Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NIS...Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NISQ)computing.In this paper,we use the bit-flip averaging(BFA)method to mitigate frequent readout errors in quantum generative adversarial networks(QGAN)for image generation,which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance,successfully solving problems with high cost of measurement for traditional error mitigation methods.Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method,the Kullback-Leibler(KL)divergence of the generated images converges to 0.04,0.05,and 0.1 for readout error probabilities of p=0.01,p=0.05,and p=0.1,respectively.Additionally,by evaluating the fidelity of the quantum states representing the images,we observe average fidelity values of 0.97,0.96,and 0.95 for the three readout error probabilities,respectively.These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models.展开更多
This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a gen...This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.展开更多
In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
This study addresses the pressing need to assess foundation bearing capacity in Opolo,Yenagoa,Bayelsa State,Nigeria.The significance lies in the dearth of comprehensive geotechnical data for construction planning in t...This study addresses the pressing need to assess foundation bearing capacity in Opolo,Yenagoa,Bayelsa State,Nigeria.The significance lies in the dearth of comprehensive geotechnical data for construction planning in the region.Past research is limited and this study contributes valuable insights by integrating Geographic Information System(GIS)with the Generalized Reciprocal Method(GRM).To collect data,near-surface seismic refraction surveys were conducted along three designated lines,utilizing ABEM Terraloc Mark 6 equipment,Easy Refract,and ArcGIS 10.4.1 software.This methodology allowed for the determination of key geotechnical parameters essential for soil characterization at potential foundation sites.The results revealed three distinct geoseismic layers.The uppermost layer,within a depth of 0.89 to 1.50 meters,exhibited inadequate compressional and shear wave velocities and low values for oedometric modulus,shear modulus,N-value,ultimate bearing capacity,and allowable bearing capacity.This indicates the presence of unsuitable,soft,and weak alluvial deposits for substantial structural loads.In contrast,the second layer(1.52 to 3.84 m depth)displayed favorable geotechnical parameters,making it suitable for various construction loads.The third layer(15.00 to 26.05 m depth)exhibited varying characteristics.The GIS analysis highlighted the unsuitability of the uppermost layer for construction,while the second and third layers were found to be fairly competent and suitable for shallow footing and foundation design.In summary,this study highlights the importance of geotechnical surveys in Opolo’s construction planning.It offers vital information for informed choices,addresses issues in the initial layer,and suggests secure,sustainable construction options.展开更多
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu...In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].展开更多
The modified AOR method for solving linear complementarity problem(LCP(M,p))was proposed in literature,with some convergence results.In this paper,we considered the MAOR method for generalized-order linear complementa...The modified AOR method for solving linear complementarity problem(LCP(M,p))was proposed in literature,with some convergence results.In this paper,we considered the MAOR method for generalized-order linear complementarity problem(ELCP(M,N,p,q)),where M,N are nonsingular matrices of the following form:M=[D11H1K1D2],N=[D12H2K2D22],D11,D12,D21 and D22 are square nonsingular diagonal matrices.展开更多
Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that fo...Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.展开更多
In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher's equation, the nonlinear schr¨odinger equat...In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher's equation, the nonlinear schr¨odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics.展开更多
In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial f...In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.展开更多
Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatia...Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method (GMLSM) and then, discrete equations of motion based on Lagrange's equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.展开更多
A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. T...A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation(single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.展开更多
Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational pr...Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multi-variables without arty variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F, which can be readily identified by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables (such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle) and generalized variational principles with three kinds of independent variables (such as Chien's generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints.展开更多
The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation ...The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation finite-element method is a relatively new numerical model for studying shallow water flow . This method was used to simulate tidal waves of the Gulf of St. Lawrence in Canada . The very good agreement of the numerical results with the field data indicated that the model is an effective and promising numerical method for solving two-dimensional tidal wave problems .展开更多
In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise....In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).展开更多
The crystallite orientation distribution functions(ODFs)were determined for the surface, 1/4 depth and 1/2 depth layers of a cold-rolled W20 non-oriented silicon steel sheet.By extending the theory of magnetic anisotr...The crystallite orientation distribution functions(ODFs)were determined for the surface, 1/4 depth and 1/2 depth layers of a cold-rolled W20 non-oriented silicon steel sheet.By extending the theory of magnetic anisotropy to textured materials with no sample symmetry, the variation of magnetic torque versus directions in the plane of the sheet was further calcu- lated quantitatively,which fits well with the measured torque curve.展开更多
This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions an...This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.展开更多
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the for...In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.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
In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burger...In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.展开更多
基金Project supported by the Natural Science Foundation of Shandong Province,China (Grant No.ZR2021MF049)Joint Fund of Natural Science Foundation of Shandong Province (Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)。
文摘Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NISQ)computing.In this paper,we use the bit-flip averaging(BFA)method to mitigate frequent readout errors in quantum generative adversarial networks(QGAN)for image generation,which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance,successfully solving problems with high cost of measurement for traditional error mitigation methods.Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method,the Kullback-Leibler(KL)divergence of the generated images converges to 0.04,0.05,and 0.1 for readout error probabilities of p=0.01,p=0.05,and p=0.1,respectively.Additionally,by evaluating the fidelity of the quantum states representing the images,we observe average fidelity values of 0.97,0.96,and 0.95 for the three readout error probabilities,respectively.These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models.
基金Project supported by the National Research Foundation of Korea(Nos.NRF-2020R1C1C1011970 and NRF-2018R1A5A7023490)。
文摘This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
文摘This study addresses the pressing need to assess foundation bearing capacity in Opolo,Yenagoa,Bayelsa State,Nigeria.The significance lies in the dearth of comprehensive geotechnical data for construction planning in the region.Past research is limited and this study contributes valuable insights by integrating Geographic Information System(GIS)with the Generalized Reciprocal Method(GRM).To collect data,near-surface seismic refraction surveys were conducted along three designated lines,utilizing ABEM Terraloc Mark 6 equipment,Easy Refract,and ArcGIS 10.4.1 software.This methodology allowed for the determination of key geotechnical parameters essential for soil characterization at potential foundation sites.The results revealed three distinct geoseismic layers.The uppermost layer,within a depth of 0.89 to 1.50 meters,exhibited inadequate compressional and shear wave velocities and low values for oedometric modulus,shear modulus,N-value,ultimate bearing capacity,and allowable bearing capacity.This indicates the presence of unsuitable,soft,and weak alluvial deposits for substantial structural loads.In contrast,the second layer(1.52 to 3.84 m depth)displayed favorable geotechnical parameters,making it suitable for various construction loads.The third layer(15.00 to 26.05 m depth)exhibited varying characteristics.The GIS analysis highlighted the unsuitability of the uppermost layer for construction,while the second and third layers were found to be fairly competent and suitable for shallow footing and foundation design.In summary,this study highlights the importance of geotechnical surveys in Opolo’s construction planning.It offers vital information for informed choices,addresses issues in the initial layer,and suggests secure,sustainable construction options.
基金supported by Scientific Research Fund of Sichuan Provincial Education Department (09ZB102)Scientific Research Fund of Science and Technology Deportment of Sichuan Provincial (2011JYZ011)
文摘In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].
文摘The modified AOR method for solving linear complementarity problem(LCP(M,p))was proposed in literature,with some convergence results.In this paper,we considered the MAOR method for generalized-order linear complementarity problem(ELCP(M,N,p,q)),where M,N are nonsingular matrices of the following form:M=[D11H1K1D2],N=[D12H2K2D22],D11,D12,D21 and D22 are square nonsingular diagonal matrices.
基金This work is supported by the Foundatiorl of Zhongshan University Advanced Research Centre
文摘Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.
基金The NSF(11001042) of ChinaSRFDP(20100043120001)FRFCU(09QNJJ002)
文摘In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher's equation, the nonlinear schr¨odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics.
基金Project supported in part by the National Natural Science Foundation of China(Grant No.11071177)
文摘In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.
文摘Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method (GMLSM) and then, discrete equations of motion based on Lagrange's equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.
基金Project supported by the National Natural Science Foundation of China (No.10272118) the Hong Kong Polytechnic University Research Grant (No.A-PE28) the Research Fund for the Doctoral Program of Ministry of Education of China (No.20020558013)
文摘A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation(single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.
文摘Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multi-variables without arty variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F, which can be readily identified by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables (such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle) and generalized variational principles with three kinds of independent variables (such as Chien's generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints.
文摘The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation finite-element method is a relatively new numerical model for studying shallow water flow . This method was used to simulate tidal waves of the Gulf of St. Lawrence in Canada . The very good agreement of the numerical results with the field data indicated that the model is an effective and promising numerical method for solving two-dimensional tidal wave problems .
基金partially supported by the National Natural Science Foundation of China(11871382,12071361)partially supported by the National Natural Science Foundation of China(11971361,11731012)。
文摘In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).
文摘The crystallite orientation distribution functions(ODFs)were determined for the surface, 1/4 depth and 1/2 depth layers of a cold-rolled W20 non-oriented silicon steel sheet.By extending the theory of magnetic anisotropy to textured materials with no sample symmetry, the variation of magnetic torque versus directions in the plane of the sheet was further calcu- lated quantitatively,which fits well with the measured torque curve.
基金Project supported by the National Natural Science Foundations of China(Grant Nos.10735030,10475055,10675065 and 90503006)the National Basic Research Program of China(Grant No.2007CB814800)
文摘This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
基金supported by the Natural Science Foundation of Ningbo City,Zhejiang Province,China (Grant Nos. 2012A610038 and 2012A610023)the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110007)
文摘In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.
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In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.