The Good Wife is an American TV series that focuses on women’s independence,politics,and law.The drama has been remade in China,Japan,and South Korea.This research aims to use Nida’s Functional Equivalence Theory to...The Good Wife is an American TV series that focuses on women’s independence,politics,and law.The drama has been remade in China,Japan,and South Korea.This research aims to use Nida’s Functional Equivalence Theory to analyze the methods of its English-to-Chinese subtitle translation by considering social,cultural,and historic backgrounds between China and America.After data collection and case analysis,the study found that:(1)Five major translation methods are adopted in the subtitle translation of The Good Wife.They are free translation,variation,literal translation,addition,and omission.Among them,free translation is the most frequently used,while omission is used least.(2)The subtitle translation of films and TV series is limited by time and space restrictions,social-cultural differences,and other factors.When translating,translators should try to use humorous words,euphemism,intonation,and other ways,and combine different methods such as literal translation,free translation,variation,addition,omission,and other methods to seek equivalence both in the meaning and function of subtitles under the guidance of Functional Equivalence Theory.展开更多
Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct dou...Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct doubly-periodic solutions of the Zakharov-Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus k →1, these solutions reduce to the solitary wave solutions of the equation.展开更多
This paper elucidates the effectiveness of combining the Poincare-Lighthill-Kuo method (PLK method, for short) and symbolic computation. Firstly, the idea and history of the PLK method are briefly introduced. Then, th...This paper elucidates the effectiveness of combining the Poincare-Lighthill-Kuo method (PLK method, for short) and symbolic computation. Firstly, the idea and history of the PLK method are briefly introduced. Then, the difficulty of intermediate expression swell, often encountered in symbolic computation, is outlined. For overcoming the difficulty, a semi-inverse algorithm was proposed by the author, with which the lengthy ports of intermediate expressions are first frozen in the form of symbols till the Fnal stage of seeking perturbation solutions. Tn discuss the applications of the above algorithm, the related work of the author and his research group on nonlinear oscillations and waves is concisely reviewed. The computer-extended perturbation solution of the Duffing equation shows that the asymptotic solution obtained with the PLK method possesses the convergence radius of 1 and thus the range of validity of the solution is considerably enlarged. The studies on internal solitary waves in stratified fluid and on the head-on collision between two solitary waves in a hyperelastic rod indicate that by means of the presented methods, very complicated manipulation, unconceivable in hand calculation, can be conducted and thus result in higher-order evolution equations and asymptotic solutions. The examples illustrate that the algorithm helps to realize the symbolic computation on micro-commputers. Finally, it is concluded that,vith the aid of symbolic computation, the vitality of the PLK method is greatly. Strengthened and at least for the solutions to conservative systems of oscillations and waves, it is a powerful tool.展开更多
This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulat...This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.展开更多
In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact so...In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the （2＋1）-dimensional Breaking soliton equation are derived by using the extended multiple Riccatl equations expansion method.展开更多
Quantifying the post-earthquake functional recovery of railway stations presents significant challenges.This paper first establishes a post-earthquake function calculation method for railway stations,encompassing the ...Quantifying the post-earthquake functional recovery of railway stations presents significant challenges.This paper first establishes a post-earthquake function calculation method for railway stations,encompassing the establishment of relationships between the station’s function and the damage state,function loss,and failure probability of components and professional equipment in each layer.Also,the“4 stages-6 sequences”post-earthquake repair method is present,taking into account the functional and structural characteristics of railway stations.Additionally,a novel piecewise function for the post-earthquake functional dynamic recovery of railway stations is developed.A case study is conducted on a typical railway station to demonstrate the analysis procedure.Results indicate that under fortification,rare,and extremely rare earthquake scenarios,the interlayer drift ratio(IDR)of the railway station were 1/276,1/143,and 1/52,respectively,and corresponding peak floor acceleration(PFA)were 6.31 m/s^(2),7.82 m/s^(2),and 8.57 m/s^(2),respectively.The post-earthquake function of the railway station was 93.21%,82.33%,and 64.16%of its initial function.The repair times were 6.66 days,18.65 days,and 37.42 days.The displacement-sensitive,non-structural components were identified as the most vulnerable to damage.And the first repair stage(R_(1))which was mainly used to repair structural components and non-structural transport components,accounted for the highest proportion of total repair time.展开更多
A novel parameter identification method for magnetic levitation bearing rotor systems is proposed,based on the modulation function method.The fundamental principle of the modulation function method for parameter ident...A novel parameter identification method for magnetic levitation bearing rotor systems is proposed,based on the modulation function method.The fundamental principle of the modulation function method for parameter identification is derived on the basis of the characteristics of the modulation function.The transformation of the differential equation model of a continuous system into a general algebraic equation model is effectively achieved,thereby avoiding the influence of errors introduced by the initial value and differential derivation of the system.Modulation function method parameter identification models have been established for single-degree-of-freedom and multi-degree-of-freedom magnetic levitation bearing rotor systems.The influence of different parameters of Hartley modulation function on the accuracy of system parameter identification has been investigated,thus providing a basis for the design of Hartley modulation function parameters.Simulation and experimental results demonstrate that the modulation function method can effectively identify system parameters despite the presence of system noise.展开更多
Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of thes...Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of these missing data is highly valuable for engineering and scientific research.In this study,the radial basis function(RBF)method is used to estimate the spatial distribution of total suspended matter(TSM)concentration in Hangzhou Bay using remote sensing data with severe data gaps.The estimation precision is validated by comparing the results with those of other commonly used interpolation methods,such as the Kriging method and the basic spline(B-spline)method.In addition,the applicability of the RBF method is explored.Results show that the estimation of the RBF method is significantly close to the observation in Hangzhou Bay.The average of the mean absolute error,mean relative error,and root mean square error in all the experiments is evidently smaller than those of the Kriging and B-spline interpolations,indicating that the proposed method is more appropriate for estimating the spatial distribution of the TSM in Hangzhou Bay.Finally,the TSM distribution in the blank observational area is predicted.This study can provide some reference values for handling watercolor remote sensing data.展开更多
This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the acc...This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.展开更多
A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the re...A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions.The conditions for the validity of this approximation are also discussed.Furthermore,a formula that incorporates waveguide effects for the modal group velocity is derived,revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes.The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions,but also provides a wider range of depth applicability.Additionally,this method exhibits strong agreement with numerical methods and offers valuable physical insights.Finally,the method is applied to the study of very-low-frequency sound propagation in the South China Sea,leading to sound transmission loss predictions that closely align with experimental observations.展开更多
The concepts of complementary cofactor pairs, normal double-graphs and feasible torn vertex seta are introduced. By using them a decomposition theorem for first-order cofactor C(Y) is derived. Combining it with the mo...The concepts of complementary cofactor pairs, normal double-graphs and feasible torn vertex seta are introduced. By using them a decomposition theorem for first-order cofactor C(Y) is derived. Combining it with the modified double-graph method, a new decomposition analysis-modified double-graph decomposition analysis is presented for finding symbolic network functions. Its advantages are that the resultant symbolic expressions are compact and contain no cancellation terms, and its sign evaluation is very simple.展开更多
In this paper, symbolic code matrix ,constant matrix and count matrix are defined .The first twomatrices are used to describe the elemental expression of augmented matrix and the nede admittance equa-tion is thus obta...In this paper, symbolic code matrix ,constant matrix and count matrix are defined .The first twomatrices are used to describe the elemental expression of augmented matrix and the nede admittance equa-tion is thus obtained. The third matrix is used to obtain the incoming degree matrix, and according to thematrix all the 1- factors of the Coates graph are given. By using the data code, the determinant is expandedand the same items in the expansion are merged. Thus the symbolic network function in which no term can-cellation occurs is generated.展开更多
We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground...We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.展开更多
In a recent article [Commun. Theor. Phys. （Beijing, China） 47 （2007） 270], Cao et al. gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, whic...In a recent article [Commun. Theor. Phys. （Beijing, China） 47 （2007） 270], Cao et al. gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, which are in the form of q-deformed hyperbolic and triangular functions as new solutions. In this comment, we will show that these solutions are just the special cases of some known solutions of the Riccati equation and thus they are not new solutions.展开更多
Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded...Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit. Nested form is neither canonical nor amenable to symbolic manipulation. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. This algorithm, called totally coded method (TCM), consists of representing the symbolic determinant of a circuit matrix by code series and performing symbolic analysis by code manipulation. We describe an efficient code-ordering heuristic and prove that it is optimum for ladder-structured circuits. For practical analog circuits, TCM not only covers all advantages of the algorithm via determinant decision diagrams (DDD) but is more simple and efficient than DDD method.展开更多
Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instr...Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instrument function,is measured in X-ray Thom-son scattering(XRTS)experiments,which allow the study of electronic structure properties at the microscopic level.Among the various ab initio methods,linear-response time-dependent density-functional theory(LR-TDDFT)is a key framework for simulating the DSF.The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation.A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases,making LR-TDDFT impractical for modeling XRTS measurements over large energy scales,such as in backward scattering geometry.In this work,we consider and test an alternative approach to LR-TDDFT that employs the Liouville–Lanczos(LL)method for simulating the DSF of WDM.This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed.We compare the results obtained from the LL method with those from the solution of Dyson’s equation using the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen.Additionally,we utilize exact path integral Monte Carlo results for the imaginary-time density-density correlation function(ITCF)of warm dense hydrogen to rigorously benchmark the LL approach.We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers,the effects of pseudopotentials,and the role of Lorentzian smearing.The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape,supporting experimental efforts and advancing WDM theory.展开更多
Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algor...Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.展开更多
This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functio...This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.展开更多
Sandwich functionally graded(FG)auxetic beams are extensively utilized in aerospace,automotive,and biomedical industries due to their excellent strength-toweight ratio,impact resistance,and tunable mechanical properti...Sandwich functionally graded(FG)auxetic beams are extensively utilized in aerospace,automotive,and biomedical industries due to their excellent strength-toweight ratio,impact resistance,and tunable mechanical properties.The integration of FG materials with auxetic structures enhances their adaptability in advanced engineering applications.However,understanding their dynamic behavior under external excitations is essential for optimal design and structural reliability.Nonlinear interactions in such structures pose significant challenges in vibration analysis,necessitating robust analytical methods.This study presents a closed-form solution for the nonlinear forced vibration analysis of sandwich FG auxetic beams,offering an accurate and efficient method for predicting their dynamic response.The beam consists of two FG face sheets with material properties varying through the thickness and a re-entrant honeycomb auxetic core with an adjustable Poisson's ratio.The governing nonlinear equations of motion are derived using the first-order shear deformation theory(FSDT),the modified Gibson model,and the von Kármán relations,formulated through Hamilton's principle.A closed-form solution is obtained via the Galerkin method and multiple-scale technique.The results demonstrate that FG layers enable control of the overweight and dynamic response amplitude,with positive power law indexes reducing weight.Comparisons with finite element results confirm the accuracy of the proposed formulation.展开更多
文摘The Good Wife is an American TV series that focuses on women’s independence,politics,and law.The drama has been remade in China,Japan,and South Korea.This research aims to use Nida’s Functional Equivalence Theory to analyze the methods of its English-to-Chinese subtitle translation by considering social,cultural,and historic backgrounds between China and America.After data collection and case analysis,the study found that:(1)Five major translation methods are adopted in the subtitle translation of The Good Wife.They are free translation,variation,literal translation,addition,and omission.Among them,free translation is the most frequently used,while omission is used least.(2)The subtitle translation of films and TV series is limited by time and space restrictions,social-cultural differences,and other factors.When translating,translators should try to use humorous words,euphemism,intonation,and other ways,and combine different methods such as literal translation,free translation,variation,addition,omission,and other methods to seek equivalence both in the meaning and function of subtitles under the guidance of Functional Equivalence Theory.
文摘Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct doubly-periodic solutions of the Zakharov-Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus k →1, these solutions reduce to the solitary wave solutions of the equation.
文摘This paper elucidates the effectiveness of combining the Poincare-Lighthill-Kuo method (PLK method, for short) and symbolic computation. Firstly, the idea and history of the PLK method are briefly introduced. Then, the difficulty of intermediate expression swell, often encountered in symbolic computation, is outlined. For overcoming the difficulty, a semi-inverse algorithm was proposed by the author, with which the lengthy ports of intermediate expressions are first frozen in the form of symbols till the Fnal stage of seeking perturbation solutions. Tn discuss the applications of the above algorithm, the related work of the author and his research group on nonlinear oscillations and waves is concisely reviewed. The computer-extended perturbation solution of the Duffing equation shows that the asymptotic solution obtained with the PLK method possesses the convergence radius of 1 and thus the range of validity of the solution is considerably enlarged. The studies on internal solitary waves in stratified fluid and on the head-on collision between two solitary waves in a hyperelastic rod indicate that by means of the presented methods, very complicated manipulation, unconceivable in hand calculation, can be conducted and thus result in higher-order evolution equations and asymptotic solutions. The examples illustrate that the algorithm helps to realize the symbolic computation on micro-commputers. Finally, it is concluded that,vith the aid of symbolic computation, the vitality of the PLK method is greatly. Strengthened and at least for the solutions to conservative systems of oscillations and waves, it is a powerful tool.
基金supported in part by the National Natural Science Foundation of China(62473221)the Natural Science Foundation of Shandong Province,China(ZR2024MF006)Qingdao Natural Science Foundation(24-4-4-zrjj-165-jch)。
文摘This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.
基金The project partially supported by National Natural Science Foundation of China under Grant No. 10471143 and the State 973 Project under Grant No. 2004CB318001 The authors are very grateful to Prof. Hong-Bo Li, Yong Chen, Zhen-Ya Yan, and Zhuo-Sheng Lii for their kind help and valuable suggestions. They also thank Prof. En-Gui Fan and Prof. Chun-Ping Liu for their constructive suggestions about the solutions of Riccati equation.
文摘In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the （2＋1）-dimensional Breaking soliton equation are derived by using the extended multiple Riccatl equations expansion method.
基金National Natural Science Foundation of China under Grant No.52278534the Sichuan Provincial Natural Science Foundation of China under Grant No.2022NSFSC0423。
文摘Quantifying the post-earthquake functional recovery of railway stations presents significant challenges.This paper first establishes a post-earthquake function calculation method for railway stations,encompassing the establishment of relationships between the station’s function and the damage state,function loss,and failure probability of components and professional equipment in each layer.Also,the“4 stages-6 sequences”post-earthquake repair method is present,taking into account the functional and structural characteristics of railway stations.Additionally,a novel piecewise function for the post-earthquake functional dynamic recovery of railway stations is developed.A case study is conducted on a typical railway station to demonstrate the analysis procedure.Results indicate that under fortification,rare,and extremely rare earthquake scenarios,the interlayer drift ratio(IDR)of the railway station were 1/276,1/143,and 1/52,respectively,and corresponding peak floor acceleration(PFA)were 6.31 m/s^(2),7.82 m/s^(2),and 8.57 m/s^(2),respectively.The post-earthquake function of the railway station was 93.21%,82.33%,and 64.16%of its initial function.The repair times were 6.66 days,18.65 days,and 37.42 days.The displacement-sensitive,non-structural components were identified as the most vulnerable to damage.And the first repair stage(R_(1))which was mainly used to repair structural components and non-structural transport components,accounted for the highest proportion of total repair time.
基金supported by the National Science and Technology Major Project(Grant No.J2019-Ⅳ-0003-0070).
文摘A novel parameter identification method for magnetic levitation bearing rotor systems is proposed,based on the modulation function method.The fundamental principle of the modulation function method for parameter identification is derived on the basis of the characteristics of the modulation function.The transformation of the differential equation model of a continuous system into a general algebraic equation model is effectively achieved,thereby avoiding the influence of errors introduced by the initial value and differential derivation of the system.Modulation function method parameter identification models have been established for single-degree-of-freedom and multi-degree-of-freedom magnetic levitation bearing rotor systems.The influence of different parameters of Hartley modulation function on the accuracy of system parameter identification has been investigated,thus providing a basis for the design of Hartley modulation function parameters.Simulation and experimental results demonstrate that the modulation function method can effectively identify system parameters despite the presence of system noise.
基金supported by the Open Funds for Hubei Key Laboratory of Marine Geological Resources,China University of Geosciences(No.MGR202308)the Natural Science Foundation of Shandong Province(No.ZR2020MD085)+3 种基金the National Natural Science Foundation of China(No.41821004)the Taishan Scholar Program(No.tstp2022114)the Shandong Provincial Natural Science Foundation(No.DKXZZ202206)the National Key Research and Development Program of China(No.2016YFC1402404).
文摘Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of these missing data is highly valuable for engineering and scientific research.In this study,the radial basis function(RBF)method is used to estimate the spatial distribution of total suspended matter(TSM)concentration in Hangzhou Bay using remote sensing data with severe data gaps.The estimation precision is validated by comparing the results with those of other commonly used interpolation methods,such as the Kriging method and the basic spline(B-spline)method.In addition,the applicability of the RBF method is explored.Results show that the estimation of the RBF method is significantly close to the observation in Hangzhou Bay.The average of the mean absolute error,mean relative error,and root mean square error in all the experiments is evidently smaller than those of the Kriging and B-spline interpolations,indicating that the proposed method is more appropriate for estimating the spatial distribution of the TSM in Hangzhou Bay.Finally,the TSM distribution in the blank observational area is predicted.This study can provide some reference values for handling watercolor remote sensing data.
基金supported by the Advance Research Project of Civil Aerospace Technology(Grant No.D020304)National Nat-ural Science Foundation of China(Grant Nos.52205257 and U22B2083).
文摘This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12174048 and 12204128)。
文摘A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions.The conditions for the validity of this approximation are also discussed.Furthermore,a formula that incorporates waveguide effects for the modal group velocity is derived,revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes.The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions,but also provides a wider range of depth applicability.Additionally,this method exhibits strong agreement with numerical methods and offers valuable physical insights.Finally,the method is applied to the study of very-low-frequency sound propagation in the South China Sea,leading to sound transmission loss predictions that closely align with experimental observations.
文摘The concepts of complementary cofactor pairs, normal double-graphs and feasible torn vertex seta are introduced. By using them a decomposition theorem for first-order cofactor C(Y) is derived. Combining it with the modified double-graph method, a new decomposition analysis-modified double-graph decomposition analysis is presented for finding symbolic network functions. Its advantages are that the resultant symbolic expressions are compact and contain no cancellation terms, and its sign evaluation is very simple.
基金The Project Supported by National Natural Science Foundation of China
文摘In this paper, symbolic code matrix ,constant matrix and count matrix are defined .The first twomatrices are used to describe the elemental expression of augmented matrix and the nede admittance equa-tion is thus obtained. The third matrix is used to obtain the incoming degree matrix, and according to thematrix all the 1- factors of the Coates graph are given. By using the data code, the determinant is expandedand the same items in the expansion are merged. Thus the symbolic network function in which no term can-cellation occurs is generated.
基金supported by the National Key R&D Program of China(No.2023YFA1606701)the National Natural Science Foundation of China(Nos.12175042,11890710,11890714,12047514,12147101,and 12347106)+1 种基金Guangdong Major Project of Basic and Applied Basic Research(No.2020B0301030008)China National Key R&D Program(No.2022YFA1602402).
文摘We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.
基金supported by National Natural Science Foundation of China under Grant No.10671172the Natural Science Foundation of Jiangsu Province under Grant No.BK2006064
文摘In a recent article [Commun. Theor. Phys. （Beijing, China） 47 （2007） 270], Cao et al. gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, which are in the form of q-deformed hyperbolic and triangular functions as new solutions. In this comment, we will show that these solutions are just the special cases of some known solutions of the Riccati equation and thus they are not new solutions.
文摘Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit. Nested form is neither canonical nor amenable to symbolic manipulation. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. This algorithm, called totally coded method (TCM), consists of representing the symbolic determinant of a circuit matrix by code series and performing symbolic analysis by code manipulation. We describe an efficient code-ordering heuristic and prove that it is optimum for ladder-structured circuits. For practical analog circuits, TCM not only covers all advantages of the algorithm via determinant decision diagrams (DDD) but is more simple and efficient than DDD method.
基金supported by the Center for Advanced Systems Understanding(CASUS),financed by Germany’s Federal Ministry of Education and Research(BMBF)and the Saxon State Government out of the State Budget approved by the Saxon State Parliamentfunding from the European Research Council(ERC)under the European Union’s Horizon 2022 research and innovation programme(Grant Agreement No.101076233,“PREXTREME”)funding from the European Union’s Just Transition Fund(JTF)within the project Röntgenlaser-Optimierung der Laserfusion(ROLF),Contract No.5086999001,co-financed by the Saxon State Government out of the State Budget approved by the Saxon State Parliament.
文摘Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instrument function,is measured in X-ray Thom-son scattering(XRTS)experiments,which allow the study of electronic structure properties at the microscopic level.Among the various ab initio methods,linear-response time-dependent density-functional theory(LR-TDDFT)is a key framework for simulating the DSF.The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation.A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases,making LR-TDDFT impractical for modeling XRTS measurements over large energy scales,such as in backward scattering geometry.In this work,we consider and test an alternative approach to LR-TDDFT that employs the Liouville–Lanczos(LL)method for simulating the DSF of WDM.This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed.We compare the results obtained from the LL method with those from the solution of Dyson’s equation using the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen.Additionally,we utilize exact path integral Monte Carlo results for the imaginary-time density-density correlation function(ITCF)of warm dense hydrogen to rigorously benchmark the LL approach.We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers,the effects of pseudopotentials,and the role of Lorentzian smearing.The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape,supporting experimental efforts and advancing WDM theory.
基金This work is supported by Ministry of Higher Education(MOHE)through Fundamental Research Grant Scheme(FRGS)(FRGS/1/2020/STG06/UTHM/03/7).
文摘Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.
文摘This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.
文摘Sandwich functionally graded(FG)auxetic beams are extensively utilized in aerospace,automotive,and biomedical industries due to their excellent strength-toweight ratio,impact resistance,and tunable mechanical properties.The integration of FG materials with auxetic structures enhances their adaptability in advanced engineering applications.However,understanding their dynamic behavior under external excitations is essential for optimal design and structural reliability.Nonlinear interactions in such structures pose significant challenges in vibration analysis,necessitating robust analytical methods.This study presents a closed-form solution for the nonlinear forced vibration analysis of sandwich FG auxetic beams,offering an accurate and efficient method for predicting their dynamic response.The beam consists of two FG face sheets with material properties varying through the thickness and a re-entrant honeycomb auxetic core with an adjustable Poisson's ratio.The governing nonlinear equations of motion are derived using the first-order shear deformation theory(FSDT),the modified Gibson model,and the von Kármán relations,formulated through Hamilton's principle.A closed-form solution is obtained via the Galerkin method and multiple-scale technique.The results demonstrate that FG layers enable control of the overweight and dynamic response amplitude,with positive power law indexes reducing weight.Comparisons with finite element results confirm the accuracy of the proposed formulation.
