Table of Content

15 December 2016, Volume 33 Issue 6    Next Issue

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A Dimensional Splitting Method for 3D-nonlinear Elastic Shell ZHANG Yin, LI Kai-tai 2016, 33 (6):  551-577.  doi: 10.3969/j.issn.1005-3085.2016.06.001 Abstract ( 21 )   PDF (249KB) ( 2 )   Save In this paper, a dimensional splitting method for three dimensional nonlinear elastic shell is established under a semi-geodesic coordinate system ($S$-coordinate). Then the nonlinear elastic operator can be decomposed into the sum of a membrane and bending operators in the $S$-coordinate system. Assume that the solution of the 3D nonlinear elastic shell can be expressed as the Taylor expansion with respect to the transverse variable, the approximation modelling with one-order and two order respectively are established. Meanwhile, we give the 2D-3C partial differential equations satisfied by the terms of zero-order, prove the existence of solution, give the related functions in the terms of first and second orders with respective to the term of zero-order without solving partial differential equations to obtain the terms of first and second orders. Related Articles | Metrics

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The Modified High-resolution Composite Scheme Based on the Leonard Normalized Variable NIU Yun-xia, LI Chun-guang, JING He-fang 2016, 33 (6):  578-586.  doi: 10.3969/j.issn.1005-3085.2016.06.002 Abstract ( 25 )   PDF (223KB) ( 2 )   Save Based on the normalized variable, a modified high-resolution composite scheme is proposed to solve the convection-diffusion equation, which can be used to describe boundary layer problems or locally large gradient problems. Firstly, the generic form for the composite scheme is derived according to the definition of the normalized variable. Then, the second order central difference scheme is used to discretize the temporal derivative term. The discrete algebraic equations are solved with the TDMA algorithm. Thus, the sufficient condition for the convergence of the composite scheme is obtained. The numerical tests are presented to verify the effectiveness of the scheme. The numerical results show that the new format has higher resolution, lower numerical dissipation and smaller total amount of deviation when compared with traditional formats. The new scheme is good at simulating the large gradient field variables. Related Articles | Metrics

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The Application of Variational Methods to a Boundary Value Problem on Time Scale YIN Cheng, SU You-hui 2016, 33 (6):  587-596.  doi: 10.3969/j.issn.1005-3085.2016.06.003 Abstract ( 22 )   PDF (165KB) ( 3 )   Save In this paper, we are concerned with the existence of periodic solution to a nonautonomous second order boundary value problem on time scales $\mathbb{T}$. By simultaneously utiliting the critical-point theorem and variational methods, we first transform the existence of solutions to the boundary value problem into the critical points of the associated functional by using variational methods. Some new results on the existence of at least one periodic solutions are established by means of the generalized mountain pass lemma. Our results are new even for the corresponding differential, difference equations as well as in general time scales. As an illustration, we verify the obtained results through an example. Related Articles | Metrics

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Age Structures of Discrete SCIRS Model with Application to Meningococcal Meningitis in China MA Xia, ZHOU Yi-cang 2016, 33 (6):  597-612.  doi: 10.3969/j.issn.1005-3085.2016.06.004 Abstract ( 24 )   PDF (456KB) ( 1 )   Save The dynamic characteristic of meningococcal meningitis SCIRS model with three age structures is studied. First, the basic reproduction number $\widetilde{R_0}$ is defined by using the regeneration matrix. It is proved that the disease-free equilibrium is globally asymptotically stable when $\widetilde{R_0}<1$. The disease-free equilibrium is unstable, there exists an endemic equilibrium and the system is uniformly persistent when $\widetilde{R_0}>1$. Second, using the data from the report of notifiable infectious diseases in China, the model is applied to describe the spread of meningococcal meningitis in China. For the uncertainty of many parameters in the model, we make sensitivity analysis about the parameters of the basic reproductive number. Finally, we consider the influence of seasonal factors to the incidence of meningococcal meningitis to modify the model, and predict the meningococcal meningitis in population development trend of China. The numerical simulation results show that the impact of seasonal factors on the rate of disease progression of meningococcal meningitis is greater than the effect on infection rate, this also provides advice to control the spread of meningococcal meningitis in our country. Related Articles | Metrics

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Several Nonconvex Models for Image Deblurring under Poisson Noise LIU Gang, HUANG Ting-zhu 2016, 33 (6):  613-630.  doi: 10.3969/j.issn.1005-3085.2016.06.005 Abstract ( 26 )   PDF (1460KB) ( 3 )   Save In image restoration, images are often assumed to be sparse after taking gradient. Nonconvex regularizers could produce more sparse gradients than convex regularizers. In this paper, based on some recent nonconvex regularizers, we propose several nonconvex models for image deblurring under Poisson noise. We develop efficient numerical algorithms for solving the proposed models and carry out the convergence analysis. Numerical results show that the proposed models achieve an enhanced gradient sparsity and yield restoration results competitive with some existing methods. Related Articles | Metrics

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Pricing Defaultable Bonds with Stochastic Recovery under a Hybrid Model PAN Jian, XIAO Qing-xian 2016, 33 (6):  631-650.  doi: 10.3969/j.issn.1005-3085.2016.06.006 Abstract ( 27 )   PDF (178KB) ( 1 )   Save This paper studies the pricing of a defaultable bond with stochastic recovery under the hybrid model. The pricing model with a negative correlation between the reco-very rate and the default intensity is sestablished by using the Ito's formula and arbitrage-free principle. Then a closed-form solution to the pricing model is obt-ained by applying the variable transformation technique and partial differential equation (PDE) approach, which makes it convenient for portfolio management and hedging. Finally, numerical experiments are provided to illustrate the impact of recovery parameters and intensity parameters on the bond's credit spread. The numerical results show that the credit spread under the stochastic recovery is lower than that of the corresponding fixed recovery, that is, the credit spread under the fixed recovery is overestimated. Related Articles | Metrics

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Stability of Steady States for the Holling-Tanner Predator-prey Model with Nonlinear Boundary Conditions GAO Yu, LI Yan-ling 2016, 33 (6):  651-660.  doi: 10.3969/j.issn.1005-3085.2016.06.007 Abstract ( 22 )   PDF (190KB) ( 1 )   Save In this paper, we consider a diffusion predator-prey model with nonlinear boundary conditions, which has more extensive application areas than the corresponding model with linear boundary conditions. We first show that all eigenvalues of a class of eigenvalue problems are positive by using Green's identity. The existence of positive solutions is also established by using the bifurcation theory. Moreover, we discuss the asymptotic stability of bifurcation solutions with the help of the perturbation theory. Finally, we give some examples of numerical simulations by Matlab to support the analytical results. Related Articles | Metrics