期刊：
Journal of Mathematical Biology,2024年88(4):1-30 ISSN：0303-6812
通讯作者：
Min Lu
作者机构：
[Jicai Huang; Qin Pan] School of Mathematics and Statistics, and Key Lab NAA-MOE, Central China Normal University, Wuhan, 430079, China;[Min Lu] School of Mathematics and Statistics, and Key Lab NAA-MOE, Central China Normal University, Wuhan, 430079, China. lumin@mails.ccnu.edu.cn;[Shigui Ruan] Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA
通讯机构：
[Min Lu] S;School of Mathematics and Statistics, and Key Lab NAA-MOE, Central China Normal University, Wuhan, China
关键词：
Bogdanov–Takens bifurcation;Harvesting;Holling I functional response;Hopf bifurcation;Krill–whale interaction;Predator–prey model
摘要：
In the Antarctic, the whale population had been reduced dramatically due to the unregulated whaling. It was expected that Antarctic krill, the main prey of whales, would grow significantly as a consequence and exploratory krill fishing was practiced in some areas. However, it was found that there has been a substantial decline in abundance of krill since the end of whaling, which is the phenomenon of krill paradox. In this paper, to study the krill–whale interaction we revisit a harvested predator–prey model with Holling I functional response. We find that the model admits at most two positive equilibria. When the two positive equilibria are located in the region
$$\big \{(N,P)|0\le N< 2N_c,\ P\ge 0\big \}$$
, the model exhibits degenerate Bogdanov–Takens bifurcation with codimension up to 3 and Hopf bifurcation with codimension up to 2 by rigorous bifurcation analysis. When the two positive equilibria are located in the region
$$\big \{(N,P)|N>2N_c,\ P\ge 0\big \}$$
, the model has no complex bifurcation phenomenon. When there is one positive equilibrium on each side of
$$N=2N_c$$
, the model undergoes Hopf bifurcation with codimension up to 2. Moreover, numerical simulation reveals that the model not only can exhibit the krill paradox phenomenon but also has three limit cycles, with the outmost one crosses the line
$$N=2N_c$$
under some specific parameter conditions.
期刊：
BRIEFINGS IN BIOINFORMATICS,2024年25(2) ISSN：1467-5463
通讯作者：
Xiao-Fei Zhang
作者机构：
School of Mathematics and Statistics, Central China Normal University , Wuhan 430079 , China;Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University , Wuhan 430079 , China;[Yi-Xuan Xiong; Xiao-Fei Zhang] School of Mathematics and Statistics, Central China Normal University , Wuhan 430079 , China<&wdkj&>Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University , Wuhan 430079 , China
通讯机构：
[Xiao-Fei Zhang] S;School of Mathematics and Statistics, Central China Normal University , Wuhan 430079 , China<&wdkj&>Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University , Wuhan 430079 , China
摘要：
The proliferation of single-cell RNA-seq data has greatly enhanced our ability to comprehend the intricate nature of diverse tissues. However, accurately annotating cell types in such data, especially when handling multiple reference datasets and identifying novel cell types, remains a significant challenge. To address these issues, we introduce Single Cell annotation based on Distance metric learning and Optimal Transport (scDOT), an innovative cell-type annotation method adept at integrating multiple reference datasets and uncovering previously unseen cell types. scDOT introduces two key innovations. First, by incorporating distance metric learning and optimal transport, it presents a novel optimization framework. This framework effectively learns the predictive power of each reference dataset for new query data and simultaneously establishes a probabilistic mapping between cells in the query data and reference-defined cell types. Secondly, scDOT develops an interpretable scoring system based on the acquired probabilistic mapping, enabling the precise identification of previously unseen cell types within the data. To rigorously assess scDOT’s capabilities, we systematically evaluate its performance using two diverse collections of benchmark datasets encompassing various tissues, sequencing technologies and diverse cell types. Our experimental results consistently affirm the superior performance of scDOT in cell-type annotation and the identification of previously unseen cell types. These advancements provide researchers with a potent tool for precise cell-type annotation, ultimately enriching our understanding of complex biological tissues.
作者：
Banerjee, Malay;Huang, Jicai;Pan, Qin;Zou, Lan
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2024年 ISSN：1531-3492
通讯作者：
Zou, L
作者机构：
[Banerjee, Malay] IIT Kanpur, Dept Math & Stat, Kanpur 208016, India.;[Huang, Jicai; Pan, Qin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zou, Lan; Zou, L] Capital Normal Univ, Sch Math Sci, Beijing 100089, Peoples R China.
通讯机构：
[Zou, L ] C;Capital Normal Univ, Sch Math Sci, Beijing 100089, Peoples R China.
关键词：
Key words and phrases. Generalist predator;stability;limit cycle;Hopf bifurcation;Bogdanov- Takens bifurcation
摘要：
. Consideration of generalist predators leads to relatively complex dynamics due to alternative food sources. Here, we propose and analyze a prey-predator model with a generalist predator. The availability of alternative food sources for the predator and a density-dependent growth rate induces not only bistability and tristability, but also more complicated dynamical behaviors. We have studied the possible number and geometric configurations of positive equilibria in detail. A systematic bifurcation analysis has revealed the existence of the degenerate Bogdanov-Takens bifurcation of codimension four and degenerate Hopf bifurcation of codimension three. We found that degenerate local bifurcations with a higher codimension are responsible for three limit cycles. Derivation of the analytical conditions for three limit cycles for a suitable range of parameters is a crucial finding of this work.
摘要：
In this report we propose two highly efficient ensemble algorithms incorporating the gPAV and the rotational pressure correction methods for computing Stokes-Darcy flow ensembles. All variables are fully decoupled including the three components of the velocity, leading to smaller linear systems to be solved at each time step. Moreover, all ensemble members share the same constant coefficient matrix for which the fast block CG method can be applied for computing the ensemble at one pass at significantly reduced computational cost. We prove the two new ensemble algorithms are unconditionally stable with respect to the modified energy without any constraints on the uncertain parameters or the time steps. We will provide details of implementation and discuss how to efficiently solve the corresponding linear systems. Numerical examples are presented to show the efficiency and effectiveness of the algorithms.
摘要：
In coding theory, it is important to construct codes with optimal parameters. The codes meeting the Griesmer bound are called Griesmer codes. In this paper, we prove nonexistence of some Griesmer codes of dimension four over finite fields of cardinality eight and nine using projective geometry. Moreover, we improve 24 cases on code lengths for given minimal distance and dimension four. Two precise lower bounds of code lengths have also been determined.
作者机构：
[Liang Cheng; Liang Cheng Liang Cheng Liang Cheng] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hebei, China;[Yongjia Zhang; Yongjia Zhang Yongjia Zhang Yongjia Zhang] School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China
通讯机构：
[Yongjia Zhang; Yongjia Zhang Yongjia Zhang Yongjia Zhang] S;School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China
关键词：
noncollapsing;Ricci flow;Type I ancient solution
摘要：
Abstract In this paper, we study complete Type I ancient Ricci flows with positive sectional curvature. Our main results are as follows: in the complete and noncompact case, all such ancient solutions must be noncollapsed on all scales; in the closed case, if the dimension is even, then all such ancient solutions must be noncollapsed on all scales. This furthermore gives a complete classification for three‐dimensional noncompact Type I ancient solutions without assuming the noncollapsing condition.
作者机构：
[Qingquan Deng] School of Mathematics and Statistics, Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University, Wuhan, China;[Dashan Fan] Department of Mathematical Science, University of Wisconsin-Milwaukee, Milwaukee, USA;[Ruizhi Zhao] School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
通讯机构：
[Qingquan Deng] S;School of Mathematics and Statistics, Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University, Wuhan, China
摘要：
In this paper we study the Hp–Hq estimates of the solutions for a class of dispersive equations
$$\left\{ {\matrix{{i{\partial _t}u(t,x) = - P(|\nabla |)u(t,x),} \hfill & {(t,x) \in \mathbb{R} \times {\mathbb{R}^n},} \hfill \cr {u(0,x) = {u_0}(x),} \hfill & {x \in {\mathbb{R}^n},} \hfill \cr } } \right.$$
where P: ℝ+ → ℝ is smooth away from the origin and enjoy different scalings. As applications, we obtain the decay estimates for the solutions of higher order homogeneous and inhomogeneous Schrödinger equations.
期刊：
BRITISH JOURNAL OF PSYCHOLOGY,2024年115(1):66-89 ISSN：0007-1269
通讯作者：
Zhang, Y
作者机构：
[Li, Hao; Zhang, Ying; Chen, Gaowei] Univ Hong Kong, Fac Educ, Hong Kong, Peoples R China.;[Li, Bo; Li, Na] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Zhou, Xin] Sichuan Univ, Middle Sch, Chengdu, Peoples R China.;[Zhang, Ying; Zhang, Y] Univ Hong Kong, Fac Educ, Pokfulam, Hong Kong, Peoples R China.
通讯机构：
[Zhang, Y ] U;Univ Hong Kong, Fac Educ, Pokfulam, Hong Kong, Peoples R China.
摘要：
Bullying victimization can undermine adolescents' well-being. However, few studies have comprehensively investigated the contributions of various victimization forms to well-being and compared which forms were more harmful than others. Evidence on whether resilience and social support moderate such associations is also limited. Using a sample of 12,058 Chinese adolescents in the Programme for International Student Assessment (PISA) 2018, this cross-sectional study aimed to (1) investigate the associations of physical, verbal and relational victimization with well-being; (2) compare the strengths of these associations; and (3) examine the moderating roles of resilience and teacher and parent support in these associations. Results showed that three victimization forms were associated with poorer well-being. Relational and physical victimization were more harmful to most studied well-being outcomes than verbal victimization. Furthermore, resilience weakened the negative effects of physical victimization on negative affect and life satisfaction but aggravated the negative effects of verbal victimization on both outcomes and the negative effect of relational victimization on school belonging. Teacher support intensified the negative effects of physical victimization on school belonging. Parent support was not effective in regulating the victimization-well-being association. The findings underscored the detrimental effects of bullying victimization on adolescents' well-being and the potentially harmful sides of resilience and social support. Implications for bullying prevention were discussed.
期刊：
Journal of Functional Analysis,2024年286(2):110206 ISSN：0022-1236
通讯作者：
Xie, HF
作者机构：
[Luo, Peng] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Tang, Zhongwei] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.;[Xie, Huafei] Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.
通讯机构：
[Xie, HF ] N;Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.
摘要：
In this paper we study the following eigenvalue problem {-Delta v = lambda C(alpha)(p(alpha) - epsilon)vertical bar x vertical bar(alpha)u(epsilon)(p alpha-epsilon-1)v in Omega, u=0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain containing the origin, C(alpha) = (N + alpha)(N - 2), N >= 3, p(alpha) = N+2+2 alpha/N-2, alpha > 0, epsilon > 0 is a small parameter and u(epsilon) is a single peaked solution of Henon equation {-Delta u = C(alpha)vertical bar x vertical bar(alpha)u(p alpha-epsilon) in Omega, u > 0 in Omega, u=0 on partial derivative Omega, which established by Gladiali and Grossi (2012) [21]. By using various local Pohozaev identities and blow-up analysis, we prove some asymptotic behavior of the eigen values lambda(epsilon,i) and corresponding eigen functions v(epsilon,i), i = 2, ... , Sigma(1 <= k <= 2+alpha/2) (N + 2k - 2) (N + k - 3)!/(N - 2)!k! + 2 when alpha is not an even integer. As a consequence, if 0 < alpha < 2, we have that the Morse index of the single peaked solutions is N + 1, which gives an affirmative answer to a conjecture raised by Gladiali and Grossi. (c) 2023 Elsevier Inc. All rights reserved.
期刊：
Journal of Mathematical Analysis and Applications,2024年537(1):128270 ISSN：0022-247X
通讯作者：
Jicai Huang
作者机构：
[Shuang Chen; Jicai Huang] School of Mathematics and Statistics, and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, China
通讯机构：
[Jicai Huang] S;School of Mathematics and Statistics, and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, China
摘要：
In this paper, we study the destabilization of synchronous periodic solutions for patch models. By applying perturbation theory for matrices, we derive asymptotic expressions of the Floquet spectra and provide a destabilization criterion for synchronous periodic solutions arising from closed orbits or degenerate Hopf bifurcations in terms of period functions. Finally, we apply the main results to the well-known two-patch Holling-Tanner model.
作者机构：
[Bao, Kangbo] Lanzhou Univ Finance & Econ, Sch Informat Engn & Artificial Intelligence, Lanzhou 730020, Peoples R China.;[Zhang, Xinan; Bao, Kangbo; Zhang, XA] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Liang, Guizhen] Xinxiang Univ, Sch Math & Informat Sci, Xinxiang 453003, Henan, Peoples R China.;[Tian, Tianhai] Monash Univ, Sch Math Sci, Melbourne, Vic 3800, Australia.
通讯机构：
[Zhang, XA ] C;[Tian, TH ] M;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Monash Univ, Sch Math Sci, Melbourne, Vic 3800, Australia.
摘要：
Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases. It has also been demonstrated to be related to cancer heterogeneity, which promotes the emergence of treatment-refractory cancer cell populations. Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system, we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting. We analyze the local geometric properties of the equilibria of the model. Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population. Moreover, the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength. Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.
期刊：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2024年 ISSN：0308-2105
通讯作者：
Chen, T
作者机构：
[Chen, Ting; Zi, Ruizhao; Chen, T] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zi, Ruizhao] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, T ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
MHD equations;Couette flow;stability
摘要：
In this work, we study the Sobolev stability of shear flows near Couette in the 2D incompressible magnetohydrodynamics (MHD) equations with background magneticfield (alpha,0)(T)on TxR. More precisely, for sufficiently large alpha, we show that when the initial datum of the shear flow satisfies & Vert;U(y)-y & Vert;HN+6 << 1, with N>1, and the initial perturbationsu in and b(in) satisfy & Vert;(u(in),b(in))& Vert;HN+1=<<nu 5/(6)+ delta for any fixed delta>0, then the solution of the 2D MHD equations remains nu-((1)/(3)+ (delta)/(2))is an element of-close to(e(nu t partial derivative yy)U(y),0)(T)for allt>0.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2024年29(2):812-832 ISSN：1531-3492
通讯作者：
Zhijun Liu
作者机构：
[Liu, Zhijun; Wang, Lianwen] School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China;[Chen, Siyu; Zhang, Xingan] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China
通讯机构：
[Zhijun Liu] S;School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China
摘要：
This paper is devoted to proposing a mathematical model in order to explore the dynamics of HTLV-Ⅰ (human T-cell leukemia virus type-Ⅰ) infection, in which the closely related target cell-virus-immune system interaction and the time-delay cytotoxic T lymphocyte (CTL) immune response are taken into consideration. Firstly, we give the relevant lemma for the existence of feasible equilibrium points of the model, and then further certify the global asymptotic stabilities of the infection-free equilibrium (IFFE) $ E_1 $ and the immune-free equilibrium (IMFE) $ E_2 $. Furthermore, we research the existence of Hopf bifurcation (HB) occurring at the immune equilibrium (IE) $ E^* $ due to the influence of the delay bifurcation parameter. Also, the numerical simulations confirm this fact. In addition, we obtain the explicit expressions which determine the direction and stability of HB. Finally, a succinct discussion shows that the delay in CTL response can destabilize $ E^* $ and generate HB, but not affect stabilities of $ E_1 $ and $ E_2 $.
摘要：
Subspace codes have important applications in random network coding. It is a classical problem to construct subspace codes where both their size and their minimum distance are as large as possible. In particular, cyclic constant dimension subspace codes have additional properties which can be used to make encoding and decoding more efficient. In this paper, we construct large cyclic constant dimension subspace codes with minimum distances 2k-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2k-2$$\end{document} and 2k. These codes are contained in Gq(n,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr {G}_q(n, k)$$\end{document}, where Gq(n,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr {G}_q(n, k)$$\end{document} denotes the set of all k-dimensional subspaces of the finite filed Fqn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q<^>n}$$\end{document} of qn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q<^>n$$\end{document} elements (q a prime power). Consequently, some results in [7, 15], and [23] are extended.
作者机构：
[Liu, Botao; Tu, Zhengge; Liu, BT] Cent China Normal Univ, Sch Econ & Business Adm, Wuhan 430079, Peoples R China.;[Liu, Botao; Tu, Zhengge; Liu, BT] Cent China Normal Univ, Res Ctr Low Carbon Econ & Environm Policies, Wuhan 430079, Peoples R China.;[Kong, Jiayang] Qinghai Univ Sci & Technol, Coll Comp & Informat Sci, Xining 810016, Peoples R China.;[Kong, Jiayang] Qinghai Univ, Dept Comp Technol & Applicat, Xining 810016, Peoples R China.;[Sun, Liping] Shandong Normal Univ, Audit Off, Jinan 250014, Peoples R China.
通讯机构：
[Liu, BT ] C;Cent China Normal Univ, Sch Econ & Business Adm, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Res Ctr Low Carbon Econ & Environm Policies, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
digital economy;entropy method;internet development;regional development imbalance;rural-urban income gap
摘要：
Currently, the Chinese government is considering two major strategies, namely, developing the digital economy and achieving common prosperity, to address regional development imbalances. Using panel data from 276 Chinese cities spanning from 2011 to 2019, the article first employs the entropy method to measure China’s digital economy development, digital fusion application, and Internet accessibility. Subsequently, the paper evaluates the influence of the digital economy on regional development imbalances, focusing on the rural-urban income gap. The results show a significant reduction in the rural-urban income gap due to digital economy development. Notably, digital fusion applications have a greater impact on reducing the rural-urban income gap than Internet accessibility. In addition, a heterogeneity analysis reveals that the influence of the digital economy on the rural-urban income gap is only reflected in the eastern and western regions, with a more substantial effect observed in the western region. This study, to some extent, helps Chinese government officials distinguish the diverse impacts of different dimensions and regional variations in digital economies on the rural-urban income gap. Such insights can guide the government in strategically advancing digital economy development to accelerate the mitigation of regional disparities and achieve sustainable economic development.
作者机构：
[Xia, Sijia; Zhang, Xiongjun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Qiu, Duo] Wuhan Inst Technol, Sch Math & Phys, Wuhan 430205, Peoples R China.;[Zhang, Xiongjun] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Qiu, D ] W;Wuhan Inst Technol, Sch Math & Phys, Wuhan 430205, Peoples R China.
摘要：
In this paper, we study the problem of a batch of linearly correlated image alignment, where the observed images are deformed by some unknown domain transformations, and corrupted by additive Gaussian noise and sparse noise simultaneously. By stacking these images as the frontal slices of a third-order tensor, we propose to utilize the tensor factorization method via transformed tensor-tensor product to explore the low-rankness of the underlying tensor, which is factorized into the product of two smaller tensors via transformed tensor-tensor product under any unitary transformation. The main advantage of transformed tensor-tensor product is that its computational complexity is lower compared with the existing literature based on transformed tensor nuclear norm. Moreover, the tensor
$$\ell _p$$
$$(0<p<1)$$
norm is employed to characterize the sparsity of sparse noise and the tensor Frobenius norm is adopted to model additive Gaussian noise. A generalized Gauss-Newton algorithm is designed to solve the resulting model by linearizing the domain transformations, and a proximal Gauss-Seidel algorithm is developed to solve the corresponding subproblem. Furthermore, the convergence of the proximal Gauss-Seidel algorithm is established according to Kurdyka-Łojasiewicz property, whose convergence rate is also analyzed. Extensive numerical examples on real-world image datasets are carried out to demonstrate the superior performance of the proposed method as compared to several state-of-the-art methods in both accuracy and computational time.
作者机构：
[Bao, Kangbo] School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China. Electronic address: baokangbo@163.com;[Liang, Guizhen] School of Mathematics and Information Science, Xinxiang University, Xinxiang, 453003, PR China. Electronic address: lgz3361@163.com;[Tian, Tianhai] School of Mathematics, Monash University, Melbourne, VIC 3800, Australia. Electronic address: tianhai.tian@monash.edu;[Zhang, Xinan] School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China. Electronic address: xinanzhang@mail.ccnu.edu.cn
通讯机构：
[Zhang, Xinan; Tian, Tianhai; Bao, Kangbo; Liang, Guizhen] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China. Electronic address:;School of Mathematics and Information Science, Xinxiang University, Xinxiang, 453003, PR China. Electronic address:;School of Mathematics, Monash University, Melbourne, VIC 3800, Australia. Electronic address: tianhai.
关键词：
Drug resistance;Global stability;Immunotherapy;Mathematical model;Targeted therapy
摘要：
Drug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried out to verify the stability of equilibria and treatment outcomes using a set of collected model parameters and experimental data on murine colon carcinoma. Simulation results suggest that immunotherapy combined with chemotherapy contributes significantly to the control of tumor growth compared to monotherapy. Sensitivity analysis is performed to identify the importance of model parameters on the variations of model outcomes.
期刊：
Communications in Algebra,2024年 ISSN：0092-7872
通讯作者：
Gao, ZC
作者机构：
[Miao, Long; Zhou, Wenxia] Hohai Univ, Sch Math, Nanjing, Peoples R China.;[Gao, Zhichao] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Gao, Baijun] Yili Normal Univ, Coll Math & Stat, Yining, Xinjiang, Peoples R China.;[Liu, Wei] Yangzhou Univ, Sch Math Sci, Yangzhou, Peoples R China.
通讯机构：
[Gao, ZC ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
phi-simple subgroups;Frattini subgroups;maximal subgroups;second maximal subgroups;the core of subgroups
摘要：
In this paper, we will investigate the structure of groups with the property of the core relation between some second maximal subgroups and corresponding maximal subgroups, and obtained some new results about finite groups.ARTICLE HISTORY Received 7 September 2023 Revised 13 December 2023 Communicated by Mandi Schaeffer Fry
