Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K ...Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.展开更多
The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation wit...The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.展开更多
In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation m...In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation methods which converge strongly to the fixed points of nonexpansive nonself-mappings. The results presented in this paper extend and improve the results of Song-Chen [1] and Song-Li [2].展开更多
The wall-adapting local eddy-viscosity(WALE)and Vreman subgrid scale models for large eddy simulations are compared within the framework of a generalised lattice Boltzmann method.Fully developed turbulent flows near a...The wall-adapting local eddy-viscosity(WALE)and Vreman subgrid scale models for large eddy simulations are compared within the framework of a generalised lattice Boltzmann method.Fully developed turbulent flows near a flat wall are simulated with the two models for the shear(or friction)Reynolds number of 183.6.Compared to the direct numerical simulation(DNS),damped eddy viscosity in the vicinity of the wall and a correct velocity profile in the transitional region are achieved by both the models without dynamic procedures.The turbulent statistics,including,e.g.,root-mean-square velocity fluctuations,also agree well with the DNS results.The comparison also shows that the WALE model predicts excellent damped eddy viscosity near the wall.展开更多
To evaluate the water storage and project the future evolution of glaciers, the ice-thickness of glaciers is an essential input. However, direct measurements of ice thickness are labo- rious, not feasible everywhere, ...To evaluate the water storage and project the future evolution of glaciers, the ice-thickness of glaciers is an essential input. However, direct measurements of ice thickness are labo- rious, not feasible everywhere, and necessarily restricted to a small number of glaciers. In this article, we develop a simple method to estimate the ice-thickness along flow-line of mountain glaciers. Different from the traditional method based on shallow ice approximation （SIA）, which gives a relationship be- tween ice thickness, surface slope, and yield stress of glaciers, the improved method considers and pre- sents a simple way to calibrate the influence of valley wall on ice discharge. The required inputs are the glacier surface topography and outlines. This shows the potential of the method for estimating the ice-thickness distribution and volume of glaciers without using of direct thickness measurements.展开更多
This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation techn...This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...展开更多
The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the bas...The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.展开更多
In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of th...In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].展开更多
Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the...Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the design variables as independent optimization variables. However, at each iteration of the conventional optimization procedure, multidisciplinary analysis (MDA) is numerously performed that results in extreme expense and low optimization efficiency. The intrinsic weakness of MDF is due to the times that it loop fixed-point iterations in MDA, which drive us to improve MDF by building inexpensive approximations as surrogates for expensive MDA. An simple example is presented to demonstrate the usefulness of the improved MDF. Results show that a significant reduction in the number of multidisciplinary analysis required for optimization is obtained as compared with original MDF and the efficiency of optimization is increased.展开更多
A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions ar...A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.展开更多
Intrinsic viscosities for a given polyelectrolyte in salt free and low-salt solvents reported in literatures are normally not comparable, because of inadequate valuation procedures. This article describes a theoretica...Intrinsic viscosities for a given polyelectrolyte in salt free and low-salt solvents reported in literatures are normally not comparable, because of inadequate valuation procedures. This article describes a theoretically justified reliable method, which is free of any model assumptions： The so called Wolf plot （logarithm of the relative viscosity as a function of polymer concentration） enables the unequivocal determination of intrinsic viscosities for all kinds of macromolecules, irrespective of whether they are chain molecules of different architecture or globular polymers, whether they are charged or uncharged. The validation of the method was examined by evaluation of the viscosities of a polyelectrolyte, some uncharged polymers of different architectures, uncharged polymer blends, and some literature data.展开更多
The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory;however,it still faces the challenges of large deviation from the optimal solution and inability to satisfy...The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory;however,it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints.In this paper,a modified shape approximation low-thrust model is presented,and a novel constrained optimization algorithm is developed to solve this problem.The proposed method aims at settling the bi-objective optimization orbit involving the twin objectives of minimum flight time and low fuel consumption and enhancing the accuracy of optimized orbit.In particular,a transformed high-order polynomial model based on finite Fourier series is proposed,which can be characterized as a multi-constraint optimization problem.Then,a novel optimization algorithm is specifically developed to optimize the large-scale multi-constraint dynamical equations of shape trajectory.The key performance indicators of the index include minimum flight time,low fuel consumption and bi-objective optimization of the two.Simulation results prove that this approach possesses both the high precision achievable by numerical methods and low computational complexity offered by shape approximation techniques.Besides,the Pareto front of the fuel-time bi-objective optimization orbit is firstly introduced to analyze an intact optimal solution set.Furthermore,we have demonstrated that our proposed approach is appropriate to generate the preliminary orbit for pseudo-spectral method.展开更多
In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpin...In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(l + l/2n-3)s≤Hs(S)≤ Pn(S). An algorithm is presented to get Pn(S) for n ≤5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S)≥0.5631.展开更多
The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(M...The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.展开更多
An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator...An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.展开更多
A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved...A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.展开更多
Accurate gas viscosity determination is an important issue in the oil and gas industries.Experimental approaches for gas viscosity measurement are timeconsuming,expensive and hardly possible at high pressures and high...Accurate gas viscosity determination is an important issue in the oil and gas industries.Experimental approaches for gas viscosity measurement are timeconsuming,expensive and hardly possible at high pressures and high temperatures(HPHT).In this study,a number of correlations were developed to estimate gas viscosity by the use of group method of data handling(GMDH)type neural network and gene expression programming(GEP)techniques using a large data set containing more than 3000 experimental data points for methane,nitrogen,and hydrocarbon gas mixtures.It is worth mentioning that unlike many of viscosity correlations,the proposed ones in this study could compute gas viscosity at pressures ranging between 34 and 172 MPa and temperatures between 310 and 1300 K.Also,a comparison was performed between the results of these established models and the results of ten wellknown models reported in the literature.Average absolute relative errors of GMDH models were obtained 4.23%,0.64%,and 0.61%for hydrocarbon gas mixtures,methane,and nitrogen,respectively.In addition,graphical analyses indicate that the GMDH can predict gas viscosity with higher accuracy than GEP at HPHT conditions.Also,using leverage technique,valid,suspected and outlier data points were determined.Finally,trends of gas viscosity models at different conditions were evaluated.展开更多
In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processe...In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.展开更多
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th...A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.展开更多
文摘Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.
基金This work was supported by China State Major Key Project for Basic Researches.
文摘The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.
文摘In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation methods which converge strongly to the fixed points of nonexpansive nonself-mappings. The results presented in this paper extend and improve the results of Song-Chen [1] and Song-Li [2].
基金Supported by the Research Fund for the Doctoral Program of Higher Education of China,the National Natural Science Foundation of China under Grant Nos 10902087,11172241the National Hi-Tech Research and Development Program of China under Grant No 2012AA011803.
文摘The wall-adapting local eddy-viscosity(WALE)and Vreman subgrid scale models for large eddy simulations are compared within the framework of a generalised lattice Boltzmann method.Fully developed turbulent flows near a flat wall are simulated with the two models for the shear(or friction)Reynolds number of 183.6.Compared to the direct numerical simulation(DNS),damped eddy viscosity in the vicinity of the wall and a correct velocity profile in the transitional region are achieved by both the models without dynamic procedures.The turbulent statistics,including,e.g.,root-mean-square velocity fluctuations,also agree well with the DNS results.The comparison also shows that the WALE model predicts excellent damped eddy viscosity near the wall.
基金supported by the National Basic Research Program of China (No. 2007CB411501)the Knowledge Innovation Project of the Chinese Academy of Sciences (No. KZCX2-EW-311)+1 种基金the National Natural Science Foundation of China (Nos. 91025012, J0930003/J0109)the Project for Outstanding Young Scientists of the National Natural Science Foundation of China (No. 40121101)
文摘To evaluate the water storage and project the future evolution of glaciers, the ice-thickness of glaciers is an essential input. However, direct measurements of ice thickness are labo- rious, not feasible everywhere, and necessarily restricted to a small number of glaciers. In this article, we develop a simple method to estimate the ice-thickness along flow-line of mountain glaciers. Different from the traditional method based on shallow ice approximation （SIA）, which gives a relationship be- tween ice thickness, surface slope, and yield stress of glaciers, the improved method considers and pre- sents a simple way to calibrate the influence of valley wall on ice discharge. The required inputs are the glacier surface topography and outlines. This shows the potential of the method for estimating the ice-thickness distribution and volume of glaciers without using of direct thickness measurements.
基金supported by the NSF China#10571075NSF-Guangdong China#04010473+1 种基金The research of the second author was supported by Jinan University Foundation#51204033the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State education Ministry#2005-383
文摘This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...
文摘The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.
基金the Thailand Research Fund for financial support under Grant BRG5280016
文摘In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].
文摘Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the design variables as independent optimization variables. However, at each iteration of the conventional optimization procedure, multidisciplinary analysis (MDA) is numerously performed that results in extreme expense and low optimization efficiency. The intrinsic weakness of MDF is due to the times that it loop fixed-point iterations in MDA, which drive us to improve MDF by building inexpensive approximations as surrogates for expensive MDA. An simple example is presented to demonstrate the usefulness of the improved MDF. Results show that a significant reduction in the number of multidisciplinary analysis required for optimization is obtained as compared with original MDF and the efficiency of optimization is increased.
基金supported by the Natural Science Foundation of Yibin University (No.2009Z3)
文摘A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.
基金financially supported by the National Natural Science Foundation of China(No.51273166)the National Basic Research Program of China(No.2010CB732203)the Scientific and Technological Innovation Platform of Fujian Province of China(No.2009J1009)
文摘Intrinsic viscosities for a given polyelectrolyte in salt free and low-salt solvents reported in literatures are normally not comparable, because of inadequate valuation procedures. This article describes a theoretically justified reliable method, which is free of any model assumptions： The so called Wolf plot （logarithm of the relative viscosity as a function of polymer concentration） enables the unequivocal determination of intrinsic viscosities for all kinds of macromolecules, irrespective of whether they are chain molecules of different architecture or globular polymers, whether they are charged or uncharged. The validation of the method was examined by evaluation of the viscosities of a polyelectrolyte, some uncharged polymers of different architectures, uncharged polymer blends, and some literature data.
基金supported by the National Natural Science Foundation of China(Nos.61627810,61790562,61403096).
文摘The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory;however,it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints.In this paper,a modified shape approximation low-thrust model is presented,and a novel constrained optimization algorithm is developed to solve this problem.The proposed method aims at settling the bi-objective optimization orbit involving the twin objectives of minimum flight time and low fuel consumption and enhancing the accuracy of optimized orbit.In particular,a transformed high-order polynomial model based on finite Fourier series is proposed,which can be characterized as a multi-constraint optimization problem.Then,a novel optimization algorithm is specifically developed to optimize the large-scale multi-constraint dynamical equations of shape trajectory.The key performance indicators of the index include minimum flight time,low fuel consumption and bi-objective optimization of the two.Simulation results prove that this approach possesses both the high precision achievable by numerical methods and low computational complexity offered by shape approximation techniques.Besides,the Pareto front of the fuel-time bi-objective optimization orbit is firstly introduced to analyze an intact optimal solution set.Furthermore,we have demonstrated that our proposed approach is appropriate to generate the preliminary orbit for pseudo-spectral method.
文摘In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(l + l/2n-3)s≤Hs(S)≤ Pn(S). An algorithm is presented to get Pn(S) for n ≤5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S)≥0.5631.
基金supported by the Board of Research in Nuclear Sciences of the Department of Atomic Energy,India(2012/36/69-BRNS/2012)
文摘The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11172093 and 11372102)the Hunan Provincial Innovation Foundation for Postgraduate,China(Grant No.CX2012B159)
文摘An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.
文摘A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.
文摘Accurate gas viscosity determination is an important issue in the oil and gas industries.Experimental approaches for gas viscosity measurement are timeconsuming,expensive and hardly possible at high pressures and high temperatures(HPHT).In this study,a number of correlations were developed to estimate gas viscosity by the use of group method of data handling(GMDH)type neural network and gene expression programming(GEP)techniques using a large data set containing more than 3000 experimental data points for methane,nitrogen,and hydrocarbon gas mixtures.It is worth mentioning that unlike many of viscosity correlations,the proposed ones in this study could compute gas viscosity at pressures ranging between 34 and 172 MPa and temperatures between 310 and 1300 K.Also,a comparison was performed between the results of these established models and the results of ten wellknown models reported in the literature.Average absolute relative errors of GMDH models were obtained 4.23%,0.64%,and 0.61%for hydrocarbon gas mixtures,methane,and nitrogen,respectively.In addition,graphical analyses indicate that the GMDH can predict gas viscosity with higher accuracy than GEP at HPHT conditions.Also,using leverage technique,valid,suspected and outlier data points were determined.Finally,trends of gas viscosity models at different conditions were evaluated.
文摘In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
基金This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada(Grant OGPIN-336)and by the"Ministere de l'Education du Quebec"(FCAR Grant-ER-0725)
文摘A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.
