The quench sensitivity of 6063 alloy was investigated via constructing time-temperature-property(TTP) curves by interrupted quenching technique and transmission electron microscopy(TEM) analysis.The results show t...The quench sensitivity of 6063 alloy was investigated via constructing time-temperature-property(TTP) curves by interrupted quenching technique and transmission electron microscopy(TEM) analysis.The results show that the quench sensitivity of 6063 alloy is lower than that of 6061 or 6082 alloy,and the critical temperature ranges from 300 to 410℃ with the nose temperature of about 360℃.From TEM analysis,heterogeneous precipitate β-Mg2Si is prior to nucleate on the(AlxFeySiz) dispersoids in the critical temperature range,and grows up most rapidly at the nose temperature of 360℃.The heterogeneous precipitation leads to a low concentration of solute,which consequently reduces the amount of the strengthening phase β'' after aging.In the large-scale industrial production of 6063 alloy,the cooling rate during quenching should be enhanced as high as possible in the quenching sensitive temperature range(410-300℃) to suppress the heterogeneous precipitation to get optimal mechanical properties,and it should be slowed down properly from the solution temperature to 410℃ and below 300℃ to reduce the residual stress.展开更多
An incremental redundancy hybrid automatic repeat- request (IR-HARQ)scheme based on irregular repeat-accumulate (IRA)codes is proposed. The design of rate compatible punctured IRA codes suitable for an IR-HARQ sch...An incremental redundancy hybrid automatic repeat- request (IR-HARQ)scheme based on irregular repeat-accumulate (IRA)codes is proposed. The design of rate compatible punctured IRA codes suitable for an IR-HARQ scheme is well formulated and efficiently solved by a linear-programming method, along with a one-dimensional approach for density evolution. Compared to IR-HARQ schemes based on turbo codes, simulation shows that the proposed IR-HARQ schemes based on IRA codes may achieve almost the same performance at a block size of 1 024, but better throughput at a block size of 4 096. The advantages of the proposed scheme in implementation, including decoding complexity and parallelism, make it more attractive in practice than the IR-HARQ schemes based on both turbo and LDPC codes.展开更多
The effects of tillage methods on percent surface residue cover remaining and decomposition rates of crop residues were evaluated in this study. The line transect method was used to measure residue cover percentage on...The effects of tillage methods on percent surface residue cover remaining and decomposition rates of crop residues were evaluated in this study. The line transect method was used to measure residue cover percentage on continuous corn ( Zea mays L.) plots under no tillage (NT), conventional tillage (CT), chisel plow (CH), and disk tillage (DT). Samples of rye ( Secale cereale L.) and hairy vetch ( Vicia villosa Roth) were used for residue decomposition study. Results showed that the percentage of residue cover remaining was significantly higher for NT than for CH and DT and that for CT was the lowest (<10%). For the same tillage system, the percent residue cover remaining was significantly higher in the higher fertilizer N rate treatments relative to the lower fertilizer N treatments. Weight losses of rye and vetch residues followed a similar pattern under CT and DT, and they were significantly faster in CT and DT than in NT system. Also, the amounts of residue N remaining during the first 16 weeks were always higher under NT than under CT and DT.展开更多
To promote the performance of the traditional multichannel filter bank which leads to speech quality degradation,an efficient design method of the non-uniform cosine modulated filter bank(CMFB) based on the audiogra...To promote the performance of the traditional multichannel filter bank which leads to speech quality degradation,an efficient design method of the non-uniform cosine modulated filter bank(CMFB) based on the audiogram for digital hearing aids is proposed. First, a low-pass prototype filter is designed by the linear iterative algorithm. Secondly,the uniform CMFB is achieved on the basis of the principle formulas. Then, the adjacent channels of a uniform filter bank which have low or gradual slopes are merged according to the trend of audiogram of the hearing impaired person. Finally,the corresponding non-uniform CMFB is obtained. Simulation results show that the signal processed by the proposed filter bank is similar to the original signal in a time-domain waveform and spectrogram without significant distortion or difference. The speech quality results show that the personal evaluation of speech quality(PESQ) of non-uniform CMFB is 35% higher than that of the traditional design, and the hearing-aid speech quality index(HASQI) increases by about 40%.展开更多
The SMART (System-integrated Modular Advanced ReacTor) which is a 330 MWt advanced integral PWR was developed by the KAERI (Korea Atomic Energy Institute) for electricity generation and seawater desalination. To e...The SMART (System-integrated Modular Advanced ReacTor) which is a 330 MWt advanced integral PWR was developed by the KAERI (Korea Atomic Energy Institute) for electricity generation and seawater desalination. To enhance its safety, the various design concepts were adopted such as the most containing of the RCS (reactor coolant system) components and a PRHRS (passive residual heat removal system). To ensure the safety and performance of the SMART, a thermal hydraulic evaluation and safety analysis are performed by the TASS/SMR-S code. It uses a one dimensional node/path modeling and point kinetics for the core power simulation. The code also has specific models reflecting the design features of the SMART such as a helical tube and PRHRS heat transfer models. In this study, the validation of the core heat transfer model in the TASS/SMR-S code on the steady conditions was performed with the Bennett's heated tube tests and THTF (thermal hydraulic test facility) experiment. From the results of the TASS/SMR-S code calculation, the CHF (critical heat flux) point and the fuel rod surface temperature were predicted conservatively compared to the test results.展开更多
The earthquake stress-drop values of two sequences were accurately calculated after taking away the effects due to regional earthquake anelastic attenuation and station site response,using waveform data and seismic ph...The earthquake stress-drop values of two sequences were accurately calculated after taking away the effects due to regional earthquake anelastic attenuation and station site response,using waveform data and seismic phase data of sequences of the Jinggu M_S6. 6,and Ludian M_S6. 5 earthquakes in Yunnan. These results show that the stress drop with magnitude increases within the scope of this study of magnitude. After eliminating the influence of the magnitude,the average value of stress-drop in the Jinggu sequence is higher than that of the Ludian sequence at the same magnitude range. This may be related to the stress state in different regions. In terms of the changes of time and space of stress-drop,before M_S5. 8 strong aftershock,the stress-drop is "slowing down-turning up-keeping a high value"after the mainshock,meanwhile,almost all of the abnormally high stress drop value is distributed around the M_S5. 8 strong aftershock, showing that the stress environment in the region was increasing after the mainshock. And after the M_S5. 9 strong aftershock,stress-drop rapidly declines to a relatively stable state,meanwhile,the high value of stress-drop is distributed around the strong aftershock,showing that the regional tectonic stress gets more fully release,its stress environment begins to rapidly decrease.For the Ludian sequence without a strong aftershock occurring,the average value of stress drop is lower than that of the Jinggu earthquake sequence at the same magnitude range,while at the same time,the stress-drop of the aftershock sequence almost hasn't changed much. In the time after the mainshock,combined with the release characteristics of the main energy,the stress in the region is excessively released,the subsequent stress in the region gradually returns to normal. This may be the reason why the activity of Ludianaftershocks significantly was weaker and subsequently there were no strong aftershocks occurred.展开更多
Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbo...Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation展开更多
This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified var...This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method (MVIM) coupled with auxiliary parameter is used to cope with the complexity of the model which subse- quently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the pro- posed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He's polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm.展开更多
The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find inter...The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.展开更多
Using the single particle states and the residual interaction derived from the relativistic point-coupling model with the PC-F1 parameter set,the second-order core polarization corrections to nuclear magnetic moments ...Using the single particle states and the residual interaction derived from the relativistic point-coupling model with the PC-F1 parameter set,the second-order core polarization corrections to nuclear magnetic moments of LS closed shell nuclei ±1 nucleon with A = 15,17,39 and 41 are studied and compared with previous non-relativistic results.It is found that the second-order corrections are significant.With these corrections,the isovector magnetic moments of the concerned nuclei are well reproduced,especially those for A = 17 and A = 41.展开更多
Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg(X)|deg(Y)and ...Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg(X)|deg(Y)and codim Y Y ≥codimPN X,where Y is the linear span of Y.These bounds are sharp.As an application,we classify smooth projective n-dimensional quadratic varieties swept out by m≥[n/2]+1 dimensional quadrics passing through one point.展开更多
Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This ...Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.展开更多
This article proposes a simple nonparametric estimator of quantile residual lifetime function under left-truncated and right-censored data. The asymptotic consistency and normality of this estimator are proved and the...This article proposes a simple nonparametric estimator of quantile residual lifetime function under left-truncated and right-censored data. The asymptotic consistency and normality of this estimator are proved and the variance expression is calculated. Two bootstrap procedures are employed in the simulation study,where the latter bootstrap from Zeng and Lin(2008) is 4000 times faster than the former naive one, and the numerical results in both methods show that our estimating approach works well. A real data example is used to illustrate its application.展开更多
This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found frui...This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time series.The results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.展开更多
文摘The quench sensitivity of 6063 alloy was investigated via constructing time-temperature-property(TTP) curves by interrupted quenching technique and transmission electron microscopy(TEM) analysis.The results show that the quench sensitivity of 6063 alloy is lower than that of 6061 or 6082 alloy,and the critical temperature ranges from 300 to 410℃ with the nose temperature of about 360℃.From TEM analysis,heterogeneous precipitate β-Mg2Si is prior to nucleate on the(AlxFeySiz) dispersoids in the critical temperature range,and grows up most rapidly at the nose temperature of 360℃.The heterogeneous precipitation leads to a low concentration of solute,which consequently reduces the amount of the strengthening phase β'' after aging.In the large-scale industrial production of 6063 alloy,the cooling rate during quenching should be enhanced as high as possible in the quenching sensitive temperature range(410-300℃) to suppress the heterogeneous precipitation to get optimal mechanical properties,and it should be slowed down properly from the solution temperature to 410℃ and below 300℃ to reduce the residual stress.
基金The National High Technology Research and Develop-ment Program of China(863Program)(No.2006AA01Z263)the National Natural Science Foundation of China(No.60672081)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK2006502)the Open Research Fund of National Mobile Communications Research Laboratory of Southeast Uni-versity(No.2008N01)
文摘An incremental redundancy hybrid automatic repeat- request (IR-HARQ)scheme based on irregular repeat-accumulate (IRA)codes is proposed. The design of rate compatible punctured IRA codes suitable for an IR-HARQ scheme is well formulated and efficiently solved by a linear-programming method, along with a one-dimensional approach for density evolution. Compared to IR-HARQ schemes based on turbo codes, simulation shows that the proposed IR-HARQ schemes based on IRA codes may achieve almost the same performance at a block size of 1 024, but better throughput at a block size of 4 096. The advantages of the proposed scheme in implementation, including decoding complexity and parallelism, make it more attractive in practice than the IR-HARQ schemes based on both turbo and LDPC codes.
文摘The effects of tillage methods on percent surface residue cover remaining and decomposition rates of crop residues were evaluated in this study. The line transect method was used to measure residue cover percentage on continuous corn ( Zea mays L.) plots under no tillage (NT), conventional tillage (CT), chisel plow (CH), and disk tillage (DT). Samples of rye ( Secale cereale L.) and hairy vetch ( Vicia villosa Roth) were used for residue decomposition study. Results showed that the percentage of residue cover remaining was significantly higher for NT than for CH and DT and that for CT was the lowest (<10%). For the same tillage system, the percent residue cover remaining was significantly higher in the higher fertilizer N rate treatments relative to the lower fertilizer N treatments. Weight losses of rye and vetch residues followed a similar pattern under CT and DT, and they were significantly faster in CT and DT than in NT system. Also, the amounts of residue N remaining during the first 16 weeks were always higher under NT than under CT and DT.
基金The National Natural Science Foundation of China(No.61375028,61673108)China Postdoctoral Science Foundation(No.2016M601696)+2 种基金Qing Lan Projectthe Program for Special Talent in Six Fields of Jiangsu Province(No.2016-DZXX-023)Jiangsu Planned Projects for Postdoctoral Research Funds(No.1601011B)
文摘To promote the performance of the traditional multichannel filter bank which leads to speech quality degradation,an efficient design method of the non-uniform cosine modulated filter bank(CMFB) based on the audiogram for digital hearing aids is proposed. First, a low-pass prototype filter is designed by the linear iterative algorithm. Secondly,the uniform CMFB is achieved on the basis of the principle formulas. Then, the adjacent channels of a uniform filter bank which have low or gradual slopes are merged according to the trend of audiogram of the hearing impaired person. Finally,the corresponding non-uniform CMFB is obtained. Simulation results show that the signal processed by the proposed filter bank is similar to the original signal in a time-domain waveform and spectrogram without significant distortion or difference. The speech quality results show that the personal evaluation of speech quality(PESQ) of non-uniform CMFB is 35% higher than that of the traditional design, and the hearing-aid speech quality index(HASQI) increases by about 40%.
文摘The SMART (System-integrated Modular Advanced ReacTor) which is a 330 MWt advanced integral PWR was developed by the KAERI (Korea Atomic Energy Institute) for electricity generation and seawater desalination. To enhance its safety, the various design concepts were adopted such as the most containing of the RCS (reactor coolant system) components and a PRHRS (passive residual heat removal system). To ensure the safety and performance of the SMART, a thermal hydraulic evaluation and safety analysis are performed by the TASS/SMR-S code. It uses a one dimensional node/path modeling and point kinetics for the core power simulation. The code also has specific models reflecting the design features of the SMART such as a helical tube and PRHRS heat transfer models. In this study, the validation of the core heat transfer model in the TASS/SMR-S code on the steady conditions was performed with the Bennett's heated tube tests and THTF (thermal hydraulic test facility) experiment. From the results of the TASS/SMR-S code calculation, the CHF (critical heat flux) point and the fuel rod surface temperature were predicted conservatively compared to the test results.
基金supported by the“Catalogue of Earthquake Sequence in the Chinese Mainland”of Department of Monitoring and Prediction,China Earthquake Administration(1740503502)
文摘The earthquake stress-drop values of two sequences were accurately calculated after taking away the effects due to regional earthquake anelastic attenuation and station site response,using waveform data and seismic phase data of sequences of the Jinggu M_S6. 6,and Ludian M_S6. 5 earthquakes in Yunnan. These results show that the stress drop with magnitude increases within the scope of this study of magnitude. After eliminating the influence of the magnitude,the average value of stress-drop in the Jinggu sequence is higher than that of the Ludian sequence at the same magnitude range. This may be related to the stress state in different regions. In terms of the changes of time and space of stress-drop,before M_S5. 8 strong aftershock,the stress-drop is "slowing down-turning up-keeping a high value"after the mainshock,meanwhile,almost all of the abnormally high stress drop value is distributed around the M_S5. 8 strong aftershock, showing that the stress environment in the region was increasing after the mainshock. And after the M_S5. 9 strong aftershock,stress-drop rapidly declines to a relatively stable state,meanwhile,the high value of stress-drop is distributed around the strong aftershock,showing that the regional tectonic stress gets more fully release,its stress environment begins to rapidly decrease.For the Ludian sequence without a strong aftershock occurring,the average value of stress drop is lower than that of the Jinggu earthquake sequence at the same magnitude range,while at the same time,the stress-drop of the aftershock sequence almost hasn't changed much. In the time after the mainshock,combined with the release characteristics of the main energy,the stress in the region is excessively released,the subsequent stress in the region gradually returns to normal. This may be the reason why the activity of Ludianaftershocks significantly was weaker and subsequently there were no strong aftershocks occurred.
基金Supported by National Natural Science Foundation of China under Grant No.10926057 Foundation of Zhejiang Educational Committee under Grant No.Y200908784
文摘Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation
文摘This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method (MVIM) coupled with auxiliary parameter is used to cope with the complexity of the model which subse- quently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the pro- posed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He's polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm.
基金Supported by the National Natural Science Foundations of China under Grant No.11175092Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148K.C.Wong Magna Fund in Ningbo University
文摘The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.
基金supported by the Major State Basic Research Developing Program (Grant No.2007CB815000)the National Natural Science Foundation of China(Grant Nos.10775004,10720003, 10947013, 10975008, 10975007, and 11005069)the Southwest University Initial Research Foundation Grant to Doctor (Grant No.SWU109011)
文摘Using the single particle states and the residual interaction derived from the relativistic point-coupling model with the PC-F1 parameter set,the second-order core polarization corrections to nuclear magnetic moments of LS closed shell nuclei ±1 nucleon with A = 15,17,39 and 41 are studied and compared with previous non-relativistic results.It is found that the second-order corrections are significant.With these corrections,the isovector magnetic moments of the concerned nuclei are well reproduced,especially those for A = 17 and A = 41.
文摘Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg(X)|deg(Y)and codim Y Y ≥codimPN X,where Y is the linear span of Y.These bounds are sharp.As an application,we classify smooth projective n-dimensional quadratic varieties swept out by m≥[n/2]+1 dimensional quadrics passing through one point.
基金Supported by the Key Foundation of Anhui Education Bureau under Grant No.KJ2013A028the 211 Project of Anhhui University under Grant No.J18520104+2 种基金Scientific Training Project for University StudentsNational Natural Science Foundation of China under Grant Nos.11471015,11571016Natural Science Foundation of Anhui Province under Grant No.1408085MA02
文摘Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.
基金supported by National Natural Science Foundation of China(Grant No.71271128)the State Key Program of National Natural Science Foundation of China(Grant No.71331006)+2 种基金NCMIS and Shanghai University of Finance and Economics through Project 211 Phase IVShanghai Firstclass Discipline A,Outstanding Ph D Dissertation Cultivation Funds of Shanghai University of Finance and EconomicsGraduate Education Innovation Funds of Shanghai University of Finance and Economics(Grant No.CXJJ-2011-438)
文摘This article proposes a simple nonparametric estimator of quantile residual lifetime function under left-truncated and right-censored data. The asymptotic consistency and normality of this estimator are proved and the variance expression is calculated. Two bootstrap procedures are employed in the simulation study,where the latter bootstrap from Zeng and Lin(2008) is 4000 times faster than the former naive one, and the numerical results in both methods show that our estimating approach works well. A real data example is used to illustrate its application.
文摘This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time series.The results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.