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| 1 | Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2 ?ΔΔ C T Method显示文摘 | Kenneth J. Livak Thomas D. Schmittgen | 2001 | Methods2001，，4： | 42 |
| 2 | A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection显示文摘Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods.This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection.This algorithm is used in PHG,Parallel Hierarchical Grid (http://gffzz8065c2988e934515h5wc5oox59ox666vp.ffgz.tsg.suse.edu.cn/phg/),a toolbox under active development for parallel adaptive finite element solutions of partial differential equations.The algorithm proposed is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices.Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given,which is useful in better understanding the behaviour of the bisectioning refinement procedure. | Lin-Bo Zhang | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，1： | 27 |
| 3 | Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2 ?ΔΔ C T Method显示文摘 | Kenneth J. Livak Thomas D. Schmittgen | 2001 | Methods2001，，4： | 20 |
| 4 | 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 |
| 5 | Fast Texture Segmentation Based on Semi-Local Region Descriptor and Active Contour显示文摘In this paper,we present an efficient approach for unsupervised segmentation of natural and textural images based on the extraction of image features and a fast active contour segmentation model.We address the problem of textures where neither the gray-level information nor the boundary information is adequate for object extraction.This is often the case of natural images composed of both homogeneous and textured regions.Because these images cannot be in general directly processed by the gray-level information,we propose a new texture descriptor which intrinsically defines the geometry of textures using semi-local image information and tools from differential geometry.Then,we use the popular Kullback-Leibler distance to design an active contour model which distinguishes the background and textures of interest.The existence of a minimizing solution to the proposed segmentation model is proven.Finally, a texture segmentation algorithm based on the Split-Bregman method is introduced to extract meaningful objects in a fast way.Promising synthetic and real-world results for gray-scale and color images are presented. | Nawal Houhou Jean-Philippe Thiran Xavier Bresson | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，4： | 10 |
| 6 | Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2 ?ΔΔ C T Method显示文摘 | Kenneth J. Livak Thomas D. Schmittgen | 2001 | Methods2001，，4： | 9 |
| 7 | [14] Analysis of total phenols and other oxidation substrates and antioxidants by means of folin-ciocalteu reagent显示文摘 | Vernon L. Singleton Rudolf Orthofer Rosa M. Lamuela-Raventós | 1999 | Methods in Enzymology1999，，： | 8 |
| 8 | Real-Time Quantitative PCR显示文摘 | Thomas D. Schmittgen | 2001 | Methods2001，，4： | 8 |
| 9 | Correction to: Correction Radiation Detection Technology and Methods Editorial Office显示文摘 | Radiation Detection Technology and Methods Editorial Office | 2018 | Radiation Detection Technology and Methods2018，2，1： | 6 |
| 10 | Advances in Studies and Applications of Centroidal Voronoi Tessellations显示文摘Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating. | Qiang Du Max Gunzburger Lili Ju | 2010 | Numerical Mathematics(Theory,Methods and Applications)2010，3，2： | 6 |
| 11 | On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline Space S_(3)^(1,2)(∆_(mn)^((2)))显示文摘In this paper,based on the basis composed of two sets of splines with distinct local supports,cubic spline quasi-interpolating operators are reviewed on nonuniform type-2 triangulation.The variation diminishing operator is defined by discrete linear functionals based on a fixed number of triangular mesh-points,which can reproduce any polynomial of nearly best degrees.And by means of the modulus of continuity,the estimation of the operator approximating a real sufficiently smooth function is reviewed as well.Moreover,the derivatives of the nearly optimal variation diminishing operator can approximate that of the real sufficiently smooth function uniformly over quasi-uniform type-2 triangulation.And then the convergence results are worked out. | Jiang Qian Fan Wang | 2014 | Numerical Mathematics(Theory,Methods and Applications)2014，7，1： | 6 |
| 12 | A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization显示文摘This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method. | Zheng-Jian Bai Michael K. Ng Liqun Qi | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，4： | 6 |
| 13 | A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation显示文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results. | Ningning Yan Zhaojie Zhou | 2008 | Numerical Mathematics(Theory,Methods and Applications)2008，1，3： | 5 |
| 14 | A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations显示文摘In this paper,we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LET model with a parameter functionθ.The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models.In particular, the errors of the compound algorithm in L2 norm between the exact images and corresponding restored images are the smallest among the three models.For images with strong noises,the restored images of the compound algorithm are the best in the corresponding restored images.The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration.It is found that the combination of these methods is efficient and robust in the image restoration. | Qianshun Chang Xuecheng Tai Lily Xing | 2009 | Numerical Mathematics(Theory,Methods and Applications)2009，2，4： | 5 |
| 15 | The Simultaneous Approximation Average Errors for Bernstein Operators on the r-Fold Integrated Wiener Space显示文摘For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space. | Guiqiao Xu | 2012 | Numerical Mathematics(Theory,Methods and Applications)2012，5，3： | 5 |
| 16 | Superconvergence and L^(∞)-Error Estimates of RT1Mixed Methods for Semilinear Elliptic Control Problems with an Integral Constraint显示文摘In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral constraint.The state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear functions.We derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant functions.Moreover,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear functions.Finally,some numerical examples are given to demonstrate the theoretical results. | Yanping Chen Tianliang Hou | 2012 | Numerical Mathematics(Theory,Methods and Applications)2012，5，3： | 5 |
| 17 | Real-Time Quantitative PCR显示文摘 | Thomas D. Schmittgen | 2001 | Methods2001，，4： | 5 |
| 18 | Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems显示文摘In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods.The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k≥0).A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained.Finally,we present some numerical examples which confirm our theoretical results. | Kang Deng Yanping Chen Zuliang Lu | 2011 | Numerical Mathematics(Theory,Methods and Applications)2011，4，2： | 4 |
| 19 | A Second-Order Method for the Electromagnetic Scattering from a Large Cavity显示文摘In this paper,we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane,which is modelled by Helmholtz equations.By introducing nonlocal transparent boundary con- ditions,the problem in the open cavity is reduced to a bounded domain problem.A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases,respectively.A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper- singular integral operator on the aperture and the Helmholtz in the cavity,respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers.A fast algorithm for the second-order approximation is pro- posed for solving the cavity model with layered media.Numerical results show the second-order accuracy and efficiency of the fast algorithm.More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media. | Yingxi Wang Kui Du Weiwei Sun | 2008 | Numerical Mathematics(Theory,Methods and Applications)2008，1，4： | 4 |
| 20 | A Collocation Method for Initial Value Problems of Second-Order ODEs by Using Laguerre Functions显示文摘We propose a collocation method for solving initial value problems of secondorder ODEs by using modified Laguerre functions.This new process provides global numerical solutions.Numerical results demonstrate the efficiency of the proposed algorithm. | Jian-Ping Yan Ben-Yu Guo 无 | 2011 | Numerical Mathematics(Theory,Methods and Applications)2011，4，2： | 4 |
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