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15 April 2021, Volume 38 Issue 2 Previous Issue    Next Issue

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Dynamics Model of Hepatitis B Immunoglobulin Blocking the Transmission of Hepatitis B Virus between Mother and Infant LI Dong-mei, LIU Wei-hua, WANG Qi, GUO Mei-jing 2021, 38 (2):  151-166.  doi: 10.3969/j.issn.1005-3085.2021.02.001 Abstract ( 423 )   PDF (366KB) ( 178 )   Save This paper is concerned with the transmission mechanism of hepatitis B virus between mother and infant and the inhibitory effect of hepatitis B immunoglobulin on hepatitis B virus, and the dynamics mode of blocking the transmission of hepatitis B virus between mother and infant is established. Applying Lyapunov function and composite matrix theory, the stability of equilibrium point of model is studied. The rationality of the model is analyzed by Matlab based on the clinical data of hepatitis B immunoglobulin dosage and detection of hepatitis B virus DNA. The numbers of hepatitis B virus in pregnant women with hepatitis B virus carriers and hepatitis B virus infections at different dosages are obtained by numerically simulation. Moreover, the number of hepatitis B virus in fetuses is predicted, which provides a theoretical basis for clinical medication. Related Articles | Metrics

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Stochastic Response Analysis of a Nonlinear Business Cycle Model with Random Income Disturbance ZHAO Jun 2021, 38 (2):  167-179.  doi: 10.3969/j.issn.1005-3085.2021.02.002 Abstract ( 277 )   PDF (4945KB) ( 173 )   Save The evolution of a business cycle has  nonlinear and stochastic characteristics, and it is improtant to find its evolution law. Firstly, a nonlinear business cycle dynamic model with first-order and third-order terms of the difference between preincome and prior income to simulate a generic nonlinear impact of incomes on the investment is established in this paper. Two independent Gaussian white noise random functions are used to simulate the interference of uncertain factors and random income, respectively. Then a path integral method, based on short-term Gaussian transition probability density and Gauss-Legendre integration scheme, is applied to solve the probability density function of income and income change rate. Finally, the effects of income random disturbance and supplementary saving rate on the evolution of the nonlinear business cycle are studied. The results show that the fluctuation of the income in the random interference is significant in the early stage, and it tends to be stable in the later period. The increase of income random interference significantly increases the randomness of income, making income more difficult to be predicted and controlled. In addition, the enhancement of supplementary saving rate decreases the probability of high income. Related Articles | Metrics

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Statistical Diagnostics for Joint Location, Scale and Skewness Models with Skew-normal Data WU Liu-cang, NIE Xing-feng, ZHENG Gui-fen 2021, 38 (2):  180-194.  doi: 10.3969/j.issn.1005-3085.2021.02.003 Abstract ( 288 )   PDF (479KB) ( 212 )   Save There is such a kind of data as heteroscedasticity, contains multiple outliers or strong influence points and skewness in the fields of economy, biomedicine and environmental science. Based on the data, this paper is concerned with the statistical diagnosis of joint location, scale and skewness models. Firstly, the Pena distance under the normal distribution is extended to the skew-normal distribution, so this method has a more widely application. Secondly, the likelihood distance, Cook distance, Pena distance and local influence analysis are used to compare the diagnostic methods, and Pena distance is better than Cook and likelihood distance  under certain conditions. Finally, through Monte Carlo simulation experiments and a real data analysis, it indicates that the theories and proposed methods in this paper are scientific and reasonable. Related Articles | Metrics

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Application of Inertia Relaxation Factor in Lattice Boltzmann Method WANG Ying-juan, GONG Guang-cai, SHI Xing, GONG Zi-che, LIU Yong-chao 2021, 38 (2):  195-206.  doi: 10.3969/j.issn.1005-3085.2021.02.004 Abstract ( 197 )   PDF (5856KB) ( 211 )   Save As a robust numerical simulation method, the lattice Boltzmann method has been widely used in various fields, especially in solving the problem of porous media. When the flow problem is too complicated, the calculation efficiency is low. Therefore, the inertia relaxation factor is introduced into the lattice Boltzmann method in this paper. The numerical simulation of the two-dimensional and three-dimensional lid-driven cavity flow are carried out. The simulation compares with the results obtained by using different inertia relaxation factors with the benchmark solutions from the aspects of computational efficiency, calculation accuracy and computational stability. The simulation results can improve the calculation efficiency while maintaining high precision, when the inertia relaxation factor is between 0.03 and 0.05. Then, the calculation efficiency develops with the increase of the inertia relaxation factor. They are important applications in engineering materials and the energy environmental fields. Related Articles | Metrics

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The Concavity of Multi-body Quantum Entanglement Measurements WEI Na-na, WANG Zhen, ZHANG Pei-jun 2021, 38 (2):  207-213.  doi: 10.3969/j.issn.1005-3085.2021.02.005 Abstract ( 353 )   PDF (149KB) ( 165 )   Save Quantum entanglement is the most important physical resource in quantum information and quantum computation. Based on the basic theory of two-body quantum entanglement measurement, the important properties of the entanglement measurement of multi-body quantum pure state is discussed by the topological analysis and control theory in this paper. Firstly, the concavity of entanglement measurement of two-body quantum pure states is obtained by Schmidt decomposition. Secondly, the concavity of the convex combination of the entanglement measurement of multi-body quantum pure states is considered by the topological analysis and inequality theory. Finally, the upper bound of two-body quantum pure states is precisely studied by the control theory and Schur convex function. The concavity is analytic and able to calculate, and the topological order of states is described more successfully in the Kitaev model. Therefore, this work is broadened to topological quantum computation and quantum precision measurement. Related Articles | Metrics

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A Dynamic Analysis of Cannibalism Model with Two-stage Structure ZHU Xue, LIN Xiao-lin, LI Jian-quan 2021, 38 (2):  214-228.  doi: 10.3969/j.issn.1005-3085.2021.02.006 Abstract ( 342 )   PDF (465KB) ( 284 )   Save Based on the assumptions that the adult could kill and eat the juvenile of the same species and that there is the natural death of the juvenile, a two-stage-structured model with cannibalism is proposed in this paper. In the absence of cannibalism, the conditions ensuring the global stabilities of the population extinction and survival equilibria of the model are obtained by constructing the corresponding Lyapunov functions. In the presence of cannibalism, it is found that the model may have two population survival equilibria and that the saddle-node bifurcation can occur for certain parameter region, and the global dynamics is determined by constructing the Dulac function to rule out the existence of periodic solutions. The existence of two positive equilibria and the occurrence of the saddle-node bifurcation imply that the final state of the population growth depends on the initial condition of the model. The theoretic results obtained are verified by numerical simulation. Related Articles | Metrics

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Stability and Error Estimate of the Second-order Mixed Finite Volume Method for Solving the Navier-Stokes Problems ZHANG Jie-hua, HAN Ming-hua 2021, 38 (2):  229-248.  doi: 10.3969/j.issn.1005-3085.2021.02.007 Abstract ( 377 )   PDF (626KB) ( 233 )   Save In the numerical simulation of many practical problems of fluid mechanics, the finite volume method is a very important and popular numerical method due to the local conservation and the capability of discretizing domains with complex geometry. A second-order mixed finite volume method is proposed in this paper to solve the Navier-Stokes equations. Specifically, on the triangular meshes, the trial function space for velocity of the Navier-Stokes equations is taken as the hierarchical quadratic conforming finite element space, and the corresponding test function space is composed of the piecewise constant functions and the piecewise quadratic polynomial functions. Both the trial function space and the test function space for pressure are chosen as the piecewise linear finite element space. The nonlinear terms in the Navier-Stokes equations are directly discretized on the control volumes of the finite volume method. Under the standard assumption that the viscosity parameter satisfies certain conditions, the stability of the proposed mixed finite volume method is proved and the optimal order error estimates for velocity and pressure of the Navier-Stokes equations are obtained, which are consistent with that of the corresponding finite element method.  The numerical examples are presented to verify the correctness of the theoretical results  and the effectiveness of the proposed numerical method. Related Articles | Metrics

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Estimation on Upper Bounds for the Infinity Norms of Inverses Matrix of Strictly Diagonally Dominant $M$-matrices ZHAO Ren-qing, GAN Xiao-ting, ZHANG Kun 2021, 38 (2):  249-256.  doi: 10.3969/j.issn.1005-3085.2021.02.008 Abstract ( 487 )   PDF (146KB) ( 295 )   Save $M$-matrix is a kind of special matrix which has wide applications. Many problems in biology, physics and social science and so on have close connection with $M$-matrice, hence researches on $M$-matrix is valuable. In this paper, firstly, some new notations are introduced, and two inequalities of element relation on strictly diagonally dominant $M$-matrix and the inverse matrix are given. Secondly, some new upper bounds for the infinity norm of inverse matrix are obtained. Finally, the lower bound of the smallest eigenvalue of matrix $A$ is presented, which only depends on the elements of matrix $A$. The theoreical analysis and numerical examples show that the new upper bounds improve the related results. Related Articles | Metrics

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Digital Power Exchange Option Pricing under Jump-diffusion Model LI Wen-han, ZHONG Ying, LV Gui-wen 2021, 38 (2):  257-270.  doi: 10.3969/j.issn.1005-3085.2021.02.009 Abstract ( 456 )   Save In this paper, we propose a new option named as digital power exchange option by adding an indicator function of the ratio of the two underlying assets prices (denoted power forms) to the payoff of the power exchange option. This proposed model can be used to avoid the risk caused by the excessive price deviation of two underlying assets. Based on the above work, we obtain the explicit pricing formulas of the digital power exchange option under the jump-diffusion model by choosing the different numeraire. Finally, we take some historical data of the adjusted closing prices of two real stocks to discuss the prices of the digital power exchange option. Related Articles | Metrics

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Partial Monotonicities of Extropy and Cumulative Residual Entropy Measure of Uncertainty PU Ming-yue, QIU Guo-xin 2021, 38 (2):  271-281.  doi: 10.3969/j.issn.1005-3085.2021.02.010 Abstract ( 168 )   PDF (155KB) ( 379 )   Save Uncertainty is closely related to amount of information and has been extensively studied in a variety of scientific fields including communication theory, probability theory and statistics. Given the information that the outcome of a random variable is in an interval, the uncertainty is expected to reduce when the interval shrinks. However, this conclusion is not always true. In this paper, we present the conditions under which the conditional extropy/cumulative residual entropy is a partially monotonic function of interval. Similar result is obtained for extropy of convolution of two independent and identically distributed random variables if their probability density functions are log-concave. Related Articles | Metrics

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Persistence Properties for a New Generalized Two-component Camassa-Holm-type System YU Hao-yang, CHONG Ge-zi 2021, 38 (2):  282-292.  doi: 10.3969/j.issn.1005-3085.2021.02.011 Abstract ( 157 )   PDF (124KB) ( 377 )   Save The long time behavior of solutions is one of important problems in the study of partial differential equations. To a great degree, the properties of solutions will depend on those of initial values. The persistence properties imply that the solutions of the equations decay at infinity when the initial data satisfies the condition of decaying at infinity. In this paper, we consider the persistence properties of solutions to the initial value problem for a new generalized two-component Camassa-Holm-type system by using weight functions. Furthermore, we give an optimal decaying estimate. Related Articles | Metrics

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Some Properties on the $b$-chromatic Number of Special Graphs WANG Guo-xing, CAO Xiao-jun 2021, 38 (2):  293-300.  doi: 10.3969/j.issn.1005-3085.2021.02.012 Abstract ( 237 )   PDF (204KB) ( 295 )   Save Graph coloring is one of the most hot issues in graph theory and has important applications in many fields. For a connected graph $G$, we use $\chi(G)$ and $\varphi (G)$ to denote the chromatic number and $b$-chromatic number of $G$, respectively. Let $R,S$ be two connected graphs. Then $G$ is said to be $\{R, S\}$-free if $G$ does not contain $R$ and $S$ as induced subgraphs. In this paper, we prove that for any connected graphs $R$ and $S$ of order at least 4, every connected (2-edge-connected or 2-connected) $\{R, S\}$-free graph $G$ implies $\chi(G)=\varphi (G)$ if and only if $\{R, S\}\preceq\{P_5, Z_1\}$, where $P_5$ is a path of order 5 and $Z_1$ is the graph obtained by identifying one vertex of $P_2$ and one vertex of a triangle. Besides, we give the lower bound of $b$-chromatic numbers of two special classes of interlacing graphs $IG_{n, 2}$ and $IG_{n, 3}$. Related Articles | Metrics