Does traditional Chinese economic thought possess genuine analytical rigor?This question lies at the heart of any serious evaluation of its theoretical value and historical significance.It also matters for understandi...Does traditional Chinese economic thought possess genuine analytical rigor?This question lies at the heart of any serious evaluation of its theoretical value and historical significance.It also matters for understanding how best to preserve,build on its remarkable achievements,and develop its intellectual legacy.Critics such as Schumpeter and Taylor have long argued that the economic reasoning found in ancient China cannot compare with that of classical Greece or medieval Europe.Yet this view often reflects the narrow assumptions of mainstream economics,defining analysis almost entirely in terms of market exchange.As a result,it tends to overlook traditions built around statecraft,governance,and the management of economic order.A careful re-examination and Sino-Western comparative analysis of key thinkers-including Mencius,Guanzi,and Sima Qian-tells a different story.Rooted in China’s distinctive cultural and philosophical heritage,traditional Chinese economic thought not only contains the analytical dimensions(as defined by Schumpeter)but also displays a broader and more diverse set of economic reasoning.Notably,its systematic depth and intellectual precision were,in many respects,remarkably advanced.Therefore,advancing the construction of a Chinese school of economics in the new era under the framework of the“Second Integration”,i.e.,integrating the basic tenets of Marxism with China’s fine traditional culture,should,and indeed can draw essential insights from this analytical tradition.展开更多
In the linguistic field,L1transfer is a complex and controversial field in second language acquisition.In this article,Firstly,it will discuss some historical theories of L1 transfer.Secondly,it will analyze some mani...In the linguistic field,L1transfer is a complex and controversial field in second language acquisition.In this article,Firstly,it will discuss some historical theories of L1 transfer.Secondly,it will analyze some manifestations of L1 transfer.Thirdly,it will explain the struc tural and the nonstructural factors in L1 transfer.Fourthly,it will discuss the problems in the study of L1transfer.Finally,it will give some my opinions of L1transfer.展开更多
Second language acquisition(SLA)studies shows that first language(L1)transfer is one of the important factors that influence SLA.This paper mainly summarizes some non-linguistic factors affecting language transfer in ...Second language acquisition(SLA)studies shows that first language(L1)transfer is one of the important factors that influence SLA.This paper mainly summarizes some non-linguistic factors affecting language transfer in order to help whose who are interested in this field have a preliminary understanding of it.展开更多
This essay mainly talks about usage of L1 and L2 from various perspectives.Throughout the article some knowledge related to fields of L1 and L2 will be mentioned.
More focuses of foreign language teaching theory and practice are on the study of first language and second language acquisition. The article deals with the concept of first and second language acquisition, the relati...More focuses of foreign language teaching theory and practice are on the study of first language and second language acquisition. The article deals with the concept of first and second language acquisition, the relationship between them and the factors influencing on them. The characteristics of the children acquisition and adult acquisition are also studied.展开更多
Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one ...Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）展开更多
This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating ...This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is established.This formula is expressed in terms of a certain terminating hypergeometric function of the type_(4)F_(3)(1).This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type 3 F 2(1)which can be summed with the aid of Watson’s identity.Six illustrative examples are presented to ensure the applicability and accuracy of the proposed algorithm.展开更多
A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variatio...A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.展开更多
We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second...We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.展开更多
Objective To identify and determine the optimal method to screening for fetal Down's syndrome(DS).Methods Three large cohorts with 17118,39903,16646 subjects were enrolled for the first trimester double marker(pre...Objective To identify and determine the optimal method to screening for fetal Down's syndrome(DS).Methods Three large cohorts with 17118,39903,16646 subjects were enrolled for the first trimester double marker(pregnancy-associated plasma protein A and free[B-human chorionic gonadotropin)screening(FTDMS),second trimester double marker(c{-fetoprotein and free B-human chorionic gonadotropin)screening(STDMS),and second trimester triple marker(a-fetoprotein,free 13-human chorionic gonadotropin and unconjugated estriol 3)screening(STTMS),respectively.The sensitivity,specificity,false positive rate(FPR),false negative rate(FNR)and the areas under ROC curves(AUCs)were estimated in order to determine the optimal screening method in women under or above 35 years old.Results For women under 35 years old,STTMS was the best method with a detection rate of 68.8%and FPR of 4.3%followed by the STDMS with a detection rate(sensitivity)of 66.7%and FPR of 4.9%.The FTDMS had a lower detection rate of 61.1%and FPR of 6.3%.For women above 35 years old,the detection rate of all the methods was similar,but STTMS method had a lowest FPR of 15.9%.For women under 35 years old AUCs were 0.77(95%CI,0.64 to 0.91),0.81(95%CI,0.71 to 0.91),and 0.82(95%CI,0.69 to 0.96)for FTDMS,STDMS,and STTMS methods,respectively;for those above 35 years old,AUCs were 0.70(95%CI,0.56 to 0.83),0.70(95%CI,0.59 to 0.82),0.78(95%Cl,0.58 to 0.97)for FTDMS,STDMS and SITMS,respectively.Conclusion Findings from our study revealed that STDMS is optimal for the detection of fetal DS in pregnant women aged under 35.For individual women,if economic condition permits,STFMS is the best choice,while for women aged above 35,STTMS is the best choice in this regard.展开更多
This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homoge...This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homogenized initial system method （HISM）. In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.展开更多
In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a...In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.展开更多
In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergen...In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework.展开更多
L1 and L2 acquisition, in some respects, are similar. Language development in children goes hand in hand with physical and cognitive development. Children learn their first language by imitation, but not always and no...L1 and L2 acquisition, in some respects, are similar. Language development in children goes hand in hand with physical and cognitive development. Children learn their first language by imitation, but not always and not only by imitation. There seems to be some "innate capacities" that make children start to speak at the same time they do and in the way they do it. Adults learning a second language usually are controlled more by their motivation. But language input is important for both L1 and L2 acquisition. Though there are differences between CL1 and between CL2 and AL2, the way in which these learners acquire some of the grammatical morphemes is similar. This, together with some other evidence, shows that it is not only children who can acquire language. Adults can also acquire a language. But when adults acquire a language, they should also learn it. Some of the ways in which children acquire their language can be used as a model for L2 acquisition, even for Chinese students whose language is unrelated to English and whose culture is different. Learning the culture of the English-speaking countries will benefit the learning of the language. Like children, listening should also be well in advance of speaking in L2 acquisition. To train listening comprehension skills, Asher’s TPR approach proves more effective. TPR approach is at the moment limited to the beginning stage only. In order for students to gain all the five skills in a second language learning, namely, listening, speaking, reading, writing, and interpreting/translating, other methods should be used at the same time, or at later stages.展开更多
In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit n...In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.展开更多
The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By a...The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.展开更多
In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the...In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations.展开更多
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational...The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.展开更多
We show how to use the Lucas polynomials of the second kind in the solution of a homogeneous linear differential system with constant coefficients, avoiding the Jordan canonical form for the relevant matrix.
基金supported by the National Social Science Fund of China(NSSFC):NSSFC Major Project“Exploration and Practice in the Development of Chinese Economics Since the Modern Era”(Grant No.17ZDA034)NSSFC Key Project“The Status and Value of Traditional Chinese Economic Thought”(Grant No.17AJL006)NSSFC General Project“The Transformation and Evolution of Chinese Economic Thought During the Republican Era”(Grant No.22BJL130).
文摘Does traditional Chinese economic thought possess genuine analytical rigor?This question lies at the heart of any serious evaluation of its theoretical value and historical significance.It also matters for understanding how best to preserve,build on its remarkable achievements,and develop its intellectual legacy.Critics such as Schumpeter and Taylor have long argued that the economic reasoning found in ancient China cannot compare with that of classical Greece or medieval Europe.Yet this view often reflects the narrow assumptions of mainstream economics,defining analysis almost entirely in terms of market exchange.As a result,it tends to overlook traditions built around statecraft,governance,and the management of economic order.A careful re-examination and Sino-Western comparative analysis of key thinkers-including Mencius,Guanzi,and Sima Qian-tells a different story.Rooted in China’s distinctive cultural and philosophical heritage,traditional Chinese economic thought not only contains the analytical dimensions(as defined by Schumpeter)but also displays a broader and more diverse set of economic reasoning.Notably,its systematic depth and intellectual precision were,in many respects,remarkably advanced.Therefore,advancing the construction of a Chinese school of economics in the new era under the framework of the“Second Integration”,i.e.,integrating the basic tenets of Marxism with China’s fine traditional culture,should,and indeed can draw essential insights from this analytical tradition.
文摘In the linguistic field,L1transfer is a complex and controversial field in second language acquisition.In this article,Firstly,it will discuss some historical theories of L1 transfer.Secondly,it will analyze some manifestations of L1 transfer.Thirdly,it will explain the struc tural and the nonstructural factors in L1 transfer.Fourthly,it will discuss the problems in the study of L1transfer.Finally,it will give some my opinions of L1transfer.
文摘Second language acquisition(SLA)studies shows that first language(L1)transfer is one of the important factors that influence SLA.This paper mainly summarizes some non-linguistic factors affecting language transfer in order to help whose who are interested in this field have a preliminary understanding of it.
文摘This essay mainly talks about usage of L1 and L2 from various perspectives.Throughout the article some knowledge related to fields of L1 and L2 will be mentioned.
文摘More focuses of foreign language teaching theory and practice are on the study of first language and second language acquisition. The article deals with the concept of first and second language acquisition, the relationship between them and the factors influencing on them. The characteristics of the children acquisition and adult acquisition are also studied.
基金Supported by the National Nature Science Foundation.
文摘Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）
文摘This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is established.This formula is expressed in terms of a certain terminating hypergeometric function of the type_(4)F_(3)(1).This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type 3 F 2(1)which can be summed with the aid of Watson’s identity.Six illustrative examples are presented to ensure the applicability and accuracy of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China(10201026,10672111)
文摘A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.
基金This work was supported by the National Research Foundation of Korea(NRF)Grant Funded by the Korea Government(No.2020R1F1A1A01071564).
文摘We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.
基金supported by the National Natural Science Foundation of China(81101655)the grant from the China Postdoctoral Science Foundation(2011M501282)the grant from Hunan Provincial Science&Tecnology Departemnt(2009SK3048)
文摘Objective To identify and determine the optimal method to screening for fetal Down's syndrome(DS).Methods Three large cohorts with 17118,39903,16646 subjects were enrolled for the first trimester double marker(pregnancy-associated plasma protein A and free[B-human chorionic gonadotropin)screening(FTDMS),second trimester double marker(c{-fetoprotein and free B-human chorionic gonadotropin)screening(STDMS),and second trimester triple marker(a-fetoprotein,free 13-human chorionic gonadotropin and unconjugated estriol 3)screening(STTMS),respectively.The sensitivity,specificity,false positive rate(FPR),false negative rate(FNR)and the areas under ROC curves(AUCs)were estimated in order to determine the optimal screening method in women under or above 35 years old.Results For women under 35 years old,STTMS was the best method with a detection rate of 68.8%and FPR of 4.3%followed by the STDMS with a detection rate(sensitivity)of 66.7%and FPR of 4.9%.The FTDMS had a lower detection rate of 61.1%and FPR of 6.3%.For women above 35 years old,the detection rate of all the methods was similar,but STTMS method had a lowest FPR of 15.9%.For women under 35 years old AUCs were 0.77(95%CI,0.64 to 0.91),0.81(95%CI,0.71 to 0.91),and 0.82(95%CI,0.69 to 0.96)for FTDMS,STDMS,and STTMS methods,respectively;for those above 35 years old,AUCs were 0.70(95%CI,0.56 to 0.83),0.70(95%CI,0.59 to 0.82),0.78(95%Cl,0.58 to 0.97)for FTDMS,STDMS and SITMS,respectively.Conclusion Findings from our study revealed that STDMS is optimal for the detection of fetal DS in pregnant women aged under 35.For individual women,if economic condition permits,STFMS is the best choice,while for women aged above 35,STTMS is the best choice in this regard.
基金Hunan Provincial Natural Science Foundation Under Grant No.02JJY2085
文摘This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homogenized initial system method （HISM）. In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.
文摘In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.
基金The NSF(0611005)of Jiangxi Province and the SF(2007293)of Jiangxi Provincial Education Department.
文摘In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework.
文摘L1 and L2 acquisition, in some respects, are similar. Language development in children goes hand in hand with physical and cognitive development. Children learn their first language by imitation, but not always and not only by imitation. There seems to be some "innate capacities" that make children start to speak at the same time they do and in the way they do it. Adults learning a second language usually are controlled more by their motivation. But language input is important for both L1 and L2 acquisition. Though there are differences between CL1 and between CL2 and AL2, the way in which these learners acquire some of the grammatical morphemes is similar. This, together with some other evidence, shows that it is not only children who can acquire language. Adults can also acquire a language. But when adults acquire a language, they should also learn it. Some of the ways in which children acquire their language can be used as a model for L2 acquisition, even for Chinese students whose language is unrelated to English and whose culture is different. Learning the culture of the English-speaking countries will benefit the learning of the language. Like children, listening should also be well in advance of speaking in L2 acquisition. To train listening comprehension skills, Asher’s TPR approach proves more effective. TPR approach is at the moment limited to the beginning stage only. In order for students to gain all the five skills in a second language learning, namely, listening, speaking, reading, writing, and interpreting/translating, other methods should be used at the same time, or at later stages.
基金supported by the National Natural Science Foundation of China(Grants 11472161,11102102,and 91130017)the Independent Innovation Foundation of Shandong University(Grant 2013ZRYQ002)the Natural Science Foundation of Shandong Province(Grant ZR2014AQ015)
文摘In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.
文摘The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.
文摘In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations.
文摘The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.
文摘We show how to use the Lucas polynomials of the second kind in the solution of a homogeneous linear differential system with constant coefficients, avoiding the Jordan canonical form for the relevant matrix.
