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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）（388）       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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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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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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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 （193）      PDF（pc） （356KB）（252）       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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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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Space-Time Legendre Spectral Collocation Methods for Korteweg-de Vries Equation WANG Chuan, QIAO Yan Chinese Quarterly Journal of Mathematics    Accepted: 12 April 2023

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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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A Test on High-Dimensional Intraclass Correlation Structure TANG Ping, XIAO Nan-nan, XIE Jun-shan Chinese Quarterly Journal of Mathematics    2022, 37 (1): 10-25.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.002 Abstract （137）      PDF（pc） （462KB）（184）       Knowledge map    Save The paper considers a high-dimensional likelihood ratio (LR) test on the intraclass correlation structure of the multivariate normal population. When the dimension p and sample size N satisfy N − 1 >p→∞ , it is proved that the logarithmic LR statistic asymptotically obeys Gaussian distribution, and the explicit expressions of the mean and the variance are also obtained. The simulations demonstrate that our high-dimensional LR test method outperforms the traditional Chi-square approximation method or F-approximation method, and performs as efficient as the accurate high-dimensional Edgeworth expansion method and the more accurate high-dimensional Edgeworth expansion method in analyzing the intraclass covariance structure of highdimensional data. Related Articles | Metrics

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Expressions of Two Classes of Infinite Series in Terms of Bernoulli Numbers GUO Dong-wei, CHEN Yu-lei Chinese Quarterly Journal of Mathematics    2022, 37 (1): 79-87.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.008 Abstract （114）      PDF（pc） （321KB）（181）       Knowledge map    Save In this paper, the expressions of two classes of infinite series in terms of finite series involving Bernoulli numbers are obtained. As applications, we derive some special series including Dirichlet beta function β ( s ) with argument 2 n +1 and Dirichlet lambda function λ ( s ) with argument 2 n . In addition, we solve the problem proposed recently by Zhou (2021). Related Articles | Metrics

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Stability and Hopf Bifurcation of an Eco-Epidemiological Model with Delay BAI Hong-fang Chinese Quarterly Journal of Mathematics    2023, 38 (2): 157-183.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.005 Abstract （126）      PDF（pc） （1289KB）（173）       Knowledge map    Save In this paper, an eco-epidemiological model with time delay is studied. The local stability of the four equilibria, the existence of stability switches about the predation- free equilibrium and the coexistence equilibrium are discussed. It is found that Hopf bifurcations occur when the delay passes through some critical values. Formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Some numerical simulations are carried out to illustrate the theoretical results. Related Articles | Metrics

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Differential Identities in Prime Rings with Involution HUANG Shu-liang Chinese Quarterly Journal of Mathematics    2023, 38 (2): 134-144.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.003 Abstract （87）      PDF（pc） （319KB）（163）       Knowledge map    Save Let R be a prime ring of characteristic different from two with the sec- ond involution ∗ and α an automorphism of R . An additive mapping F of R is called a generalized ( α,α )-derivation on R if there exists an ( α,α )-derivation d of R such that F ( xy )= F ( x ) α ( y )+ α ( x ) d ( y ) holds for all x,y∈R. The paper deals with the s- tudy of some commutativity criteria for prime rings with involution. Precisely, we describe the structure of R admitting a generalized ( α,α )-derivation F satisfying any one of the following properties: ( i ) F ( xx∗) −α ( xx∗) ∈Z ( R ). ( ii ) F ( xx∗ )+ α ( xx∗ ) ∈Z ( R ). ( iii ) F ( x ) F ( xx∗) −α ( xx∗) ∈Z ( R ). ( iv ) F ( x ) F (x∗)+ α ( xx∗) ∈Z ( R ). ( v ) F ( xx∗) −F ( x ) F (x∗ ) ∈Z ( R ). ( vi ) F ( xx∗) −F (x∗) F ( x )=0 for all x∈R . Also, some examples are given to demonstrate that the restriction of the various results is not superfluous. In fact, our results unify and extend several well known theorems in literature. 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 （153）      PDF（pc） （279KB）（161）       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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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 （137）      PDF（pc） （330KB）（160）       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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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 （131）      PDF（pc） （348KB）（158）       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

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Vertex Operators, Littlewood-Richardson Rule for Generalized Symplectic Schur Functions HUANG Fang, CHU Yan-jun Chinese Quarterly Journal of Mathematics    2022, 37 (3): 301-316.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.007 Abstract （112）      PDF（pc） （375KB）（158）       Knowledge map    Save  Littlewood-Richardson rule gives the expansion formula for decomposing a product of two Schur functions as a linear sum of Schur functions, while the decomposition formula for the multiplication of two symplectic Schur function is also given by the combinatorial method. In this paper, we will construct the algebraic forms of the decomposition formula for the product of two symplectic Schur functions by using the generating functions and vertex operator realizations, and then extend these results to generalized symplectic Schur functions. Related Articles | Metrics

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Virtual Element Method of the Allen-Cahn Equation WANG Pei-zhen, TIAN Xu Chinese Quarterly Journal of Mathematics    2023, 38 (1): 20-29.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.002 Abstract （113）      PDF（pc） （307KB）（153）       Knowledge map    Save  In this article, the virtual element method of the Allen-Cahn equation on a polygon grid is discussed in the fully discrete formulation. With the help of the energy projection operator, we give the corresponding error estimates in the L2 norm and H1 norm. 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 （154）      PDF（pc） （363KB）（148）       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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Homology of Bihom-Lie Algebras CHENG Yong-sheng, WANG Meng-ping Chinese Quarterly Journal of Mathematics    2022, 37 (3): 237-247.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.002 Abstract （97）      PDF（pc） （286KB）（147）       Knowledge map    Save  The purpose of this paper is to define Hochschild type homology of Bihom- associative algebras and Chevalley-Eilenberg type homology of Bihom-Lie algebras with non-trivial coefficients in their bimodules respectively. In particular, we give their low order homology in detail. Related Articles | Metrics

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Existence and Exponential Stability of Almost Periodic Solutions to General BAM Neural Networks with Leakage Delays on Time Scales DONG Yan-shou, HAN Yan, DAI Ting-ting Chinese Quarterly Journal of Mathematics    2022, 37 (2): 189-202.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.008 Abstract （117）      PDF（pc） （885KB）（145）       Knowledge map    Save  In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations and fixed point theorem. Then, the exponential stability of almost periodic solutions to such BAM neural networks on time scales is discussed by utilizing differential inequality. Finally, an example is given to support our results in this paper and the results are up-to-date. Related Articles | Metrics