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| 1 | 42,573 cases of hepatectomy in China: a multicenter retrospective investigation显示文摘Hepatectomy is currently routinely performed in most hospitals in China. China owns the largest population of liver diseases and the biggest number of liver resection cases. A nationwide multicenter retrospective investigation involving 112 hospitals was performed, and focused on liver resection for patients with hepatocellular carcinoma(HCC). 42,573 cases of hepatectomy were enrolled, and 18,275 valid cases of liver resection for HCC patients were selected for statistical analysis. The epidemiology of HCC, distribution of hepatectomy, postoperative complications and prognosis were finally analyzed. In the 18,275 HCC patients,81% had hepatitis B virus infection and 10% had hepatitis C virus infection. 38% of the HCC patients had normal Alphafetoprotein(AFP) level, and other 35% had an AFP level lower than 400 ng mL^(-1). In the study period, 97% of the hepatectomy for HCC were treated with open surgery, and 23.81% had vascular exclusion techniques. The operation time was(191.7±105.6) min,the blood loss was(546.0±562.8) m L, and blood transfusion was(543.0±1,035.2) m L. The median survival for HCC patients was 631 days, with 1-, 3-, and 5-year overall survival of 73.2%, 28.8% and 19.6%, respectively. Liver cirrhosis, multiple nodules,tumor thrombosis and high AFP level were risk factors that affect postoperative survival. | Binhao Zhang Bixiang Zhang Zhiwei Zhang Zhiyong Huang Yifa Chen Minshan Chen Ping Bie Baogang Peng Liqun Wu Zhiming Wang Bo Li Jia Fan Lunxiu Qin Ping Chen Jingfeng Liu Zhe Tang Jun Niu Xinmin Yin Deyu Li Songqing He Bin Jiang Yilei Mao Weiping Zhou Xiaoping Chen | 2018 | Science China(Life Sciences)2018，61，6： | 39 |
| 2 | Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations显示文摘The block-by-block method,proposed by Linz for a kind of Volterra integral equations with nonsingular kernels,and extended by Kumar and Agrawal to a class of initial value problems of fractional differential equations(FDEs)with Caputo derivatives,is an efficient and stable scheme.We analytically prove and numerically verify that this method is convergent with order at least 3 for any fractional order indexα>0. | Jianfei Huang Yifa Tang Luis Vázquez | 2012 | Numerical Mathematics(Theory,Methods and Applications)2012，5，2： | 11 |
| 3 | A second order finite difference-spectral method for space fractional diffusion equations显示文摘A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis. | HUANG JianFei NIE NingMing TANG YiFa | 2014 | Science China Mathematics2014，57，6： | 3 |
| 4 | Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems显示文摘Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in the formal energies. With the help of B-series and Bernoulli functions, we prove that in the formal energy of the mid-point rule, the coefficient sequence of the merging products of an arbitrarily given rooted tree and the bushy trees of height 1(whose subtrees are vertices), approaches 0 as the number of branches goes to ∞; in the opposite direction, the coefficient sequence of the bushy trees of height m(m ≥ 2), whose subtrees are all tall trees, approaches ∞ at large speed as the number of branches goes to +∞. The conclusion extends successfully to the modified differential equations of other Runge-Kutta methods. This disproves a conjecture given by Tang et al.(2002), and implies:(1) in the inequality of estimate given by Benettin and Giorgilli(1994) for the terms of the modified formal vector fields, the high order of the upper bound is reached in numerous cases;(2) the formal energies/formal vector fields are nonconvergent in general case. | ZHANG RuiLi TANG YiFa ZHU BeiBei TU XiongBiao ZHAO Yue | 2016 | Science China Mathematics2016，59，2： | 2 |
| 5 | Explicit Symplectic Methods for the Nonlinear Schrodinger Equation显示文摘By performing a particular spatial discretization to the nonlinear Schrodinger equation(NLSE),we obtain a non-integrable Hamiltonian system which can be decomposed into three integrable parts(L-L-N splitting).We integrate each part by calculating its phase flow,and develop explicit symplectic integrators of different orders for the original Hamiltonian by composing the phase flows.A 2nd-order reversible constructed symplectic scheme is employed to simulate solitons motion and invariants behavior of the NLSE.The simulation results are compared with a 3rd-order non-symplectic implicit Runge-Kutta method,and the convergence of the formal energy of this symplectic integrator is also verified.The numerical results indicate that the explicit symplectic scheme obtained via L-L-N splitting is an effective numerical tool for solving the NLSE. | Hua Guan Yandong Jiao Ju Liu Yifa Tang | 2009 | Communications in Computational Physics2009，6，8： | 1 |
| 6 | Order properties of Symplectic Runge-Kutta-Nystrm methods显示文摘 | Xiao Aiguo Tang Yifa | | Computers Math Appli0，，： | 1 |
| 7 | Symplectic and multi-symplectic metods for the nonlinear Schrodinger equation显示文摘 | Chen Jingbo Qin Mengzhao Tang Yifa | 2002 | Computers and Mathematics with Applications2002，43，： | 1 |
| 8 | Colloidal gold probe- based immunochromatographic assay for the rapid detection of lead ions in water samples显示文摘 | TANG Yong ZHAI Yifa XIANG Junjian | 2010 | Environmental Pollution2010，158，6： | 1 |
| 9 | Finite element multigrid method for multi-term time fractional advection diffusion equations显示文摘In this paper,a class of multi-term time fractional advection diffusion equations(MTFADEs)is considered.By finite difference method in temporal direction and finite element method in spatial direction,two fully discrete schemes of MTFADEs with different definitions on multi-term time fractional derivative are obtained.The stability and convergence of these numerical schemes are discussed.Next,a V-cycle multigrid method is proposed to solve the resulting linear systems.The convergence of the multigrid method is investigated.Finally,some numerical examples are given for verification of our theoretical analysis. | Weiping Bu Xiangtao Liu Yifa Tang Jiye Yang | 2015 | International Journal of Modeling, Simulation, and Scientific Computing2015，6，1： | 1 |
| 10 | NON-EXISTENCE OF CONJUGATE-SYMPLECTIC MULTI-STEP METHODS OF ODD ORDER显示文摘我们证明那是形式 m &summation 的任何线性多步方法 G<sub>1</sub><sup>τ</sup> ;k=0 α<sub>k</sub>Z<sub>k</sub>=τ
m &summation;有奇怪的顺序 u 的 k=0 β<sub>k</sub>J<sup>-1</sup>λ
H (Z<sub>k</sub>)(u ≥
3 ) 不能是结合到一个 symplectic 方法(顺序 w 的 G<sub>2</sub><sup>τ</sup>(w ≥
u ) 经由形式 m &summation 的任何概括线性多步方法 G<sub>3</sub><sup>τ</sup> ;k=0 α<sub>k</sub>Z<sub>k</sub> m &summation;k=0 β<sub>k</sub>J<sup>-1</sup>λ
H (m &summation;l=0 γ<sub>kl</sub>Z<sub>l</sub>) 。我们也给一个必要条件让这种概括线性多步方法是 conjugate-symplectic。当 G<sub>3</sub><sup>τ</sup> 是一个更一般的操作符时,我们也证明这些结果调用容易被扩大到盒子。 | Yandong Jiao Guidong Dai Quandong Feng Yifa Tang | 2007 | Journal of Computational Mathematics2007，25，6： | 1 |
| 11 | ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS显示文摘As is known,there exist numerous alternating direction implicit(ADI)schemes for the two-dimensional linear time fractional partial differential equations(PDEs).However,if the ADI schemes for linear problems combined with local linearization techniques are applied to solve nonlinear problems,the stability and convergence of the methods are often not clear.In this paper,two ADI schemes are developed for solving the two-dimensional time fractional nonlinear super-diffusion equations based on their equivalent partial integrodifferential equations.In these two schemes,the standard second-order central difference approximation is used for the spatial discretization,and the classical first-order approximation is applied to discretize the Riemann-Liouville fractional integral in time.The solvability,unconditional stability and L2 norm convergence of the proposed ADI schemes are proved rigorously.The convergence order of the schemes is 0(τ+hx^2+hy^2),where τ is the temporal mesh size,hx and hy are spatial mesh sizes in the x and y directions,respectively.Finally,numerical experiments are carried out to support the theoretical results and demonstrate the performances of two ADI schemes. | Jianfei Huang Yue Zhao Sadia Arshad Kuangying Li Yifa Tang | 2019 | Journal of Computational Mathematics2019，37，3： | 1 |
| 12 | Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems显示文摘With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical work focusing on neural networks in solving interface problems.In this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface problems.Specifically,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions.It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases.Numerical experiments are provided to demonstrate our theoretical analysis. | Sidi Wu Aiqing Zhu Yifa Tang Benzhuo Lu | 2023 | Communications in Computational Physics2023，33，2： | 0 |
| 13 | L1 scheme on graded mesh for the linearized time fractional KdV equation with initial singularity显示文摘Numerical approximation for a linearized time fractional KdV equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with appropriate choice of the grading parameter,whereα(0<α<1)is the order of temporal Caputo fractional derivative.A fully discrete spectral scheme is constructed combing a Petrov-Galerkin spectral method for the spatial discretization,and its stability and convergence are theoretically proved.Some numerical results are provided to verify the theoretical analysis and demonstrated the sharpness of the error analysis. | Hu Chen Xiaohan Hu Jincheng Ren Tao Sun Yifa Tang | 2019 | International Journal of Modeling, Simulation, and Scientific Computing2019，10，1： | 0 |
| 14 | Poisson Integrators Based on Splitting Method for Poisson Systems显示文摘We propose Poisson integrators for the numerical integration of separable Poisson systems.We analyze three situations in which Poisson systems are separated in threeways and Poisson integrators can be constructed by using the splittingmethod.Numerical results show that the Poisson integrators outperform the higher order non-Poisson integrators in terms of long-termenergy conservation and computational cost.The Poisson integrators are also shown to be more efficient than the canonicalized sympletic methods of the same order. | Beibei Zhu Lun Ji Aiqing Zhu Yifa Tang | 2022 | Communications in Computational Physics2022，32，9： | 0 |
| 15 | Symmetric and symplectic methods for gyrocenter dynamics in time-independent magnetic fields显示文摘We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system.The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation.Furthermore,they are much faster than the midpoint rule applied to the canonicalized system to reach given precision. | Beibei Zhu Zhenxuan Hu Yifa Tang Ruili Zhang | 2016 | International Journal of Modeling, Simulation, and Scientific Computing2016，7，2： | 0 |
| 16 | Finite element methods for fractional diffusion equations显示文摘Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast growing.This paper gives a concise overview on finite element methods for these equations,which are divided into time fractional,space fractional and time-space fractional diffusion equations.Besides,we also involve some relevant topics on the regularity theory,the well-posedness,and the fast algorithm. | Yue Zhao Chen Shen Min Qu Weiping Bu Yifa Tang | 2020 | International Journal of Modeling, Simulation, and Scientific Computing2020，11，4： | 0 |
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