This paper considers the problem of applying data mining techniques to aeronautical field.The truncation method,which is one of the techniques in the aeronautical data mining,can be used to efficiently handle the air-...This paper considers the problem of applying data mining techniques to aeronautical field.The truncation method,which is one of the techniques in the aeronautical data mining,can be used to efficiently handle the air-combat behavior data.The technique of air-combat behavior data mining based on the truncation method is proposed to discover the air-combat rules or patterns.The simulation platform of the air-combat behavior data mining that supports two fighters is implemented.The simulation experimental results show that the proposed air-combat behavior data mining technique based on the truncation method is feasible whether in efficiency or in effectiveness.展开更多
An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an as...An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜ 〈｜〈s＋1｜ （s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.展开更多
Calculating the resistance of ventilation air-conditioning ducts under nonfully developed flow is a crucial problem that must be addressed. Based on the characteristics of the resistance in ventilation air-conditionin...Calculating the resistance of ventilation air-conditioning ducts under nonfully developed flow is a crucial problem that must be addressed. Based on the characteristics of the resistance in ventilation air-conditioning ducts, the truncation method-a computational method that is appropriate for nonfully developed flow boundary conditions-was proposed in this study. The resistance distributions in the upstream and downstream ducts from typical local components, including reducers, bends and tee ducts, were investigated. Using the resistance values of the local components under fully developed flow, the resistances that did not belong to nonfully developed flow were truncated and removed. Finally, the calculation steps of the proposed method were discussed, an engineering case study was presented, and the accuracy of the developed model was analyzed. The results showed that for the local components in the system (reducers, bends and tee ducts), their proportions of the total resistance exhibited similar trends under different width-to-height ratios. The resistance of these local components included upstream resistance, downstream resistance and their own resistance. The upstream resistance accounted for 2%–6% of the total resistance, whereas the downstream resistance of the reducers, bends and tee ducts accounted for 40%–60% of the total resistance. A functional relationship was established between the local resistance and cutoff distance of the reducers, bends and tee ducts. Hence, the truncation method can calculate the local resistance from the cutoff distance. Moreover, in the presented engineering case study, the error between the actual measured resistance values and those simulated with the truncation method was only 4.28%, which was far less than that of the results simulated with the traditional calculation methods (53.64%).展开更多
Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Pain...Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.展开更多
Recently,the authors of[Commun.Theor.Phys.56(2011)397]made a number of useful observations on Exp-function method.In this study,we focus on another vital issue,namely,the misleading results of double Exp-function method.
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We the...In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.展开更多
The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coef...The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.展开更多
In this letter, the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions can be solved by a truncated series method. A series of solitary solutions of the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions have be obtained.
In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diff...In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diffusion coefficient is polynomially growing or linearly growing,the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval[0.T],respectively.In both situations,the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required.Two examples are provided to illustrate the theory.展开更多
This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior p...This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.展开更多
The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of sing...The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare. For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands. In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip in the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation results show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.展开更多
Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rol...Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rolling process was established. Model of distributed stress was built based on rolling theory. And then, vibration model of moving strip with distributed stress was established. The partial differential equation was discretized by Galerkin truncation. The natural frequency and stability of the moving strip were investigated and simulation in time domain was made by numerical method. Taking the moving strip between the second stand and third stand of some tandem mill as a subject for investigation, distributions of stress, natural frequencies and stability of moving strip were de- termined under six different rolling conditions which are ＂uniform distribution of stress＂, ＂flat roll flat＂, ＂flat roll convex＂, ＂flat roll concave＂, ＂convex roll flat＂ and ＂concave roll flat＂. At last, three-dimensional dynamic simulation was made and the moving law of the strip was determined. This model can be used to study the stability of moving strip, depress the shape wave of strip and develop new rolling technology from the aspect of dynamics.展开更多
A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued...A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.展开更多
Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and ...Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.展开更多
This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed b...Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending of a saturated poroelastic cantilever beam with fixed end impermeable and flee end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Gaierkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are compared, and the differences between them are revealed. It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory, and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.展开更多
A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobiell...A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.展开更多
The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explici...The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.展开更多
Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-...Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation is this kind of equation,</span></span></span><span><span><b><span style="font-family:""> </span></b></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">t</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">he solutions are very interest. Several new exact solutions for the nonlinear equation are obtained by using truncated expansion method in this paper. The numerical simulations with different parameters for the new exact solutions of Benjamin</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation are given.</span></span></span>展开更多
This article introduces the current situation of the smart then describes the relationship of meter reliability characteristics meter＇s reliability and the failure mechanisms at first, and combined with its Bathtub C...This article introduces the current situation of the smart then describes the relationship of meter reliability characteristics meter＇s reliability and the failure mechanisms at first, and combined with its Bathtub Curve. It also introduces both the feasible failure tree model for meter lifecycle prediction based on actual experiences and meter reliability prediction methodology by SN 29500 norms based on this model. This article also brings forward that it is necessary that the ＂Learning Factor＂ shall be adopted in meter reliability prediction for new materials, new process, and customized parts by referring to GJB/Z299C. Thereafter, this article also tries to apply IEC 62059 and JB/T 50070 to introduce the feasible method for the lifecycle prediction result verification by accelerated lifecycle test. Furthermore, the article also explores ways to increase the firmware reliability in smart meter.展开更多
文摘This paper considers the problem of applying data mining techniques to aeronautical field.The truncation method,which is one of the techniques in the aeronautical data mining,can be used to efficiently handle the air-combat behavior data.The technique of air-combat behavior data mining based on the truncation method is proposed to discover the air-combat rules or patterns.The simulation platform of the air-combat behavior data mining that supports two fighters is implemented.The simulation experimental results show that the proposed air-combat behavior data mining technique based on the truncation method is feasible whether in efficiency or in effectiveness.
基金supported by the National Natural Science Foundation of China(No.11101149)the Basic Academic Discipline Program of Shanghai University of Finance and Economics(No.2013950575)
文摘An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜ 〈｜〈s＋1｜ （s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.
基金This research project was sponsored by the National Key R&D Program of China(No.2017YFC0702800)National Natural Science Foundation of China(No.51878533 and No.51508442)+1 种基金and Natural Science Foundation of Shaanxi Province(No.2019JM-233)Industrialization fund of Shaanxi Provincial Department of Education(No.19JC023).
文摘Calculating the resistance of ventilation air-conditioning ducts under nonfully developed flow is a crucial problem that must be addressed. Based on the characteristics of the resistance in ventilation air-conditioning ducts, the truncation method-a computational method that is appropriate for nonfully developed flow boundary conditions-was proposed in this study. The resistance distributions in the upstream and downstream ducts from typical local components, including reducers, bends and tee ducts, were investigated. Using the resistance values of the local components under fully developed flow, the resistances that did not belong to nonfully developed flow were truncated and removed. Finally, the calculation steps of the proposed method were discussed, an engineering case study was presented, and the accuracy of the developed model was analyzed. The results showed that for the local components in the system (reducers, bends and tee ducts), their proportions of the total resistance exhibited similar trends under different width-to-height ratios. The resistance of these local components included upstream resistance, downstream resistance and their own resistance. The upstream resistance accounted for 2%–6% of the total resistance, whereas the downstream resistance of the reducers, bends and tee ducts accounted for 40%–60% of the total resistance. A functional relationship was established between the local resistance and cutoff distance of the reducers, bends and tee ducts. Hence, the truncation method can calculate the local resistance from the cutoff distance. Moreover, in the presented engineering case study, the error between the actual measured resistance values and those simulated with the truncation method was only 4.28%, which was far less than that of the results simulated with the traditional calculation methods (53.64%).
基金Project supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)the National Natural Science Foundation of China (Grant No. 10771072)
文摘Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.
文摘Recently,the authors of[Commun.Theor.Phys.56(2011)397]made a number of useful observations on Exp-function method.In this study,we focus on another vital issue,namely,the misleading results of double Exp-function method.
基金The project supported by the China NKBRSF(2001CB409604)
文摘In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.
基金the Natural Science Foundation of Zhejiang Province of China (100039)
文摘The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.
基金The project supported by National Natural Science Foundation of China under Grant No. 10575026.Acknowledgments The author thanks Prof. S.Y. Lou for helpful discussions.
文摘In this letter, the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions can be solved by a truncated series method. A series of solitary solutions of the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions have be obtained.
文摘In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diffusion coefficient is polynomially growing or linearly growing,the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval[0.T],respectively.In both situations,the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required.Two examples are provided to illustrate the theory.
基金supported by the National Natural Science Foundation of China (Grant No.60872116)
文摘This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.
基金supported by National Natural Science Foundation of China (Grant No. 50875231)Hebei Provincial Major Natural Science Foundation of China (Grant No. E2006001038)
文摘The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare. For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands. In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip in the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation results show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.
基金Item Sponsored by National Natural Science Foundation of China(50875231)Great Natural Science Foundation of Hebei Province of China(E2006001038)
文摘Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rolling process was established. Model of distributed stress was built based on rolling theory. And then, vibration model of moving strip with distributed stress was established. The partial differential equation was discretized by Galerkin truncation. The natural frequency and stability of the moving strip were investigated and simulation in time domain was made by numerical method. Taking the moving strip between the second stand and third stand of some tandem mill as a subject for investigation, distributions of stress, natural frequencies and stability of moving strip were de- termined under six different rolling conditions which are ＂uniform distribution of stress＂, ＂flat roll flat＂, ＂flat roll convex＂, ＂flat roll concave＂, ＂convex roll flat＂ and ＂concave roll flat＂. At last, three-dimensional dynamic simulation was made and the moving law of the strip was determined. This model can be used to study the stability of moving strip, depress the shape wave of strip and develop new rolling technology from the aspect of dynamics.
基金supported in part by National Natural Science Foundation of China (Grant No 10772110)
文摘A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.
基金Project (No. 10471126) supported by the National Natural Science Foundation of China
文摘Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
基金the National Natural Science Foundation of China(No.10272070)Shanghai Leading Academic Discipline Project(No.Y0103)
文摘Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending of a saturated poroelastic cantilever beam with fixed end impermeable and flee end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Gaierkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are compared, and the differences between them are revealed. It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory, and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.
基金National Natural Science Foundation of China under Grant Nos 10472063 and 10772110
文摘A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.
基金Supported by the National Natural Science Foundation of Zhejiang Province under Grant No.LZ15A050001the National Natural Science Foundation of China under Grant No.11675146
文摘The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.
文摘Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation is this kind of equation,</span></span></span><span><span><b><span style="font-family:""> </span></b></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">t</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">he solutions are very interest. Several new exact solutions for the nonlinear equation are obtained by using truncated expansion method in this paper. The numerical simulations with different parameters for the new exact solutions of Benjamin</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation are given.</span></span></span>
文摘This article introduces the current situation of the smart then describes the relationship of meter reliability characteristics meter＇s reliability and the failure mechanisms at first, and combined with its Bathtub Curve. It also introduces both the feasible failure tree model for meter lifecycle prediction based on actual experiences and meter reliability prediction methodology by SN 29500 norms based on this model. This article also brings forward that it is necessary that the ＂Learning Factor＂ shall be adopted in meter reliability prediction for new materials, new process, and customized parts by referring to GJB/Z299C. Thereafter, this article also tries to apply IEC 62059 and JB/T 50070 to introduce the feasible method for the lifecycle prediction result verification by accelerated lifecycle test. Furthermore, the article also explores ways to increase the firmware reliability in smart meter.
