Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a ...Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a few examples are given as applications.展开更多
In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a me...In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.展开更多
The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimati...The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.展开更多
In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expre...In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.展开更多
To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a powe...To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.展开更多
Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help...Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.展开更多
The Raman interaction of a trapped ultracold ion with two traveling wave lasers is studied analytically by series expansion technique without the need of rotating wave approximation and the limitations of both the Lam...The Raman interaction of a trapped ultracold ion with two traveling wave lasers is studied analytically by series expansion technique without the need of rotating wave approximation and the limitations of both the Lamb–Dicke limit and the weak excitation regime. As an example, a scheme for the preparation of Schr?dinger-cat states in such a process is proposed beyond the weak excitation regime.展开更多
By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Comp...By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain （FDTD） based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity.展开更多
For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind o...For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.展开更多
This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (t...This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.展开更多
Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact ...Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.展开更多
This paper addresses a digital controller for a real time magnetic levitation system using series expansion of pulse transfer function, which achieves desired closed loop response. The proposed digital controller desi...This paper addresses a digital controller for a real time magnetic levitation system using series expansion of pulse transfer function, which achieves desired closed loop response. The proposed digital controller designed, based on series expansion of pulse transfer function by solving a linear equation using the method of least squares, which improves the transient performance and step tracking capability of the compensated system. The designed algorithm used for the control input is not iterative, so the calculation is very fast. The proposed control scheme has successfully applied on maglev system and also validated through the simulation and hardware experimental results.展开更多
In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the br...In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.展开更多
Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functio...Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup><em>x</em> </sup>)</span> . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(<em>i</em> + <em>x</em>)</span> are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.展开更多
The magnetic properties of （Cox Fe1-x）A （Zn1-x Fe1＋x）B O4 are studied using mean-field theory and the probability distribution law to obtain the saturation magnetization, the coercive field, the critical temperat...The magnetic properties of （Cox Fe1-x）A （Zn1-x Fe1＋x）B O4 are studied using mean-field theory and the probability distribution law to obtain the saturation magnetization, the coercive field, the critical temperature, and the exchange interactions with different values of D （nm） and x. High-temperature series expansions （HTSEs） combined with the Pade approximant are used to calculate the critical temperature of （CoxFe1-x）A（Znl-xFe1＋x）BO4, and the critical exponent associated with magnetic susceptibility is obtained.展开更多
How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was der...How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.展开更多
This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, ...This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employ- ing the Fourier-Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential func- tion and the modal coordinates of wave height. Based on the B ernoulli-Euler beam theory and the D＇Alembert＇s prin- ciple, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordi- nate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the cou- pling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange＇s equations in terms of quasi-coordinates. Lastly, the cou-piing dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.展开更多
Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is e...Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is essential and critical. In this paper, we have solved two problems regarding to how to determine the position relation between points and curves without revealing any private information. Two protocols have been proposed in order to solve the problems in different conditions. In addition, some building blocks have been developed, such as scalar product protocol, so that we can take advantage of them to settle the privacy-preserving computational geometry problems which are a kind of special secure multi-party computation problems. Moreover, oblivious transfer and power series expansion serve as significant parts in our protocols. Analyses and proofs have also been given to argue our conclusion.展开更多
Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. The...Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.展开更多
As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial h...As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.展开更多
文摘Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a few examples are given as applications.
文摘In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.
基金supported by The National Natural Science Foundation (Grant Nos.41874126, 42004114)the Key Research and development project of Jiangxi Province in China (Grant No.20192ACB80006)+1 种基金the Natural Science Foundation of Jiangxi Province (Grant Nos. 20202BAB211010, 20212BAB203005)Open Foundation of State Key Laboratory of Nuclear Resources and Environment (2020NRE25)
文摘The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.
基金The first author,Mrs.Yan Hong,was partially supported by the Natural Science Foundation of Inner Mongolia(Grant No.2019MS01007)by the Science Research Fund of Inner Mongolia University for Nationalities(Grant No.NMDBY15019)by the Foun-dation of the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZY19157 and NJZY20119)in China。
文摘In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.
基金Project supported by the National Natural Science Foundation of China (No.50425926)
文摘To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.
文摘Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.
文摘The Raman interaction of a trapped ultracold ion with two traveling wave lasers is studied analytically by series expansion technique without the need of rotating wave approximation and the limitations of both the Lamb–Dicke limit and the weak excitation regime. As an example, a scheme for the preparation of Schr?dinger-cat states in such a process is proposed beyond the weak excitation regime.
文摘By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain （FDTD） based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity.
文摘For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.
文摘This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.
文摘Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.
文摘This paper addresses a digital controller for a real time magnetic levitation system using series expansion of pulse transfer function, which achieves desired closed loop response. The proposed digital controller designed, based on series expansion of pulse transfer function by solving a linear equation using the method of least squares, which improves the transient performance and step tracking capability of the compensated system. The designed algorithm used for the control input is not iterative, so the calculation is very fast. The proposed control scheme has successfully applied on maglev system and also validated through the simulation and hardware experimental results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12274046,11874094,and 12147102)Chongqing Natural Science Foundation(Grant No.CSTB2022NSCQ-JQX0018)Fundamental Research Funds for the Central Universities(Grant No.2021CDJZYJH-003).
文摘In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.
文摘Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup><em>x</em> </sup>)</span> . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(<em>i</em> + <em>x</em>)</span> are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.
文摘The magnetic properties of （Cox Fe1-x）A （Zn1-x Fe1＋x）B O4 are studied using mean-field theory and the probability distribution law to obtain the saturation magnetization, the coercive field, the critical temperature, and the exchange interactions with different values of D （nm） and x. High-temperature series expansions （HTSEs） combined with the Pade approximant are used to calculate the critical temperature of （CoxFe1-x）A（Znl-xFe1＋x）BO4, and the critical exponent associated with magnetic susceptibility is obtained.
基金This work was financially supported by Key Program of the National Natural Science Foundation of China(No.50639020)the National High Technology Research and Development Program of China(863Program)(No.2006AA09Z332)
文摘How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.
基金project was supported by the National Natural Science Foundation of China (Grants 11472041, 11302244, 11532002)Guangxi Natural Science Foundation (2015GXNSFBA 139013)
文摘This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employ- ing the Fourier-Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential func- tion and the modal coordinates of wave height. Based on the B ernoulli-Euler beam theory and the D＇Alembert＇s prin- ciple, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordi- nate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the cou- pling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange＇s equations in terms of quasi-coordinates. Lastly, the cou-piing dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.
基金Supported by the National Natural Science Foundation of China (No. 61070189, 60673065)the National High Technology Development Program (No. 2008AA01Z419)
文摘Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is essential and critical. In this paper, we have solved two problems regarding to how to determine the position relation between points and curves without revealing any private information. Two protocols have been proposed in order to solve the problems in different conditions. In addition, some building blocks have been developed, such as scalar product protocol, so that we can take advantage of them to settle the privacy-preserving computational geometry problems which are a kind of special secure multi-party computation problems. Moreover, oblivious transfer and power series expansion serve as significant parts in our protocols. Analyses and proofs have also been given to argue our conclusion.
基金Project supported by the National Natural Science Foundation of China(Nos.11672223,11402187,and 51178390)the China Postdoctoral Science Foundation(No.2014M560762)the Fundamental Research Funds for the Central Universities of China(No.xjj2015131)
文摘Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.
基金This research was supported by the National Natural Science Foundation of China(41701499)the Sichuan Science and Technology Program(2018GZ0265)+3 种基金the Geomatics Technology and Application Key Laboratory of Qinghai Province,China(QHDX-2018-07)the Major Scientific and Technological Special Program of Sichuan Province,China(2018SZDZX0027)the Key Research and Development Program of Sichuan Province,China(2018SZ027,2019-YF09-00081-SN)Technology Planning Project of Guangdong Province(NO.2018B020207012)。
文摘As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.
