       Knowledge map    Save The filled function algorithm is an important method to solve global optimization problems. In this paper, a parameter-free filled function is proposed for solving general global optimization problem, discuss the theoretical properties of this function and give the corresponding algorithm. The numerical experiments on some typical test problems using the algorithm and the numerical results show that the algorithm is effective. Applying the filled function method to the parameter solving problem in the logical population growth model, and then can be effectively applied to Chinese population prediction. The experimental results show that the algorithm has good practicability in practical application. Related Articles | Metrics

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The Polynomial Function Model in Born-Infeld Theory DAI Bing-bing, ZHANG Rui-feng Chinese Quarterly Journal of Mathematics    2022, 37 (3): 221-236.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.001 Abstract （117）      PDF（pc） （413KB）（88）       Knowledge map    Save  Based on the Lagrangian action density under Born-Infeld type dynamics and motivated by the one-dimensional prescribed mean curvature equation, we investigate the polynomial function model in Born-Infeld theory in this paper with the form of −([1−a(ϕ')2 ]ϕ' )' =λf(ϕ(x)), where λ> 0 is a real parameter, f ∈C2 (0 , + ∞ ) is a nonlinear function. We are interested in the exact number of positive solutions of the above nonlinear equation. We specifically develop for the problem combined with a careful analysis of a time-map method. 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 （114）      PDF（pc） （315KB）（162）       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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Auslander Categories and Free Normalizing Extensions GU Qin-qin, ZHUO Yuan-fan Chinese Quarterly Journal of Mathematics    2021, 36 (2): 204-209.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.009 Abstract （114）      PDF（pc） （299KB）（139）       Knowledge map    Save  Let RCS be a semidualizing (R,S)-bimodule. Then RCS induces an equivalent between the Auslander class AC (S) and the Bass class BC (R). Let A and B be free normalizing extensions of R and S respectively. In this paper, we prove that HomS(BBS,RCS) is a semidualizing (A,B)-bimodule under some suitable conditions, and so HomS(BBS,RCS) induces an equivalence between the Auslander class AHomS (BBS,RCS )(B) and the Bass class BHomS (BBS,RCS )(A). Furthermore, under a suitable condition on RCS, we develop a generalized Morita theory for Auslander categories Related Articles | Metrics

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On the Eigenvalues and Eigenfunctions of the Sturm-Liouville Operator with the Barrier Potential SARWAR Qanitah, HUANG Zhen-you, ZAHID Abdul Hannan, XU Xin-Jian Chinese Quarterly Journal of Mathematics    2023, 38 (1): 50-61.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.004 Abstract （112）      PDF（pc） （279KB）（131）       Knowledge map    Save We aim to find the eigenvalues and eigenfunctions of the barrier potential case for Strum-Liouville operator on the finite interval [0 ,π ] when λ> 0. Generally, the eigenvalue problem for the Sturm-Liouville operator is often solved by using integral equations, which are sometimes complex to solve, and difficulties may arise in computing the boundary values. Considering the said complexity, we have successfully developed a technique to give the asymptotic formulae of the eigenvalue and the eigenfunction for Sturm-Liouville operator with barrier potential. The results are of significant interest in the field of quantum mechanics and atomic systems to observe discrete energy levels. Related Articles | Metrics

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An Efficient Algorithm for Low Rank Matrix Restoration Problem with Unknown Noise Level JIN Zheng-fen, WANG Duo, SHANG You-lin, LV Jin-man Chinese Quarterly Journal of Mathematics    2021, 36 (4): 356-368.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.04.002 Abstract （111）      PDF（pc） （363KB）（115）       Knowledge map    Save Recovering an unknown high dimensional low rank matrix from a small set of entries is widely spread in the fields of machine learning, system identification and image restoration, etc. In many practical applications, the few observations are always corrupted by noise and the noise level is also unknown. A novel model with nuclear norm and square root type estimator has been proposed, which does not rely on the knowledge or on an estimation of the standard deviation of the noise. In this paper, we firstly reformulate the problem to an equivalent variable separated form by introducing an auxiliary variable. Then we propose an efficient alternating direction method of multipliers(ADMM) for solving it. Both of resulting subproblems admit an explicit solution, which makes our algorithm have a cheap computing. Finally, the numerical results show the benefits of the model and the efficiency of the proposed method. Related Articles | Metrics

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Simplistic Universal Protocols for Remotely Preparing Arbitrary Equatorial States MA Song-ya LI Xiang, LI Qi Chinese Quarterly Journal of Mathematics    2022, 37 (3): 260-273.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.004 Abstract （108）      PDF（pc） （348KB）（135）       Knowledge map    Save  We first put forward a deterministic protocol to realize the remote preparation of arbitrary multi-qubit equatorial states via EPR pairs. A set of useful measurement basis is constructed which plays a key role. The receiver just needs to perform Pauli Z operations to recover the target state. Comparing with the previous protocols, the recovery operation is simplified and expressed by a general formula. As there are no universal protocols for high-dimensional systems, we further generalize to the case of multi-qudit equatorial states by means of Fourier transformation. It is worth mentioning that the proposed schemes can be extended to multi-party controlled remote state preparation. Moreover, we consider the effect of two-type decoherence noises. Related Articles | Metrics