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2021, Vol. 41 No. 1   Published date: 30 March 2021
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• Research on a Class of COVID-19 SIRC Stochastic Model with Nonlinear Perturbation

  2021, 41(1): 1. doi:

  Abstract ( 1217 )   PDF (326KB) ( 353 )   　　

  Considering that environmental noise has a significant impact on COVID-19, In this paper, a stochastic SIRC model of nonlinear perturbation with cross immunity term is proposed and its stochastic properties are studied. First, the stochastic stochastically ultimately boundedness and stochastic persistence of the system solution are proved, and then sufficient conditions for the unique ergodic stationary distribution of the system and the extinction of the disease are obtained by establishing an appropriate Lyapunov function. Finally, the above conclusions were verified by numerical simulation, and the time of disease extinction under different intensities of noise was analyzed. The results showed that the greater the intensity of noise interference, the more conducive to disease prevention and control.

• Study on Individual Flocking Dynamics under the Influence of Multiplicative Noise

  2021, 41(1): 12. doi:

  Abstract ( 1138 )   PDF (713KB) ( 350 )   　　

  The cluster effect is an evolution phenomenon that often appears in natural and social sciences. The in-depth study of this kind of phenomenon is expected to fundamentally solve the reliability problem of the relevant system, and thus has considerable application value. The purpose of this paper is to study the individual clustering problem driven by the environmental noise. By using ordinary differential equation and stochastic differential equation to model the phenomenon, analyze and compare the asymptotic behavior of the solution, we get an important conclusion: under the same assumptions, ordinary differential equations do not produce clustering effect, while stochastic differential equations produce clustering effect, that is, the environmental noise can promote the individual clustering phenomenon. Finally, by giving specific values to the model's parameters and aplotting a comparison diagram, it is intuitively shown that the environmental noise leads to individual cluster effect, which is consistent with our theoretical results.

• Further Discussion for Generalized Normal Sectors in Class II

  2021, 41(1): 22. doi:

  Abstract ( 1183 )   PDF (300KB) ( 403 )   　　

• Distance Integral Graphs Generated by Strong Sum and Strong Product

  2021, 41(1): 33. doi:

  Abstract ( 1421 )   PDF (170KB) ( 329 )   　　

  For two connected graphs $G$ and $H$, the strong sum $G\oplus H$ is the graph with vertex set $V(G)\times V(H)$ and edge set $\{(u,v)(u',v')\mid uu'\in E(G),v=v'\}\cup\{(u,v)(u',v')\mid uu'\in E(G),vv'\in E(H)\}$, and the strong product $G\otimes H$ is the graph with vertex set $V(G)\times V(H)$ and edge set $\{(u,v)(u',v')\mid uu'\in E(G),v=v'\}\cup\{(u,v)(u',v')\mid uu'\in E(G),vv'\in E(H)\}\cup\{(u,v)(u',v')\mid u=u',vv'\in E(H)\}$. In this paper we completely obtain the distances in the $G\oplus H$ and $G\otimes H$ when $H$ has diameter less than $3$. Furthermore, we get the distance spectra of $G\oplus H$ and $G\otimes H$ when $G$ and $H$ satisfy some conditions. As applications, some distance integral graphs generated by strong sum and strong product are obtained. Especially, we get a new infinite class of distance integral graphs generated by strong product.

• Well-posedness and Dispersive Limit Behavior for the Solutions to a Generalized Hyperelastic-rod Wave Equation

  2021, 41(1): 44. doi:

  Abstract ( 1266 )   PDF (190KB) ( 589 )   　　

• An Improved Image Fusion Method Based on Wavelet Transform

  2021, 41(1): 58. doi:

  Abstract ( 1406 )   PDF (1660KB) ( 435 )   　　

  Image fusion aims to construct images that are more appropriate and understandable for human and machine perception. In remote sensing applications, the fusion of the high-resolution panchromatic (PAN) image and the low-resolution multi-spectral (MS) image has always been a problem and has drawn much attention. In this paper, we proposed a PAN and MS image fusion algorithm based on wavelet transform. After performing a wavelet transform on both images, the PAN image's low-frequency component is fused into the MS image's low-frequency component using the edge intensity factor (EIF). Then, the high-frequency components of images are fused to obtain high-frequency features based on the maximum local standard deviation criterion (MLSTD). Finally, the high-resolution and multi-spectral fused image can be obtained by wavelet inverse transform from the fused low-frequency and high-frequency components. Examples illustrated that the fused images are well equipped with desired features, and the proposed algorithm performs better than several classics methods.

• Existence of Positive Solutions for a Critical Kirchhoff Type Equation with a Sign Changing Potential

  2021, 41(1): 71. doi:

  Abstract ( 1133 )   PDF (234KB) ( 396 )   　　

• A Counterexample On H₁⊊L_u¹ in Martingale Theory

  2021, 41(1): 91-101. doi:

  Abstract ( 1179 )   PDF (188KB) ( 407 )   　　

• Well-posedness of Time-dependent Nonclassical Diffusion Equation with Memory

  2021, 41(1): 102-111. doi:

  Abstract ( 1370 )   PDF (176KB) ( 458 )   　　

  In this paper, we mainly discuss an important class of nonclassical diffusion equation which the additional damping terms

  vary over time. The existence of global weak solution is obtained by using the method of Faedo-Galerkin and analytical techniques. Meanwhile, we also prove the uniqueness of the solution and the continuous dependence on initial value, where the nonlinearity f satisfies arbitrary polynomial growth.

• The Comparison of Three Different Solution Decomposition Schemes for Poisson-Boltzmann Models

  2021, 41(1): 112-125. doi:

  Abstract ( 1317 )   PDF (408KB) ( 308 )   　　

  To deal with the singularity in Poisson-Boltzmann models, which is caused by fixed charge distribution in biomolecules, several decomposition schemes have been proposed in literatures. In this paper, three commonly-used decomposition schemes for Poisson-Boltzmann models are reviewed and compared. That is, a two-term decomposition scheme, a three-term decomposition in biomolecular domain only, and a three-term decomposition in the whole domain. Numerical tests on a Born ball model with analytical solution show the performance of each scheme.