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ZI-CAI Li

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The University of Manchester

Mahatma Phule Agricultural University

Ajar Nath Yadav

INTI Interntional University

Virginia Arieta

Universidad Veracruzana

Haramaya university

Prof. Upenyu Mazarura

University of Zimbabwe

University of Mumbai

Yaghoub Fathipour

Tarbiat Modares University

UFSM - Universidade Federal de Santa Maria

Escalona Argelia

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Papers by ZI-CAI Li

Numerical methods for elliptic problems with singularities : boundary methods and nonconforming combinations

WORLD SCIENTIFIC eBooks, 1990

This book presents two kinds of numerical methods for solving elliptic boundary value problems wi... more This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.

Heuristic Method for Judging the Computational Stability of the Difference Schemes of the Biharmonic Equation

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Jan 27, 2010

In this paper, we research the standard 13-point difference schemes for solving the biharmonic eq... more

Blending curves for landing problems by numerical differential equations, III. Separation techniques

Mathematical and Computer Modelling, Dec 1, 2004

New splitting algorithms for geometric transformations of digital images and their error analysis

International Journal of Imaging Systems and Technology, Nov 15, 2011

For digital images and patterns under the nonlinear geometric transformation, T: (ξ, η) → (x, y),... more For digital images and patterns under the nonlinear geometric transformation, T: (ξ, η) → (x, y), this study develops the splitting algorithms (i.e., the pixel‐division algorithms) that divide a 2D pixel into N × N subpixels, where N is a positive integer chosen as N = 2 k(k ≥ 0) in practical computations. When the true intensity values of pixels are known, this method makes it easy to compute the true intensity errors. As true intensity values are often unknown, the proposed approaches can compute the sequential intensity errors based on the differences between the two approximate intensity values at N and N/2. This article proposes the new splitting–shooting method, new splitting integrating method, and their combination. These methods approximate results show that the true errors of pixel intensity are O(H), where H is the pixel size. Note that the algorithms in this article do not produce any sequential errors as N ≥ N0, where N0 (≥2) is an integer independent of N and H. This is a distinctive feature compared to our previous papers on this subject. The other distinct feature of this article is that the true error bound O(H) is well suited to images with all kinds of discontinuous intensity, including scattered pixels. © 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 323–335, 2011

Optimal convergence rates for the combined methods of different finite element methods

Numerical Methods for Partial Differential Equations, May 1, 1992

Coupling techniques are essential to combining different numerical methods together for the purpo... more Coupling techniques are essential to combining different numerical methods together for the purpose of solving an elliptic boundary value problem. By means of nonconforming constraints, the combinations of various Lagrange finite element methods often cause reduced rates of convergence. In this article, we present a method using penalty plus hybrid technique to match different finite element methods such that the optimal convergence rates in the 11. Ib and zero norms of errors of the solution can always be achieved. Also, such a coupling technique will lead to an optimal asymptotic condition number for the associated coefficient matrix. Moreover, this study can easily be extended for combining the finite difference method with the finite element method to also yield the optimal rate of convergence.

Superconvergence of Solution Derivatives of the Shortley–Weller Difference Approximation to Elliptic Equations with Singularities Involving the Mixed Type of Boundary Conditions

Numerical Functional Analysis and Optimization, Feb 18, 2008

This paper presents a superconvergence analysis for the Shortley-Weller finite difference approxi... more This paper presents a superconvergence analysis for the Shortley-Weller finite difference approximation of second-order self-adjoint elliptic equations with unbounded derivatives on a polygonal domain with the mixed type of boundary conditions. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h 1 5 )-order superconvergence of the solution derivatives in a discrete H 1 norm is obtained. Finally, numerical experiments are provided to support the theoretical convergence rate obtained.

Combinations of the Ritz-Galerkin and Finite Difference Methods

International Journal for Numerical Methods in Engineering, Jun 15, 1996

New discrete techniques for 3D image transformations

Computers & mathematics with applications, Aug 1, 1998

AbstractmFor facilitating images under nonlinear transformations, the splitting-shooting method, ... more AbstractmFor facilitating images under nonlinear transformations, the splitting-shooting method, the splitting-integrating method, and their combinations are presented in [1], which do not require nonlinear solutions, but have the low convergence rate O(1/N) of sequential pixel (or vo~el) greyne~, where N is the division number to split a 3D image wxel into N s subvoxeis. In this paper, new partition techniques of 3D subregions are proposed to evaluate carefully overlaps between a cube and the distorted subvoxel region and then applied to the splitting-shooting method, the splittingintegrating method, and their combinations. Error analysis is made to prove that the convergence rate O(1/N 2) can be achieved, and numerical experiments are carried out to confirm the theoretical analysis mode. A remarkable advantage of the new discrete techniques is that no solutions of nonlinear equations are required either. The discrete techniques in this paper are well suited not only to solid objects but also to surfaces and curves in three dimensions, thus to benefit the study in many topics in computer science, such as computer vision, image processing, and pattern recognition.

Boundary approximation methods for solving elliptic problems on unbounded domains

Journal of Computational Physics, Aug 1, 1990

... Permissions &amp; Reprints. Boundary approximation methods for solving elliptic problems ... more

An approach for combining the Ritz—Galerkin and finite element methods

Journal of Approximation Theory, Oct 1, 1983

It is well known that elliptic boundary value problems can be solved by several numerical procedu... more It is well known that elliptic boundary value problems can be solved by several numerical procedures, such as the Ritz-Galerkin method, the finite element method, the finite difference method, and the conservative difference scheme. However, it appears that there has been little or no work done on combining these methods. Of course, each of these methods has its advantages and shortcomings. The use of combined methods is particularly important in problems with complicated boundaries or boundary conditions, or in problems with solutions that are not smooth enough or have singularities, or in problems with unbounded solution domains. In such cases, a single method is often ineffective. In this paper we study a combined method which has been widely used. In 1973, Strang and Fix [7, p. 135] mentioned the idea of combining the Ritz-Galerkin and finite element methods. In 1977, Zienkiewciz et al. [10] gave a systematic presentation of a combined method based on the boundary integral method and the finite element method, which cannot, however, be used for general nonhomogeneous equations. In this paper, we introduce another combined method, which is nonconforming because the admissible functions are continuous only at the element nodes on the common boundary of both methods. However, it is usually the case that nonconforming effects are of little importance to the numerical solution obtained. This method has the advantages that it is valid for the general nonhomogeneous elliptic boundary value problem, and is reasonably simple to describe. 132

Shape Transformation Models and Their Applications in Pattern Recognition

International Journal of Pattern Recognition and Artificial Intelligence, Mar 1, 1990

This paper presents linear and bilinear shape transformations including basic transformations, an... more This paper presents linear and bilinear shape transformations including basic transformations, analyzes their geometric properties, and provides computer algorithms. The shape transformations can be used to simplify the recognition of Roman letters, Chinese characters and other pictorial patterns by normalizing their shapes to the standard forms. Important theoretical analyses have been performed to illustrate that the linear and bilinear transformations are applicable to computer recognition of digitized patterns. A number of pictorial examples have been computed to confirm the analyses and conclusions made.

New expansions of numerical eigenvalues for -?u = ??u by nonconforming elements

Math Comput, 2008

Blending curves for landing problems by numerical differential equations, I. Mathematical modelling

Mathematical and Computer Modelling, 2000

landing curve of airplane is a blending curve that smoothly joins the two given boundary points, ... more landing curve of airplane is a blending curve that smoothly joins the two given boundary points, which is described by the parametric functions x(s), y(s), and z(s) governed by a system of ordinary differential equations (ODEs) with certain boundary conditions. In Part I, Mathematical Modelling [1], existence and uniqueness of the ODE system are explored to produce the optimal landing curves in minimum energy. In this paper, numerical techniques are provided by the finite element method (FEM) using piecewise cubic Hermite polynomials, to give the optimal solutions. An important issue is how to deal with infinite solutions occurring in the landing problems reported in [1]. Moreover, error analysis is made, and numerical examples are carried to verify the theoretical results made. This paper displays again the effectiveness and flexibility of the ODE approach to complicated blending curves. Besides, the numerical techniques in this paper can be applied directly to other landing and trajectory problems given in [1], as well as other kinds of blending curves and surfaces of airplane, ships, grand building, and astronautic shuttle-station.

Combinations of method of fundamental solutions for Laplace's equation with singularities

Engineering Analysis With Boundary Elements, Oct 1, 2008

... 2. Method of FS. Consider Laplace's equation with the Dirichlet boundary condition, (2.1... more

$Research paper thumbnail of The prevalence and risk factors of acute kidney injury in patients undergoing hip fracture surgery: a meta-analysis$

The prevalence and risk factors of acute kidney injury in patients undergoing hip fracture surgery: a meta-analysis

Bioengineered, 2021

ABSTRACT Acute kidney injury (AKI) was a frequent complication following hip fracture surgery, bu... more ABSTRACT Acute kidney injury (AKI) was a frequent complication following hip fracture surgery, but recent studies reported inconsistent findings. Our study was aimed at clarifying the prevalence and risk factors of AKI after hip fracture surgery. Pubmed, Embase, and Web of Science were systematically searched from the inception to March 2020 to identify observational studies investigating the prevalence and risk factors of AKI in patients undergoing hip fracture surgery. Pooled prevalence and odds ratios (ORs) with 95% confidence intervals (CIs) were estimated using a random-effects model. Publication bias was evaluated with a funnel plot and statistical test. All the statistical analyses were performed using Stata version 12.0. A total of 11 studies with 16,421 patients was included in the current meta-analysis. The pooled prevalence of AKI in patients undergoing hip fracture surgery was 17% (95%CI, 14%-21%) with substantial heterogeneity (I2 = 95%). Postoperative serum albumin (OR 1.80; 95%CI, 1.38–2.36) was a significant predictor for AKI. Age (OR 1.01; 95%CI, 0.95–1.07) and ACE inhibitors (OR 1.38; 95%CI, 0.92–2.07) were associated with increased the risk of AKI, but the results were not statistically significant. No significant publication bias was identified through statistical tests (Egger’s test, p = 0.258 and Begg’s test, p = 0.087). In conclusion, our findings indicated that the pooled AKI following hip fracture surgery was approximately 17%. Postoperative serum albumin was a potential significant risk factor for AKI. GRAPHICAL ABSTRACT

Global Superconvergence of Simplified Hybrid Combinations for Elliptic Equations with Singularities, I. Basic Theorem

Computing, Jul 1, 2000

To solve the elliptic boundary value problems with singularities, the simpli®ed hybrid combinatio... more To solve the elliptic boundary value problems with singularities, the simpli®ed hybrid combinations of the Ritz-Galerkin and ®nite element methods (RGM-FEM) are explored to lead to the global superconvergence rates on the entire solution domain, based on an a posteriori interpolation techniques of Lin and Yan [12] that only cost a little more computation. Let the solution domain S S 1 S 2 C 0 and S 1 S 2 Y. Suppose that S 1 can be partitioned into quasiuniform rectangles: S 1 ij ( ij , a singular point occurs at dS 2 , and the singular functions are chosen in S 2 . Then for bilinear elements, it is proven that the simpli®ed hybrid combinations of RGM-FEM can provide the global superconvergence rate Oh 2 for solution gradients over the entire subdomains S 1 and S 2 , where h is the maximal boundary length of ( ij . The global superconvergence Oh 2 is better, compared to Oh 2Àd , 0 `d ( 1 given in . Note that numerical stability of the simpli®ed hybrid combinations of RGM-FEM is also optimal . This paper presents the important results for the general case of Poisson-problems on a polygonal domain S estimates for the Sobolev norm k Á k 1 , given in a much more general sense than known before, cf. [1±4, 14±18].

A note on Kellogg's eigenfunctions of a periodic Sturm-Liouville system

Applied Mathematics Letters, 1988

In this note, we shall supplement Kellogg's theory of interface problems, and provide complete ei... more

The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions

Applied Numerical Mathematics, Aug 1, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods

Advances in Computational Mathematics, Sep 23, 2011

The accuracy of numerical solutions near singular points is crucial for numerical methods. In thi... more The accuracy of numerical solutions near singular points is crucial for numerical methods. In this paper we develop an efficient mechanical quadrature method (MQM) with high accuracy. The following advantages of MQM show that it is very promising and beneficial for practical applications: (1) the $ O(h_{\rm {max}}^{3})$ convergence rate; (2) the $O(h_{\rm {max}}^{5})$ convergence rate after splitting extrapolation; (3) Cond = $O(h_{\rm {min}}^{-1})$; (4) the explicit discrete matrix entries. In this paper, the above theoretical results are briefly addressed and then verified by numerical experiments. The solutions of MQM are more accurate than those of other methods. Note that for the discontinuous model in Li et al. (Eng Anal Bound Elem 29:59–75, 2005), the highly accurate solutions of MQM may even compete with those of the collocation Trefftz method.

Hierarchical models for analysis and recognition of handwritten characters

Annals of Mathematics and Artificial Intelligence, Mar 1, 1994

Different hierarchical models in pattern analysis and recognition are proposed, based on occurren... more Different hierarchical models in pattern analysis and recognition are proposed, based on occurrence probability of patterns. As an important application of recognizing handprinted characters, three typical kinds of hierarchical models such as M89-89, M89-36 and M36-36 have been presented, accompanied by the computer algorithms for computing recognition rates of pattern parts. Moreover, a comparative study of their recognition rates has been conducted theoretically; and numerical experiments have been carried out to verify the analytical conclusions made. Various hierarchical models deliberated in this paper can provide users more or better choices of pattern models in practical application, and lead to a uniform computational scheme (or code). The recognition rates of parts can be improved remarkably by a suitable hierarchical model. For the model M89-36 in which case some of the Canadian standard handprinted characters have multiple occurrence probabilities, the total mean recognition rates of the given sample may reach 120% of that by the model proposed by Li et al., and 156% of that obtained from the subjective experiments reported by Suen.

Numerical methods for elliptic problems with singularities : boundary methods and nonconforming combinations

WORLD SCIENTIFIC eBooks, 1990

This book presents two kinds of numerical methods for solving elliptic boundary value problems wi... more This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.

Heuristic Method for Judging the Computational Stability of the Difference Schemes of the Biharmonic Equation

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Jan 27, 2010

In this paper, we research the standard 13-point difference schemes for solving the biharmonic eq... more

Blending curves for landing problems by numerical differential equations, III. Separation techniques

Mathematical and Computer Modelling, Dec 1, 2004

New splitting algorithms for geometric transformations of digital images and their error analysis

International Journal of Imaging Systems and Technology, Nov 15, 2011

For digital images and patterns under the nonlinear geometric transformation, T: (ξ, η) → (x, y),... more For digital images and patterns under the nonlinear geometric transformation, T: (ξ, η) → (x, y), this study develops the splitting algorithms (i.e., the pixel‐division algorithms) that divide a 2D pixel into N × N subpixels, where N is a positive integer chosen as N = 2 k(k ≥ 0) in practical computations. When the true intensity values of pixels are known, this method makes it easy to compute the true intensity errors. As true intensity values are often unknown, the proposed approaches can compute the sequential intensity errors based on the differences between the two approximate intensity values at N and N/2. This article proposes the new splitting–shooting method, new splitting integrating method, and their combination. These methods approximate results show that the true errors of pixel intensity are O(H), where H is the pixel size. Note that the algorithms in this article do not produce any sequential errors as N ≥ N0, where N0 (≥2) is an integer independent of N and H. This is a distinctive feature compared to our previous papers on this subject. The other distinct feature of this article is that the true error bound O(H) is well suited to images with all kinds of discontinuous intensity, including scattered pixels. © 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 323–335, 2011

Optimal convergence rates for the combined methods of different finite element methods

Numerical Methods for Partial Differential Equations, May 1, 1992

Coupling techniques are essential to combining different numerical methods together for the purpo... more Coupling techniques are essential to combining different numerical methods together for the purpose of solving an elliptic boundary value problem. By means of nonconforming constraints, the combinations of various Lagrange finite element methods often cause reduced rates of convergence. In this article, we present a method using penalty plus hybrid technique to match different finite element methods such that the optimal convergence rates in the 11. Ib and zero norms of errors of the solution can always be achieved. Also, such a coupling technique will lead to an optimal asymptotic condition number for the associated coefficient matrix. Moreover, this study can easily be extended for combining the finite difference method with the finite element method to also yield the optimal rate of convergence.

Superconvergence of Solution Derivatives of the Shortley–Weller Difference Approximation to Elliptic Equations with Singularities Involving the Mixed Type of Boundary Conditions

Numerical Functional Analysis and Optimization, Feb 18, 2008

This paper presents a superconvergence analysis for the Shortley-Weller finite difference approxi... more This paper presents a superconvergence analysis for the Shortley-Weller finite difference approximation of second-order self-adjoint elliptic equations with unbounded derivatives on a polygonal domain with the mixed type of boundary conditions. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h 1 5 )-order superconvergence of the solution derivatives in a discrete H 1 norm is obtained. Finally, numerical experiments are provided to support the theoretical convergence rate obtained.

Combinations of the Ritz-Galerkin and Finite Difference Methods

International Journal for Numerical Methods in Engineering, Jun 15, 1996

New discrete techniques for 3D image transformations

Computers & mathematics with applications, Aug 1, 1998

AbstractmFor facilitating images under nonlinear transformations, the splitting-shooting method, ... more AbstractmFor facilitating images under nonlinear transformations, the splitting-shooting method, the splitting-integrating method, and their combinations are presented in [1], which do not require nonlinear solutions, but have the low convergence rate O(1/N) of sequential pixel (or vo~el) greyne~, where N is the division number to split a 3D image wxel into N s subvoxeis. In this paper, new partition techniques of 3D subregions are proposed to evaluate carefully overlaps between a cube and the distorted subvoxel region and then applied to the splitting-shooting method, the splittingintegrating method, and their combinations. Error analysis is made to prove that the convergence rate O(1/N 2) can be achieved, and numerical experiments are carried out to confirm the theoretical analysis mode. A remarkable advantage of the new discrete techniques is that no solutions of nonlinear equations are required either. The discrete techniques in this paper are well suited not only to solid objects but also to surfaces and curves in three dimensions, thus to benefit the study in many topics in computer science, such as computer vision, image processing, and pattern recognition.

Boundary approximation methods for solving elliptic problems on unbounded domains

Journal of Computational Physics, Aug 1, 1990

... Permissions &amp; Reprints. Boundary approximation methods for solving elliptic problems ... more

An approach for combining the Ritz—Galerkin and finite element methods

Journal of Approximation Theory, Oct 1, 1983

It is well known that elliptic boundary value problems can be solved by several numerical procedu... more It is well known that elliptic boundary value problems can be solved by several numerical procedures, such as the Ritz-Galerkin method, the finite element method, the finite difference method, and the conservative difference scheme. However, it appears that there has been little or no work done on combining these methods. Of course, each of these methods has its advantages and shortcomings. The use of combined methods is particularly important in problems with complicated boundaries or boundary conditions, or in problems with solutions that are not smooth enough or have singularities, or in problems with unbounded solution domains. In such cases, a single method is often ineffective. In this paper we study a combined method which has been widely used. In 1973, Strang and Fix [7, p. 135] mentioned the idea of combining the Ritz-Galerkin and finite element methods. In 1977, Zienkiewciz et al. [10] gave a systematic presentation of a combined method based on the boundary integral method and the finite element method, which cannot, however, be used for general nonhomogeneous equations. In this paper, we introduce another combined method, which is nonconforming because the admissible functions are continuous only at the element nodes on the common boundary of both methods. However, it is usually the case that nonconforming effects are of little importance to the numerical solution obtained. This method has the advantages that it is valid for the general nonhomogeneous elliptic boundary value problem, and is reasonably simple to describe. 132

Shape Transformation Models and Their Applications in Pattern Recognition

International Journal of Pattern Recognition and Artificial Intelligence, Mar 1, 1990

This paper presents linear and bilinear shape transformations including basic transformations, an... more This paper presents linear and bilinear shape transformations including basic transformations, analyzes their geometric properties, and provides computer algorithms. The shape transformations can be used to simplify the recognition of Roman letters, Chinese characters and other pictorial patterns by normalizing their shapes to the standard forms. Important theoretical analyses have been performed to illustrate that the linear and bilinear transformations are applicable to computer recognition of digitized patterns. A number of pictorial examples have been computed to confirm the analyses and conclusions made.

New expansions of numerical eigenvalues for -?u = ??u by nonconforming elements

Math Comput, 2008

Blending curves for landing problems by numerical differential equations, I. Mathematical modelling

Mathematical and Computer Modelling, 2000

landing curve of airplane is a blending curve that smoothly joins the two given boundary points, ... more landing curve of airplane is a blending curve that smoothly joins the two given boundary points, which is described by the parametric functions x(s), y(s), and z(s) governed by a system of ordinary differential equations (ODEs) with certain boundary conditions. In Part I, Mathematical Modelling [1], existence and uniqueness of the ODE system are explored to produce the optimal landing curves in minimum energy. In this paper, numerical techniques are provided by the finite element method (FEM) using piecewise cubic Hermite polynomials, to give the optimal solutions. An important issue is how to deal with infinite solutions occurring in the landing problems reported in [1]. Moreover, error analysis is made, and numerical examples are carried to verify the theoretical results made. This paper displays again the effectiveness and flexibility of the ODE approach to complicated blending curves. Besides, the numerical techniques in this paper can be applied directly to other landing and trajectory problems given in [1], as well as other kinds of blending curves and surfaces of airplane, ships, grand building, and astronautic shuttle-station.

Combinations of method of fundamental solutions for Laplace's equation with singularities

Engineering Analysis With Boundary Elements, Oct 1, 2008

... 2. Method of FS. Consider Laplace's equation with the Dirichlet boundary condition, (2.1... more

$Research paper thumbnail of The prevalence and risk factors of acute kidney injury in patients undergoing hip fracture surgery: a meta-analysis$

The prevalence and risk factors of acute kidney injury in patients undergoing hip fracture surgery: a meta-analysis

Bioengineered, 2021

ABSTRACT Acute kidney injury (AKI) was a frequent complication following hip fracture surgery, bu... more ABSTRACT Acute kidney injury (AKI) was a frequent complication following hip fracture surgery, but recent studies reported inconsistent findings. Our study was aimed at clarifying the prevalence and risk factors of AKI after hip fracture surgery. Pubmed, Embase, and Web of Science were systematically searched from the inception to March 2020 to identify observational studies investigating the prevalence and risk factors of AKI in patients undergoing hip fracture surgery. Pooled prevalence and odds ratios (ORs) with 95% confidence intervals (CIs) were estimated using a random-effects model. Publication bias was evaluated with a funnel plot and statistical test. All the statistical analyses were performed using Stata version 12.0. A total of 11 studies with 16,421 patients was included in the current meta-analysis. The pooled prevalence of AKI in patients undergoing hip fracture surgery was 17% (95%CI, 14%-21%) with substantial heterogeneity (I2 = 95%). Postoperative serum albumin (OR 1.80; 95%CI, 1.38–2.36) was a significant predictor for AKI. Age (OR 1.01; 95%CI, 0.95–1.07) and ACE inhibitors (OR 1.38; 95%CI, 0.92–2.07) were associated with increased the risk of AKI, but the results were not statistically significant. No significant publication bias was identified through statistical tests (Egger’s test, p = 0.258 and Begg’s test, p = 0.087). In conclusion, our findings indicated that the pooled AKI following hip fracture surgery was approximately 17%. Postoperative serum albumin was a potential significant risk factor for AKI. GRAPHICAL ABSTRACT

Global Superconvergence of Simplified Hybrid Combinations for Elliptic Equations with Singularities, I. Basic Theorem

Computing, Jul 1, 2000

To solve the elliptic boundary value problems with singularities, the simpli®ed hybrid combinatio... more To solve the elliptic boundary value problems with singularities, the simpli®ed hybrid combinations of the Ritz-Galerkin and ®nite element methods (RGM-FEM) are explored to lead to the global superconvergence rates on the entire solution domain, based on an a posteriori interpolation techniques of Lin and Yan [12] that only cost a little more computation. Let the solution domain S S 1 S 2 C 0 and S 1 S 2 Y. Suppose that S 1 can be partitioned into quasiuniform rectangles: S 1 ij ( ij , a singular point occurs at dS 2 , and the singular functions are chosen in S 2 . Then for bilinear elements, it is proven that the simpli®ed hybrid combinations of RGM-FEM can provide the global superconvergence rate Oh 2 for solution gradients over the entire subdomains S 1 and S 2 , where h is the maximal boundary length of ( ij . The global superconvergence Oh 2 is better, compared to Oh 2Àd , 0 `d ( 1 given in . Note that numerical stability of the simpli®ed hybrid combinations of RGM-FEM is also optimal . This paper presents the important results for the general case of Poisson-problems on a polygonal domain S estimates for the Sobolev norm k Á k 1 , given in a much more general sense than known before, cf. [1±4, 14±18].

A note on Kellogg's eigenfunctions of a periodic Sturm-Liouville system

Applied Mathematics Letters, 1988

In this note, we shall supplement Kellogg's theory of interface problems, and provide complete ei... more

The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions

Applied Numerical Mathematics, Aug 1, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods

Advances in Computational Mathematics, Sep 23, 2011

The accuracy of numerical solutions near singular points is crucial for numerical methods. In thi... more The accuracy of numerical solutions near singular points is crucial for numerical methods. In this paper we develop an efficient mechanical quadrature method (MQM) with high accuracy. The following advantages of MQM show that it is very promising and beneficial for practical applications: (1) the $ O(h_{\rm {max}}^{3})$ convergence rate; (2) the $O(h_{\rm {max}}^{5})$ convergence rate after splitting extrapolation; (3) Cond = $O(h_{\rm {min}}^{-1})$; (4) the explicit discrete matrix entries. In this paper, the above theoretical results are briefly addressed and then verified by numerical experiments. The solutions of MQM are more accurate than those of other methods. Note that for the discontinuous model in Li et al. (Eng Anal Bound Elem 29:59–75, 2005), the highly accurate solutions of MQM may even compete with those of the collocation Trefftz method.

Hierarchical models for analysis and recognition of handwritten characters

Annals of Mathematics and Artificial Intelligence, Mar 1, 1994

Different hierarchical models in pattern analysis and recognition are proposed, based on occurren... more Different hierarchical models in pattern analysis and recognition are proposed, based on occurrence probability of patterns. As an important application of recognizing handprinted characters, three typical kinds of hierarchical models such as M89-89, M89-36 and M36-36 have been presented, accompanied by the computer algorithms for computing recognition rates of pattern parts. Moreover, a comparative study of their recognition rates has been conducted theoretically; and numerical experiments have been carried out to verify the analytical conclusions made. Various hierarchical models deliberated in this paper can provide users more or better choices of pattern models in practical application, and lead to a uniform computational scheme (or code). The recognition rates of parts can be improved remarkably by a suitable hierarchical model. For the model M89-36 in which case some of the Canadian standard handprinted characters have multiple occurrence probabilities, the total mean recognition rates of the given sample may reach 120% of that by the model proposed by Li et al., and 156% of that obtained from the subjective experiments reported by Suen.