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| 1 | 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://lsec.cc.ac.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 |
| 2 | 超空间上的连续对应与对应的闭图显示文摘本文的目的是在超空间上重新定义上半连续,下半连续和连续对应.改进了Klein在[1]中的定义7.1.1,得到了这些对应和它们的闭图的若干特征和性质。 | 程吉树 | 1999 | Journal of Mathematical Research with Applications1999，31，S1： | 11 |
| 3 | 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 |
| 4 | 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 |
| 5 | Majorization Properties for Certain Classes of Analytic Functions Involving a Generalized Diferential Operator显示文摘In this paper,we introduce new subclasses Sm,j,l p,q,λ [A,B;γ] and Hm,j,l p,q,λ(α,β) of certain p-valent analytic functions defined by a generalized diferential operator.Majorization properties for functions belonging to the classes Sm,j,l p,q,λ [A,B;γ] and Hm,j,l p,q,λ(α,β) are investigated.Also,we point out some new or known consequences of our main results. | Huo TANG Guantie DENG Shuhai LI | 2013 | Journal of Mathematical Research with Applications2013，33，5： | 9 |
| 6 | Autocorrelation Value of Whiteman Generalized Cyclotomic Sequence显示文摘Let p,q be distinct primes with gcd(p-1,q-1) = 4.In this paper,we calculate the autocorrelation values of binary sequences of generalized cyclotomic sets of order four in Z pq and get conditions of p and q such that they are four-valued. | Liqin HU Qin YUE | 2012 | Journal of Mathematical Research with Applications2012，32，4： | 6 |
| 7 | 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 |
| 8 | 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 |
| 9 | Bounds of Solutions of a Kind of Hyper-Chaotic Systems and Application显示文摘This paper investigates the boundedness of a kind of hyper-chaotic systems that have wide applications in the secure communications. In particular, an accurate bound estimation is attained for this kind of hyper-chaotic systems. Then, the result is applied to the chaos synchronization. Some numerical simulations are also given to verify the corresponding theoretical results. | Fuchen ZHANG Yuhuan LI Chunlai MU | 2013 | Journal of Mathematical Research with Applications2013，33，3： | 6 |
| 10 | 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 |
| 11 | The Least Eigenvalue of Graphs显示文摘In this paper we investigate the least eigenvalue of a graph whose complement is connected, and present a lower bound for the least eigenvalue of such graph. We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order. | Guidong YU Yizheng FAN Yi WANG | 2012 | Journal of Mathematical Research with Applications2012，32，6： | 6 |
| 12 | On a Generalization of Semicommutative Rings显示文摘In this paper, a generalization of the class of semicommutative rings is investigated.A ring R is called left GWZI if for any a ∈ R, l(a) is a GW-ideal of R. We prove that a ring R is left GWZI if and only if S3(R) is left GWZI if and only if Vn(R) is left GWZI for any n ≥ 2. | Cuizhen DU Long WANG Junchao WEI | 2014 | Journal of Mathematical Research with Applications2014，34，3： | 5 |
| 13 | On the Characteristic Polynomial of a Hexagonal System and Its Application显示文摘Let Ln be the hexagonal chain graph,Fnbe the hexacyclic system graph and Mn be the M¨obius hexacyclic system graph. Derflinger and Sofer gave the spectra of Ln and Fn by using group theoretical method. Later, Gutman gave the spectra of them using a polynomial result due to Godsil and McKay. In this paper, we give a simple and direct method to determine the characteristic polynomial and spectra of Fn and Ln. By the method, we give the characteristic polynomial and spectrum of Mn that is new. Additionally, the exact values of total π-electron energy and the nullities of Ln, Fn and Mn are obtained, and the bounds for the energy of Ln and Mn are also considered. | Zhenzhen LOU Qiongxiang HUANG | 2014 | Journal of Mathematical Research with Applications2014，34，3： | 5 |
| 14 | 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 |
| 15 | 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 |
| 16 | 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 |
| 17 | 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 |
| 18 | Existence of Solutions for Discrete Fractional Boundary Value Problems with p-Laplacian Operator显示文摘By establishing the corresponding variational framework, and using the critical points theorem, we give the existence of multiple solutions for a fractional difference boundary value problem with p-Laplacian operator. Under some suitable assumptions we obtain the existence of a positive parameter such that the problem admits at least three solutions. Some examples are presented to illustrate the main results. | Yansheng HE Chengmin HOU | 2014 | Journal of Mathematical Research with Applications2014，34，2： | 5 |
| 19 | Bernstein-Sikkema算子逼近显示文摘研究Bernstein-Sikkema算子的逼近问题,得到强型正定理和弱型逆定理。 | 熊庆良 曹飞龙 | 1999 | Journal of Mathematical Research with Applications1999，31，S1： | 5 |
| 20 | 分配P-代数中的0-理想显示文摘本文对分配P-代数中的0-理想进行了初步探讨. | 杨云 | 1999 | Journal of Mathematical Research with Applications1999，31，S1： | 4 |
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