This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider...This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.展开更多
The dynamics of a bacterial population exposed to the minimum inhibitory concentration （MIC） of an antibiotic is an important issue in pharmacological research. Therefore, a novel antibiotic susceptibility test is u...The dynamics of a bacterial population exposed to the minimum inhibitory concentration （MIC） of an antibiotic is an important issue in pharmacological research. Therefore, a novel antibiotic susceptibility test is urgently needed that can both precisely determine the MIC and accurately select antibiotic-resistant strains from clinical bacterial populations. For this purpose, we developed a method based on Fick＇s laws of diffusion using agar plates containing a linear gradient of antibiotic. The gradient plate contained two layers. The bottom layer consisted of 15 mL agar containing the appropriate concentration of enrofloxacin and allowed to harden in the form of a wedge with the plate slanted such that the entire bottom was just covered. The upper layer consisted of 15 mL plain nutrient agar added with the plate held in the horizontal position. After allowing vertical diffusion of the drug from the bottom agar layer for 12 h, the enrofloxacin concentration was diluted in proportion to the ratio of the agar layer thicknesses. The uniform linear concentration gradient was verified by measuring the enrofloxacin concentration on the agar surface. When heavy bacterial suspensions were spread on the agar surface and incubated for more than 12 h, only resistant cells were able to form colonies beyond the boundary of confluent growth of susceptible cells. In this way, the true MIC of enrofloxacin was determined. The MICs obtained using this linear gradient plate were consistent with those obtained using conventional antibiotic susceptibility tests. Discrete colonies were then spread onto a gradient plate with higher antibiotic concentrations; the boundary line increased significantly, and gene mutations conferring resistance were identified. This new method enables the rapid identification of resistant strains in the bacterial population. Use of the linear gradient plate can easily identify the precise MIC and reveal the dynamic differentiation of bacteria near the MIC. This method allows the study of genetic and physiological characteristics of individual strains, and may be useful for early warning of antibiotic resistance that may occur after use of certain antirnicrobial agents, and guide clinical treatment.展开更多
In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is t...In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is transformed into a boundary value problem with coupled boundary conditions.In numerical analysis,the perfectly matched layer(PML)and transparent boundary condition(TBC)are introduced to truncate the unbounded domain.Then,a linear gradient is constructed in a node-based smoothing domain(N-SD)by using a complete order of polynomial.The unknown coefficients of the smoothed linear gradient function can be solved by three linearly independent weight functions.Further,based on the weakened weak formulation,a system of linear equation with the smoothed gradient is established for NS-FEM-L with PML or TBC.Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy.It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness matrix,which effectively overcomes the instability of original NS-FEM.Moreover,the convergence rates of L 2 and H1 semi-norm errors for the two NS-FEM-L models are also higher.展开更多
The basic principle of optimal method called “moving overlapping resolution mapping Method” to select the optimal binary mobile phase composition of multi-step linear gradient liquid chromatography is discussed with...The basic principle of optimal method called “moving overlapping resolution mapping Method” to select the optimal binary mobile phase composition of multi-step linear gradient liquid chromatography is discussed with simultaneously considering effects of position of solute inside the column and mobile phase composition on peak resolution and retention value, then a BASIC program based on this principle is developed in IBM-PC computer. The validities of both principle of optimization and BASIC program are confirmed by separation of samples Containing bile acids and PAHs in RP-HPLC.展开更多
This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two p...This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two parts：a Christmas tree-shaped network for gradient generation and a broad microchannel for detection.A two-dimensional model was built to analyze the flow field and the mass transfer in the microfluidic network.The simulating results show that a series of linear and parabolic gradient profiles were generated via adjusting relative flow rate ratios of the two source solutions（R_L^2≥0.995 and _PR^2≥0.999）,which could match well with the experimental results（R_L^2≥0.987 and _PR^2≥0.996）.The proposed method is promising for the generation of linear and parabolic concentration gradient profiles,with the potential in chemical and biological applications such as combinatorial chemistry synthesis,stem cell differentiation or cytotoxicity assays.展开更多
C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolati...C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.展开更多
In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,...In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,t）＋h（x,t）u^p（x,t）=0（p 〉 1） on Riemannian manifolds.As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang （[1], Bull. London Math. Soc. 38（2006）, 1045-1053） and the author （[2], Nonlinear Anal. 74 （2011）, 5141-5146）.展开更多
Based on the mechanism of chromatographic retention (the relationship between the retention of solute and the mobile phase conditions) and method of resolution map, several methods of optimizing multi-segment linear g...Based on the mechanism of chromatographic retention (the relationship between the retention of solute and the mobile phase conditions) and method of resolution map, several methods of optimizing multi-segment linear gradient elution conditions were proposed according to the different separation requirements of various samples. These methods were verified using literature data. Moreover, the advantages and disadvantages of these methods were compared. It was proved that the third method is a fast optimization method which is capable of separating all the components with relatively high resolution.展开更多
Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method toget...Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method together with regularization is investigated to study the electricity output related to vacuum level and temperature in the turbine. Ninety percent of the data was used to train the regression parameters while the remaining ten percent was used for validation. Final results showed that 99% accuracy could be obtained with this method. This opens a new window for electricity output prediction for power plants.展开更多
Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing ...Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.展开更多
In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje...In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
This paper presents a method for lane boundaries detection which is not affected by the shadows, illumination and un-even road conditions. This method is based upon processing grayscale images using local gradient fea...This paper presents a method for lane boundaries detection which is not affected by the shadows, illumination and un-even road conditions. This method is based upon processing grayscale images using local gradient features, characteris-tic spectrum of lanes, and linear prediction. Firstly, points on the adjacent right and left lane are recognized using the local gradient descriptors. A simple linear prediction model is deployed to predict the direction of lane markers. The contribution of this paper is the use of vertical gradient image without converting into binary image(using suitable thre-shold), and introduction of characteristic lane gradient spectrum within the local window to locate the preciselane marking points along the horizontal scan line over the image. Experimental results show that this method has greater tolerance to shadows and low illumination conditions. A comparison is drawn between this method and recent methods reported in the literature.展开更多
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Bo...For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with pad6 approximation.展开更多
In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale...In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.展开更多
Some properties of the preconditioned gradient conjugate method are given.It may happen that loss of significant digits, when the norm of residual is very small. To avoid this, a variant algorithm which does not use t...Some properties of the preconditioned gradient conjugate method are given.It may happen that loss of significant digits, when the norm of residual is very small. To avoid this, a variant algorithm which does not use the residual is put forward.展开更多
Conjugate gradient method is one of successful methods for solving the unconstrained optimization problems. In this paper, absorbing the advantages of FR and CD methods, a hybrid conjugate gradient method is proposed....Conjugate gradient method is one of successful methods for solving the unconstrained optimization problems. In this paper, absorbing the advantages of FR and CD methods, a hybrid conjugate gradient method is proposed. Under the general Wolfe linear searches, the proposed method can generate the sufficient descent direction at each iterate,and its global convergence property also can be established. Some preliminary numerical results show that the proposed method is effective and stable for the given test problems.展开更多
This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization mo...This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.展开更多
基金Project supported by the National Natural Science foundation of China(No.51079095)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.51021004)
文摘This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.
基金supported by the National Natural Science Foundation of China (Grant No.81171621)Shandong Province Young and Middle-Aged Scientists Research Awards Fund (Grant No.2006BS02008)China Postdoctoral Science Foundation Funded Project (Grant No.20080440451)
文摘The dynamics of a bacterial population exposed to the minimum inhibitory concentration （MIC） of an antibiotic is an important issue in pharmacological research. Therefore, a novel antibiotic susceptibility test is urgently needed that can both precisely determine the MIC and accurately select antibiotic-resistant strains from clinical bacterial populations. For this purpose, we developed a method based on Fick＇s laws of diffusion using agar plates containing a linear gradient of antibiotic. The gradient plate contained two layers. The bottom layer consisted of 15 mL agar containing the appropriate concentration of enrofloxacin and allowed to harden in the form of a wedge with the plate slanted such that the entire bottom was just covered. The upper layer consisted of 15 mL plain nutrient agar added with the plate held in the horizontal position. After allowing vertical diffusion of the drug from the bottom agar layer for 12 h, the enrofloxacin concentration was diluted in proportion to the ratio of the agar layer thicknesses. The uniform linear concentration gradient was verified by measuring the enrofloxacin concentration on the agar surface. When heavy bacterial suspensions were spread on the agar surface and incubated for more than 12 h, only resistant cells were able to form colonies beyond the boundary of confluent growth of susceptible cells. In this way, the true MIC of enrofloxacin was determined. The MICs obtained using this linear gradient plate were consistent with those obtained using conventional antibiotic susceptibility tests. Discrete colonies were then spread onto a gradient plate with higher antibiotic concentrations; the boundary line increased significantly, and gene mutations conferring resistance were identified. This new method enables the rapid identification of resistant strains in the bacterial population. Use of the linear gradient plate can easily identify the precise MIC and reveal the dynamic differentiation of bacteria near the MIC. This method allows the study of genetic and physiological characteristics of individual strains, and may be useful for early warning of antibiotic resistance that may occur after use of certain antirnicrobial agents, and guide clinical treatment.
基金supported by the National Natural Science Foundation of China(Grant Nos.11901423,12002290 and 11771321)the Youth Science and the Technology Research Foundation of Shanxi Province(Grant Nos.201901D211104 and 201901D211107)the Shanxi Youth Top-Notch Talent Support Program(Grant No.DT18100306).
文摘In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is transformed into a boundary value problem with coupled boundary conditions.In numerical analysis,the perfectly matched layer(PML)and transparent boundary condition(TBC)are introduced to truncate the unbounded domain.Then,a linear gradient is constructed in a node-based smoothing domain(N-SD)by using a complete order of polynomial.The unknown coefficients of the smoothed linear gradient function can be solved by three linearly independent weight functions.Further,based on the weakened weak formulation,a system of linear equation with the smoothed gradient is established for NS-FEM-L with PML or TBC.Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy.It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness matrix,which effectively overcomes the instability of original NS-FEM.Moreover,the convergence rates of L 2 and H1 semi-norm errors for the two NS-FEM-L models are also higher.
文摘The basic principle of optimal method called “moving overlapping resolution mapping Method” to select the optimal binary mobile phase composition of multi-step linear gradient liquid chromatography is discussed with simultaneously considering effects of position of solute inside the column and mobile phase composition on peak resolution and retention value, then a BASIC program based on this principle is developed in IBM-PC computer. The validities of both principle of optimization and BASIC program are confirmed by separation of samples Containing bile acids and PAHs in RP-HPLC.
基金Supported by the National Natural Science Foundation of China(81372358,81527801,51303140,and 81602489)the Natural Science Foundation of Hubei Province(2014CFA029)+1 种基金the Colleges of Hubei Province Outstanding Youth Science and Technology Innovation Team(T201305)the Applied Foundational Research Program of Wuhan Municipal Science and Technology Bureau(2015060101010056)
文摘This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two parts：a Christmas tree-shaped network for gradient generation and a broad microchannel for detection.A two-dimensional model was built to analyze the flow field and the mass transfer in the microfluidic network.The simulating results show that a series of linear and parabolic gradient profiles were generated via adjusting relative flow rate ratios of the two source solutions（R_L^2≥0.995 and _PR^2≥0.999）,which could match well with the experimental results（R_L^2≥0.987 and _PR^2≥0.996）.The proposed method is promising for the generation of linear and parabolic concentration gradient profiles,with the potential in chemical and biological applications such as combinatorial chemistry synthesis,stem cell differentiation or cytotoxicity assays.
基金supported by the SDUST Spring Bud (2009AZZ021)Taian Science and Technology Development (20112001)
文摘C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.
基金supported by the National Science Foundation of China(41275063 and 11401575)
文摘In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,t）＋h（x,t）u^p（x,t）=0（p 〉 1） on Riemannian manifolds.As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang （[1], Bull. London Math. Soc. 38（2006）, 1045-1053） and the author （[2], Nonlinear Anal. 74 （2011）, 5141-5146）.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 20175029).
文摘Based on the mechanism of chromatographic retention (the relationship between the retention of solute and the mobile phase conditions) and method of resolution map, several methods of optimizing multi-segment linear gradient elution conditions were proposed according to the different separation requirements of various samples. These methods were verified using literature data. Moreover, the advantages and disadvantages of these methods were compared. It was proved that the third method is a fast optimization method which is capable of separating all the components with relatively high resolution.
文摘Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method together with regularization is investigated to study the electricity output related to vacuum level and temperature in the turbine. Ninety percent of the data was used to train the regression parameters while the remaining ten percent was used for validation. Final results showed that 99% accuracy could be obtained with this method. This opens a new window for electricity output prediction for power plants.
基金Project supported by the National Natural Science Foundation of China(Nos.5130926141030747+3 种基金41102181and 51121005)the National Basic Research Program of China(973 Program)(No.2011CB013503)the Young Teachers’ Initial Funding Scheme of Sun Yat-sen University(No.39000-1188140)
文摘Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.
文摘In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
文摘This paper presents a method for lane boundaries detection which is not affected by the shadows, illumination and un-even road conditions. This method is based upon processing grayscale images using local gradient features, characteris-tic spectrum of lanes, and linear prediction. Firstly, points on the adjacent right and left lane are recognized using the local gradient descriptors. A simple linear prediction model is deployed to predict the direction of lane markers. The contribution of this paper is the use of vertical gradient image without converting into binary image(using suitable thre-shold), and introduction of characteristic lane gradient spectrum within the local window to locate the preciselane marking points along the horizontal scan line over the image. Experimental results show that this method has greater tolerance to shadows and low illumination conditions. A comparison is drawn between this method and recent methods reported in the literature.
基金financially supported by the National Science and Technology Support Program of China(Grant No.2010BAC68B04)
文摘For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with pad6 approximation.
基金The subject is supported by Natural Science Foundation of China and Natural Science Foundation of Shandong Province.
文摘In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.
文摘Some properties of the preconditioned gradient conjugate method are given.It may happen that loss of significant digits, when the norm of residual is very small. To avoid this, a variant algorithm which does not use the residual is put forward.
文摘Conjugate gradient method is one of successful methods for solving the unconstrained optimization problems. In this paper, absorbing the advantages of FR and CD methods, a hybrid conjugate gradient method is proposed. Under the general Wolfe linear searches, the proposed method can generate the sufficient descent direction at each iterate,and its global convergence property also can be established. Some preliminary numerical results show that the proposed method is effective and stable for the given test problems.
文摘This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.
