作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Yuan, Shuai] Cent South Univ, Sch Math & Stat, Changsha 410083, Peoples R China.
通讯机构：
[Changjin Xu] G;Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, PR China
关键词：
Complex-valued neural networks;Hopf bifurcation;Leakage delay;Stability;Fractional order
摘要：
During the past decades, integer-order complex-valued neural networks have attracted great attention since they have been widely applied in in many fields of engineering technology. However, the investigation on fractional-order complex-valued neural networks, which are more appropriate to characterize the dynamical nature of neural networks, is rare. In this manuscript, we are to consider the stability and the existence of Hopf bifurcation of fractional-order complex-valued neural networks. By separating the coefficients and the activation functions into their real and imaginary parts and choosing the time delay as bifurcation parameter, we establish a set of sufficient conditions to ensure the stability of the equilibrium point and the existence of Hopf bifurcation for the involved network. The study shows that both the fractional order and the leakage delay have an important impact on the stability and the existence of Hopf bifurcation of the considered model. Some suitable numerical simulations are implemented to illustrate the pivotal theoretical predictions. At last, we ends this article with a simple conclusion. (C) 2020 Elsevier Ltd. All rights reserved.
摘要：
The exact metric of a moving Kerr black hole with an arbitrary constant velocity is derived in Kerr–Schild coordinates. We then calculate the null equatorial gravitational deflection caused by a radially moving Kerr source up to the second post-Minkowskian order, acting as an application of the weak-field limit of the metric. The bending angle of light is found to be consistent with the result given in the previous works.
期刊：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION,2021年11(3):1348-1370 ISSN：2156-907X
作者机构：
[Wang, Huilan] Univ South China, Dept Math & Phys, St Changsheng West Rd, Hengyang 421001, Peoples R China.;[Ou, Chunhua] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.;[Dai, Binxiang] Cent South Univ, Sch Math & Stat, St Lushan South Rd, Changsha 410012, Peoples R China.
关键词：
State dependent impulse;periodic solution;phase analysis;Poincare map;successor function;Bendixson domain
摘要：
In this paper, we focus on a general state-dependent Kolmogorov predator-prey model subject to non-selective harvesting along with delivery. Certain criteria are established for the existence, non-existence and multiplicity of order-1 impulsive periodic solutions to the system. Based on the geometric phase analysis and the method of Poincare map or successor function with Bendixson domain theory, three typical types of Bendixson domains (i.e., Parallel Domain, Sub-parallel Domain and Semi-ring Domain) are introduced to deal with the discontinuity of the Poincare map or successor function. We incorporate two discriminants Delta 1 and Delta 2 to link with the existence, nonexistence and multiplicity as well as the stability of order-1 periodic solutions. At the same time, we locate the order-1 periodic solutions with the help of three characteristic points and the parameters ratio of delivery over harvesting. The results show that there must exist at least one order-1 periodic solution when the trajectory, that is tangent to the mapping line, can hit the impulsive line. While the trajectory tangent to the mapping line cannot hit the impulsive line, there is not necessary the existence of an order-1 periodic solution, which means the impulsive control may be invalid after finite times stimulation or suppression. In conclusion, we reveal that the delivery can prevent the predator from extinction and stabilize the order-1 periodic solution.
作者机构：
[Wang, Wuzhou; He, Shuya; Shen, Wangtao; Qi, Huizhou; Ma, Yun] Univ South China, Inst Biochem & Mol Biol, Hengyang Med Coll, Hengyang 421001, Peoples R China.;[Qi, Huizhou] Univ South China, Hengyang Med Coll, Funct Lab Ctr, Hengyang 421001, Peoples R China.;[Wang, Wuzhou; He, Shuya; Qi, Huizhou; Xiao, Fangzhu] Univ South China, Hengyang Key Lab Biol Effects Nucl Radiat, Hengyang 421001, Peoples R China.;[Zhu, Hui] Univ South China, Inst Engn Math, Math & Phys Coll, Hengyang 421001, Peoples R China.;[He, Junyan] Univ South China, Affiliated Hosp 1, Dept Radiat Oncol, Hengyang 421001, Peoples R China.
通讯机构：
[Ma, Yun] I;[He, Shuya] H;Institute of Biochemistry and Molecular Biology, Hengyang Medical College, University of South China, Hengyang, 421001, China. Electronic address:;Hengyang Key Laboratory for Biological Effects of Nuclear Radiation, University of South China, Hengyang, 421001, China. Electronic address:
关键词：
DNA double-strand break;DSB reaction intermediate;Kinetics of DSB repair;Mathematical model
摘要：
This manuscript outlines the kinetics of two main repair pathways of DNA double-strand break (DSB) in eukaryotes: non-homologous end joining (NHEJ) and homologous recombination repair (HRR). In this review, we discuss the precise study of recruitment kinetics of repair proteins based on the latest technologies in the past two decades. Then we simulate the theoretical description of the DNA repair process by mathematical models. In our study, the consecutive reactions chain (CRC) model and continuous-time random walk (CTRW) model have been unified by us, so that we can obtain the function of the number of intermediates with time in the same framework of equations, overcome the incompatibility between the two models. On this basis, we propose a data fitting workflow using these both models. Finally, we give an overview of different real-time quantitative methods and the new mechanism complexity that can be found from the corresponding dynamic models.
摘要：
The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Applying Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential systems, we establish a new sufficient condition to ensure the stability and the emergence of Hopf bifurcation of the addressed fractional-order BAM neural networks with multiple delays. The research indicates that the delay has a vital effect on the stability and the appearance of Hopf bifurcation of fractional-order BAM neural networks. Computer simulations are put into effect to test the effectiveness of the theoretical findings. It is shown that when the sum of time delays crosses some critical values, the stability of networks loses and Hopf bifurcation will happen. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
期刊：
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS,2021年41(3):4287-4294 ISSN：1064-1246
通讯作者：
Zhang, Li
作者机构：
[Zhang, Li; Liu, Yanqi; Liu, Xueyang] Univ South China, Sch Nucl Sci & Technol, Hengyang, Hunan, Peoples R China.;[Zhang, Li] Hunan Inst Technol, Inst Human Factors & Safety Engn, Hengyang, Hunan, Peoples R China.;[Xu, Zhenghua] Univ South China, Coll Math & Phys, Hengyang, Hunan, Peoples R China.
通讯机构：
[Zhang, Li] U;[Zhang, Li] H;Univ South China, Sch Nucl Sci & Technol, Hengyang, Hunan, Peoples R China.;Hunan Inst Technol, Inst Human Factors & Safety Engn, Hengyang, Hunan, Peoples R China.
关键词：
Human reliability;accident conditions;diagnosis model;correlation matrix;approaching to
摘要：
This essay focus on the situation when the operator of the main control room can not handle the accident in time or make wrong judgment under accident condition in nuclear power plant, which may lead to the occurrence of major accidents or even more accidents concurrently. An intelligent fuzzy diagnosis model based on Grey Relational degree is constructed in this paper, by establishing accident-state correlation matrix and accident-state probability matrix, defining the vector of information weights for accident characteristic vector and monitoring result vector with linear transform, using Grey Relation to measure the relevance degree between monitoring result vector and accident characteristic vector, Searching for suspected accidents approaching to real solutions in iterative recursive algorithms, realizing automatic fuzzy diagnosis of multiple accidents. The results of simulation experiments of LOCA accidents indicate that the model and algorithm can diagnose various common accidents accurately and rapidly in complex nuclear power systems, providing strategy for operator's diagnosis decision.
作者机构：
[Wang, Hengtai; Zou, Zhiwei] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Shen, Xin] Univ South China, Coll Elect Engn, Hengyang 421001, Peoples R China.
关键词：
lie symmetry analysis;nonlinear self-adjointness;conservation law
摘要：
In the present paper, we mainly focus on the symmetry of the solutions of a given PDE via Lie group method. Meanwhile we transfer the given PDE to ODEs by making use of similarity reductions. Furthermore, it is shown that the given PDE is self-adjoining, and we also study the conservation law via multiplier approach.
摘要：
We derive the second-and-half post-Newtonian solution for the generally inclined motion of a test particle in Kerr spacetime when the effects of the spin-induced quadrupole are negligible. The next-to-leading order spin-orbit effects on the test particle's motion are obtained, which are important in fitting the motions of the extremely-mass-ratio-inspiral systems and also calculating the gravitational wave radiated by this kind of systems at the second-and-half post-Newtonian order.
期刊：
MATHEMATICAL BIOSCIENCES AND ENGINEERING,2021年18(2):1154-1168 ISSN：1547-1063
通讯作者：
Hu, Jiwen
作者机构：
[Chen, Xuekun; Liu, Yatao; Hu, Jiwen; Liu, Wenyi; Lei, Weirui] Univ South China, Coll Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Hu, Jiwen] U;Univ South China, Coll Math & Phys, Hengyang 421001, Peoples R China.
关键词：
atherosclerosis plaque;multi-physics field model;thermal lesions;HIFU;finite element method
摘要：
The aim of this study is to estimate the effects of some acoustic parameters on thermal lesions of atherosclerotic plaques in high-intensity focused ultrasound (HIFU) fields. A fluid-solid thermal coupling model is presented for describing the temperature elevation and thermal ablation of atherosclerotic plaque. A finite element approach is used to solve the coupling equations in cylindrical coordinates. The model considers the effect of the wall thickness of large arteries. The extent of the tissue lesion is determined by the accumulated thermal lesion with Arrhenius integral equation at each location. The results show the lesion size of atherosclerotic plaque is positively correlated to the excited frequency and acoustic output power with heating time. The computational model indicates HIFU may present a novel option for thermal ablation of atherosclerotic plaques with a completely non-invasive treatment paradigm.
摘要：
In this note we present the Chandrasekhar-like transformations for the electromagnetic waves and the scalar waves in Schwarzschild spacetime, which are simpler than those known before.
作者机构：
[Li, Xiao-Hua; Pan, Xiao; Liu, Hong-Ming; Zou, You-Tian] Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.;[Wu, Xi-Jun] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[He, Biao] Cent South Univ, Coll Phys & Elect, Changsha 410083, Peoples R China.;[Li, Xiao-Hua] Univ South China, Collaborat Nucl Energy & Nucl Safety, Natl Exemplary Base Int Sci & Tech, Hengyang 421001, Peoples R China.;[Li, Xiao-Hua] Univ South China, Cooperat Innovat Ctr Nucl Fuel Cycle Technol & Eq, Hengyang 421001, Peoples R China.
关键词：
half-lives;alpha decay;neptunium isotopes
摘要：
In the present work, we systematically study the alpha decay half-lives of neptunium (Z = 93) isotopes within a one-parameter model (OPM). The calculated results are in reasonable agreement with the experimental data. Noticeably, the recently measured alpha decay half-life value of 380(-110)(+260)ns for Np-222 [Phys. Rev. Lett. 125, 032 502 (2020)] has been fairly reproduced by the OPM as 780 ns within a factor of approximate to 2. In addition, we extend this model to predict alpha decay half-lives of neptunium isotopes whose alpha decay is energetically allowed or observed but not yet quantified in NUBASE2016. Meanwhile, it is found that the half-life between the neutron number N = 126 and N = 128 in Np drop sharply, this result shows that the N = 126 shell closure is still very robust at Z = 93. At last, alpha particle preformation probability P-alpha(extd) are extracted in two cases with alpha transition orbital angular momentum l = 0 and l = 1, we find a amazing phenomenon that the P-alpha(extd) are basically the same for alpha transition with the same orbital angular momentum l.
作者机构：
[Zheng, Lijing] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Kan, Haibin] Fudan Univ, Shanghai Key Lab Intelligent Informat Proc, Sch Comp Sci, Shanghai 200433, Peoples R China.;[Kan, Haibin] Shanghai Engn Res Ctr Blockchain, Shanghai 200433, Peoples R China.;[Kan, Haibin] Key Lab Informat Sci Electromagnet Waves MoE, Shanghai 200433, Peoples R China.;[Peng, Jie] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.
通讯机构：
[Haibin Kan] S;Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai 200433, China<&wdkj&>Shanghai Engineering Research Center of Blockchain, Shanghai 200433, China<&wdkj&>Key Laboratory for Information Science of Electromagnetic Waves (MoE), Shanghai 200433, China
摘要：
Let n be an even positive integer, and m < n be one of its positive divisors. In this paper, inspired by the work of Tang et al. (2017) [23] on constructing large classes of bent functions from known ones, we consider the construction of vectorial bent and vectorial plateaued (n, m)-functions of the form H(x) = G(x) + g(x), where G is a vectorial bent (n, m)-function, and g is a Boolean function. We find an efficient generic method to construct such kind of vectorial bent (plateaued) functions by establishing a link between the bentness (plateaudness) of Hand the second-order derivatives of g. This allows us to provide (at least) three new infinite families of vectorial bent functions with high algebraic degrees. New vectorial plateaued (n, m + t)-functions are also obtained (t >= 0 depending on n can be large numbers), two classes of which have the maximal number of bent components. (C) 2021 Elsevier B.V. All rights reserved.
摘要：
In this paper, we study the minimal speed (spreading speed) selection mechanism of traveling waves to a periodic diffusive Lotka-Volterra model with monostable nonlinearity. The method of upper and lower solutions pair is applied to establish the existence of traveling waves. We prove that the nature of nonlinear selection is to find a lower solution pair with the first species decaying in a faster rate. By novel constructions of various upper and lower solutions, we obtain a number of new results on the minimal speed determinacy. Numerical simulations are carried out to illustrate all of our discoveries. (C) 2020 Elsevier Inc. All rights reserved.
摘要：
In this manuscript, fuzzy delayed cellular neural networks with impulse are studied. Applying time scale calculus knowledge, mathematical inequalities and constructing Lyapunov function, we establish a sufficient criterion that guarantees the existence and exponential stability of anti-periodic solutions for fuzzy delayed cellular neural networks with impulse. In addition, an example with its numerical simulations is given to illustrate our theoretical predictions.
关键词：
cancer treatment;chemotherapy model;delay;fractional order;Hopf bifurcation;stability
摘要：
Cancer is one of the most serious diseases in the world. The investigation on cancer treatment has attracted great attention from medical workers, mathematical researchers, and scholars in various fields. To understand the intrinsic characteristics of cancer, numerous scholars have established cancer treatment models and discussed the dynamical properties. However, the main work of many scholars only focuses on the integer-order cancer treatment models, while the study on fractional-order ones is quite a few. In the present article, on the basis of previous publications, we will put up a new fractional-order chemotherapy model with two different delays. By applying the stability theory and the Hopf bifurcation of fractional-order differential equations, we obtain a series of new stability criteria of the involved model and some sufficient conditions to ensure the existence of Hopf bifurcation of the involved model. Furthermore, the impact of two different delays and the fractional order on the stability and the emergence of Hopf bifurcation of involved model is presented. To illustrate the validity of analytical predictions, we perform computer simulations with Matlab software. The theoretical results in the manuscript are innovative and play an important role in cancer treatment.
期刊：
Journal of Nonlinear Science,2020年30(6):3129-3159 ISSN：0938-8974
通讯作者：
Ou, Chunhua
作者机构：
[Wang, Hongyong] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Ou, Chunhua] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.
通讯机构：
[Ou, Chunhua] M;Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.
关键词：
Reaction diffusion equations;Bistable Lotka-Volterra competition system;Traveling wave;Propagation direction
摘要：
We study propagation direction of the traveling wave for the diffusive Lotka–Volterra competition system with bistable nonlinearity in a periodic habitat. By directly proving the strong stability of two semitrivial equilibria, we establish a new and sharper result on the existence of traveling wave. Using the method of upper and lower solutions, we provide two comparison theorems concerning the direction of traveling wave propagation. Several explicit sufficient conditions on the determination of the speed sign are established. In addition, an interval estimation of the bistable-wave speed reveals the relations among the bistable speed and the spreading speeds of two monostable subsystems. Biologically, our idea and insight provide an effective approach to find or control the direction of wave propagation for a system in heterogeneous environments.
摘要：
This paper is devoted to the Neumann problem of a stationary Lotka-Volterra model with diffusion and advection. In the model it is assumed that one population growth rate is described by weak Allee effect. We first obtain some sufficient conditions ensuring the existence of nonconstant solutions by using the Leray-Schauder degree theory. And then we study a limiting system (with nonlocal constraint) which stems from the original model as diffusion and advection of one of the species tend to infinity. Finally, we classify the global bifurcation structure of nonconstant solutions of the simplified 1D case. (C) 2020 Elsevier Ltd. All rights reserved.
