In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in ...In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in this paper,we prove that rooted products of some trees preserve real-rootedness of independence polynomials.In particular,we can obtain that their independence polynomials are unimodal and log-concave.展开更多
Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three d...Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.展开更多
Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting ...Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.展开更多
GNSS time series analysis provides an effective method for research on the earth's surface deformation,and it can be divided into two parts,deterministic models and stochastic models.The former part can be achieve...GNSS time series analysis provides an effective method for research on the earth's surface deformation,and it can be divided into two parts,deterministic models and stochastic models.The former part can be achieved by several parameters,such as polynomial terms,periodic terms,offsets,and post-seismic models.The latter contains some stochastic noises,which can be affected by detecting the former parameters.If there are not enough parameters assumed,modeling errors will occur and adversely affect the analysis results.In this study,we propose a processing strategy in which the commonly-used 1-order of the polynomial term can be replaced with different orders for better fitting GNSS time series of the Crustal Movement Network of China(CMONOC)stations.Initially,we use the Bayesian Information Criterion(BIC)to identify the best order within the range of 1-4 during the fitting process using the white noise plus power-law noise(WN+PL)model.Then,we compare the 1-order and the optimal order on the effect of deterministic models in GNSS time series,including the velocity and its uncertainty,amplitudes,and initial phases of the annual signals.The results indicate that the first-order polynomial in the GNSS time series is not the primary factor.The root mean square(RMS)reduction rates of almost all station components are positive,which means the new fitting of optimal-order polynomial helps to reduce the RMS of residual series.Most stations maintain the velocity difference(VD)within ±1 mm/yr,with percentages of 85.6%,81.9%and 63.4%in the North,East,and Up components,respectively.As for annual signals,the numbers of amplitude difference(AD)remained at ±0.2 mm are 242,239,and 200 in three components,accounting for 99.6%,98.4%,and 82.3%,respectively.This finding reminds us that the detection of the optimal-order polynomial is necessary when we aim to acquire an accurate understanding of the crustal movement features.展开更多
Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems,including electronic cooling devices and automotive components,owing to t...Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems,including electronic cooling devices and automotive components,owing to their adaptable design.Furthermore,spine fins are introduced to improve performance in applications such as automotive radiators.They can be shaped in different ways and constructed from a collection of materials.Inspired by this,the present model examines the effects of internal heat generation and radiation-convection on the thermal distribution in a wetted convex-shaped spine fin.Using dimensionless terms,the proposed fin model involving a governing nonlinear ordinary differential equation(ODE)is transformed into a dimensionless form.The study uses the operational matrix with the Charlier polynomial collocation method(OMCCM)to ensure precise and computationally efficient numerical solutions for the dimensionless equation.In order to aid in the analysis of thermal performance,the importance of major parameters on the temperature profile is graphically illustrated.The main outcome of the study reveals that as the radiation-conductive,wet,and convective-conductive parameters increase,the heat transfer rate progressively improves.Conversely,the ambient temperature and internal heat generation parameters show an inverse relationship.展开更多
Virtual coupling is a novel technology that enables trains to run closely together without physical connections through communication and automation systems.The paper addresses an adaptive polynomial approximation alg...Virtual coupling is a novel technology that enables trains to run closely together without physical connections through communication and automation systems.The paper addresses an adaptive polynomial approximation algorithm for the cooperative control of high-speed trains(HSTs)under virtual coupling.It aims to solve the cooperative tracking control problem of HST formation operations under various scenarios,including known and unknown parameters.To enable the HST formation system to achieve cooperative operation while ensuring an appropriate spacing distance,the tracking errors of displacement and speed throughout the entire operation converge to zero.The proposed control strategy focuses on adopting polynomial approximation to handle unknown parameters,which are estimated via adaptive laws.Additionally,the unknown parameters of the HSTs are estimated online through adaptive laws.Experimental results verify the effectiveness of this method.展开更多
The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first dis...The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.展开更多
This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We c...This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We consider both focusing and defocusing nonlinearities,with exponents of the nonlinearityσ∈[0,2)andσ∈[0,∞),and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method.In the focusing case,our result generalizes the earlier results in[12],whereσ=1.展开更多
This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-...This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.展开更多
As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road ...As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H_(2) robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H_(2) robust controller not only provides better performance in terms of vehicle ride comfort compared to general H_(2) robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.展开更多
This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions.Unlike traditional Merkle trees,the Verkle tree sig...This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions.Unlike traditional Merkle trees,the Verkle tree significantly reduces signature size by utilizing polynomial and vector commitments.Compact proofs also accelerate the verification process,reducing computational overhead,which makes Verkle trees particularly useful.The study proposes a new approach based on a non-positional polynomial notation(NPN)employing the Chinese Remainder Theorem(CRT).CRT enables efficient data representation and verification by decomposing data into smaller,indepen-dent components,simplifying computations,reducing overhead,and enhancing scalability.This technique facilitates parallel data processing,which is especially advantageous in cryptographic applications such as commitment and proof construction in Verkle trees,as well as in systems with constrained computational resources.Theoretical foundations of the approach,its advantages,and practical implementation aspects are explored,including resistance to potential attacks,application domains,and a comparative analysis with existing methods based on well-known parameters and characteristics.An analysis of potential attacks and vulnerabilities,including greatest common divisor(GCD)attacks,approximate multiple attacks(LLL lattice-based),brute-force search for irreducible polynomials,and the estimation of their total number,indicates that no vulnerabilities have been identified in the proposed method thus far.Furthermore,the study demonstrates that integrating CRT with Verkle trees ensures high scalability,making this approach promising for blockchain systems and other distributed systems requiring compact and efficient proofs.展开更多
In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) i...In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.展开更多
Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limi...Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limitation in the accuracy of the field profile restitution.Thus,it can deal with the guided waves in layered sandwich only when the material properties of adjacent layers do not change significantly.Despite the great efforts regarding this issue in the literature,there remain open questions.One of them is:“what is the exact threshold of contrasting material properties of adjacent layers for which this polynomial method cannot correctly restitute the roots of guided waves?”We investigated this numerical issue using the calculated guided phase velocities in 0°/φ/0°-carbon fibre reinforced plastics(CFRP)sandwich plates with gradually increasing angleφ.Then,we approached this numerical problem by varying the middle layer thickness h90°for the 0°/90°/0°-CFRP sandwich structure,and we proposed an exact thickness threshold of the middle layer for the Legendre polynomial method limitations.We showed that the polynomial method fails to calculate the quasi-symmetric Lamb mode in 0°/φ/0°-CFRP whenφ>25°.Moreover,we introduced a new Lamb mode so-called minimum-group-velocity that has never been addressed in literature.展开更多
A novel suppression method of the phase noise is proposed to reduce the negative impacts of phase noise in coherent optical orthogonal frequency division multiplexing(CO-OFDM)systems.The method integrates the sub-symb...A novel suppression method of the phase noise is proposed to reduce the negative impacts of phase noise in coherent optical orthogonal frequency division multiplexing(CO-OFDM)systems.The method integrates the sub-symbol second-order polynomial interpolation(SSPI)with cubature Kalman filter(CKF)to improve the precision and effectiveness of the data processing through using a three-stage processing approach of phase noise.First of all,the phase noise values in OFDM symbols are calculated by using pilot symbols.Then,second-order Newton interpolation(SNI)is used in second-order interpolation to acquire precise noise estimation.Afterwards,every OFDM symbol is partitioned into several sub-symbols,and second-order polynomial interpolation(SPI)is utilized in the time domain to enhance suppression accuracy and time resolution.Ultimately,CKF is employed to suppress the residual phase noise.The simulation results show that this method significantly suppresses the impact of the phase noise on the system,and the error floors can be decreased at the condition of 16 quadrature amplitude modulation(16QAM)and 32QAM.The proposed method can greatly improve the CO-OFDM system's ability to tolerate the wider laser linewidth.This method,compared to the linear interpolation sub-symbol common phase error compensation(LI-SCPEC)and Lagrange interpolation and extended Kalman filter(LRI-EKF)algorithms,has superior suppression effect.展开更多
To reduce the number of digital predistortion coefficients, a step memory polynomial （SMP）predistorter is presented. The number of predistortion coefficients is decreased by adjusting the maximum nonlinear order for...To reduce the number of digital predistortion coefficients, a step memory polynomial （SMP）predistorter is presented. The number of predistortion coefficients is decreased by adjusting the maximum nonlinear order for different memory orders in the traditional memory polynomial （MP）predistorter. The proposed SNIP predistorter is identified by an offline learning structure on which the coefficients can be extracted directly from the sampled input and output of a PA. Simulation results show that the SMP predistorter is not tied to a particular PA model and is, therefore, robust. The effectiveness of the SMP predistorter is demonstrated by simulations and experiments on an MP model, a parallel Wiener model, a Wiener-Hammerstein model, a sparsedelay memory polynomial model and a real PA which is fabricated based on the Freescale LDMOSFET MRF21030. Compared with the traditional MP predistorter, the SMP predistorter can reduce the number of coefficients by 60%.展开更多
A two-dimensional （2-D） polynomial regression model is set up to approximate the time-frequency response of slowly time-varying orthogonal frequency-division multiplexing （OFDM） systems. With this model the estima...A two-dimensional （2-D） polynomial regression model is set up to approximate the time-frequency response of slowly time-varying orthogonal frequency-division multiplexing （OFDM） systems. With this model the estimation of the OFDM time-frequency response is turned into the optimization of some time-invariant model parameters. A new algorithm based on the expectation-maximization （EM） method is proposed to obtain the maximum-likelihood （ML） estimation of the polynomial model parameters over the 2-D observed data. At the same time, in order to reduce the complexity and avoid the computation instability, a novel recursive approach （RPEMTO） is given to calculate the values of the parameters. It is further shown that this 2-D polynomial EM-based algorithm for time-varying OFDM （PEMTO） can be simplified mathematically to handle the one-dimensional sequential estimation. Simulations illustrate that the proposed algorithms achieve a lower bit error rate （BER） than other blind algorithms.展开更多
The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with ...The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.展开更多
We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To...We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To obtain the pure anomaly field,the main field and the induced field of the ionospheric and magnetospheric fields were removed from measured data.We also compared the SS model anomalies and the data obtained with Kriging interpolation（KI）.The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0-1990.0 to 2000.0.The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity.The anomalous distributions in the X-,Y-,and Z-direction and F are mainly negative.The 3DTP model anomalies suggest that the intensity in the X-direction increases from-100 nT to 0 nT with longitude,whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative.The intensity in the Z-direction and F are very similar and in most areas it is about-50 nT and higher in western Tibet.The SS model anomalies overall reflect the actual distribution of the magnetic field anomalies;however,because of the uneven distribution of measurements,it yields several big anomalies.Owing to the added altitude term,the 3DTP model offers higher precision and is consistent with KI.展开更多
Based on the frequency domain training sequences, the polynomial-based carrier frequency offset （CFO） estimation in multiple-input multiple-output （ MIMO ） orthogonal frequency division multiplexing （ OFDM ） sys...Based on the frequency domain training sequences, the polynomial-based carrier frequency offset （CFO） estimation in multiple-input multiple-output （ MIMO ） orthogonal frequency division multiplexing （ OFDM ） systems is extensively investigated. By designing the training sequences to meet certain conditions and exploiting the Hermitian and real symmetric properties of the corresponding matrices, it is found that the roots of the polynomials corresponding to the cost functions are pairwise and that both meger CFO and fractional CFO can be estimated by the direct polynomial rooting approach. By analyzing the polynomials corresponding to the cost functions and their derivatives, it is shown that they have a common polynomial factor and the former can be expressed in a quadratic form of the common polynomial factor. Analytical results further reveal that the derivative polynomial rooting approach is equivalent to the direct one in estimation at the same signal-to-noise ratio（SNR） value and that the latter is superior to the former in complexity. Simulation results agree well with analytical results.展开更多
基金supported by the National Natural Science Foundation of China(No.12271527)。
文摘In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in this paper,we prove that rooted products of some trees preserve real-rootedness of independence polynomials.In particular,we can obtain that their independence polynomials are unimodal and log-concave.
基金Supported by the National Natural Science Foundation of China (Grant No.12161074)the Talent Introduction Research Foundation of Suqian University (Grant No.106-CK00042/028)+1 种基金Suqian Sci&Tech Program (Grant No.M202206)Sponsored by Qing Lan Project of Jiangsu Province and Suqian Talent Xiongying Plan of Suqian。
文摘Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.
基金Dalian Municipal Natural Science Foundation under Grant No.2019RD01。
文摘Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.
基金supported by the National Natural Science Foundation of China(Grant Nos.42404017,42122025 and 42174030).
文摘GNSS time series analysis provides an effective method for research on the earth's surface deformation,and it can be divided into two parts,deterministic models and stochastic models.The former part can be achieved by several parameters,such as polynomial terms,periodic terms,offsets,and post-seismic models.The latter contains some stochastic noises,which can be affected by detecting the former parameters.If there are not enough parameters assumed,modeling errors will occur and adversely affect the analysis results.In this study,we propose a processing strategy in which the commonly-used 1-order of the polynomial term can be replaced with different orders for better fitting GNSS time series of the Crustal Movement Network of China(CMONOC)stations.Initially,we use the Bayesian Information Criterion(BIC)to identify the best order within the range of 1-4 during the fitting process using the white noise plus power-law noise(WN+PL)model.Then,we compare the 1-order and the optimal order on the effect of deterministic models in GNSS time series,including the velocity and its uncertainty,amplitudes,and initial phases of the annual signals.The results indicate that the first-order polynomial in the GNSS time series is not the primary factor.The root mean square(RMS)reduction rates of almost all station components are positive,which means the new fitting of optimal-order polynomial helps to reduce the RMS of residual series.Most stations maintain the velocity difference(VD)within ±1 mm/yr,with percentages of 85.6%,81.9%and 63.4%in the North,East,and Up components,respectively.As for annual signals,the numbers of amplitude difference(AD)remained at ±0.2 mm are 242,239,and 200 in three components,accounting for 99.6%,98.4%,and 82.3%,respectively.This finding reminds us that the detection of the optimal-order polynomial is necessary when we aim to acquire an accurate understanding of the crustal movement features.
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/308/46。
文摘Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems,including electronic cooling devices and automotive components,owing to their adaptable design.Furthermore,spine fins are introduced to improve performance in applications such as automotive radiators.They can be shaped in different ways and constructed from a collection of materials.Inspired by this,the present model examines the effects of internal heat generation and radiation-convection on the thermal distribution in a wetted convex-shaped spine fin.Using dimensionless terms,the proposed fin model involving a governing nonlinear ordinary differential equation(ODE)is transformed into a dimensionless form.The study uses the operational matrix with the Charlier polynomial collocation method(OMCCM)to ensure precise and computationally efficient numerical solutions for the dimensionless equation.In order to aid in the analysis of thermal performance,the importance of major parameters on the temperature profile is graphically illustrated.The main outcome of the study reveals that as the radiation-conductive,wet,and convective-conductive parameters increase,the heat transfer rate progressively improves.Conversely,the ambient temperature and internal heat generation parameters show an inverse relationship.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.62203246 and 62003127)Shandong Provincial Natural Science Foundation(Grant No.ZR2024QF041)the Natural Science Foundation of Hebei Province(Grant No.F2023202060)。
文摘Virtual coupling is a novel technology that enables trains to run closely together without physical connections through communication and automation systems.The paper addresses an adaptive polynomial approximation algorithm for the cooperative control of high-speed trains(HSTs)under virtual coupling.It aims to solve the cooperative tracking control problem of HST formation operations under various scenarios,including known and unknown parameters.To enable the HST formation system to achieve cooperative operation while ensuring an appropriate spacing distance,the tracking errors of displacement and speed throughout the entire operation converge to zero.The proposed control strategy focuses on adopting polynomial approximation to handle unknown parameters,which are estimated via adaptive laws.Additionally,the unknown parameters of the HSTs are estimated online through adaptive laws.Experimental results verify the effectiveness of this method.
基金Supported by the National Natural Science Foundation of China(12271154)the Natural Science Foundation of Hunan Province(2022JJ30234)the Postgraduate Scientific Research Innovation Project of Hunan Province(CX20231032)。
文摘The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.
基金supported by the National Key R&D Program of China(2023YFA1009200)the NSFC(11925102)the Liaoning Revitalization Talents Program(XLYC2202042)。
文摘This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We consider both focusing and defocusing nonlinearities,with exponents of the nonlinearityσ∈[0,2)andσ∈[0,∞),and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method.In the focusing case,our result generalizes the earlier results in[12],whereσ=1.
基金support from the National Natural Science Foundation of China(Grant Nos.52174123&52274222).
文摘This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.
基金Supported by National Natural Science Foundation of China(Grant No.51875256)Open Platform Fund of Human Institute of Technology(Grant No.KFA22009).
文摘As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H_(2) robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H_(2) robust controller not only provides better performance in terms of vehicle ride comfort compared to general H_(2) robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.
基金funded by the Ministry of Science and Higher Education of Kazakhstan and carried out within the framework of the project AP23488112“Development and study of a quantum-resistant digital signature scheme based on a Verkle tree”at the Institute of Information and Computational Technologies.
文摘This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions.Unlike traditional Merkle trees,the Verkle tree significantly reduces signature size by utilizing polynomial and vector commitments.Compact proofs also accelerate the verification process,reducing computational overhead,which makes Verkle trees particularly useful.The study proposes a new approach based on a non-positional polynomial notation(NPN)employing the Chinese Remainder Theorem(CRT).CRT enables efficient data representation and verification by decomposing data into smaller,indepen-dent components,simplifying computations,reducing overhead,and enhancing scalability.This technique facilitates parallel data processing,which is especially advantageous in cryptographic applications such as commitment and proof construction in Verkle trees,as well as in systems with constrained computational resources.Theoretical foundations of the approach,its advantages,and practical implementation aspects are explored,including resistance to potential attacks,application domains,and a comparative analysis with existing methods based on well-known parameters and characteristics.An analysis of potential attacks and vulnerabilities,including greatest common divisor(GCD)attacks,approximate multiple attacks(LLL lattice-based),brute-force search for irreducible polynomials,and the estimation of their total number,indicates that no vulnerabilities have been identified in the proposed method thus far.Furthermore,the study demonstrates that integrating CRT with Verkle trees ensures high scalability,making this approach promising for blockchain systems and other distributed systems requiring compact and efficient proofs.
基金supported by the National Natural Science Foundation of China(12061035)the Research Foundation of Jiangxi Science and Technology Normal University of China(2021QNBJRC003)supported by the Graduate Innovation Fund of Jiangxi Science and Technology Normal University(YC2024-X10).
文摘In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.
基金supported by the National Natural Science Foundation of China(Grant No.12102131).
文摘Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limitation in the accuracy of the field profile restitution.Thus,it can deal with the guided waves in layered sandwich only when the material properties of adjacent layers do not change significantly.Despite the great efforts regarding this issue in the literature,there remain open questions.One of them is:“what is the exact threshold of contrasting material properties of adjacent layers for which this polynomial method cannot correctly restitute the roots of guided waves?”We investigated this numerical issue using the calculated guided phase velocities in 0°/φ/0°-carbon fibre reinforced plastics(CFRP)sandwich plates with gradually increasing angleφ.Then,we approached this numerical problem by varying the middle layer thickness h90°for the 0°/90°/0°-CFRP sandwich structure,and we proposed an exact thickness threshold of the middle layer for the Legendre polynomial method limitations.We showed that the polynomial method fails to calculate the quasi-symmetric Lamb mode in 0°/φ/0°-CFRP whenφ>25°.Moreover,we introduced a new Lamb mode so-called minimum-group-velocity that has never been addressed in literature.
基金supported by the National Natural Science Foundation of China(Nos.U21A20447 and 61971079)。
文摘A novel suppression method of the phase noise is proposed to reduce the negative impacts of phase noise in coherent optical orthogonal frequency division multiplexing(CO-OFDM)systems.The method integrates the sub-symbol second-order polynomial interpolation(SSPI)with cubature Kalman filter(CKF)to improve the precision and effectiveness of the data processing through using a three-stage processing approach of phase noise.First of all,the phase noise values in OFDM symbols are calculated by using pilot symbols.Then,second-order Newton interpolation(SNI)is used in second-order interpolation to acquire precise noise estimation.Afterwards,every OFDM symbol is partitioned into several sub-symbols,and second-order polynomial interpolation(SPI)is utilized in the time domain to enhance suppression accuracy and time resolution.Ultimately,CKF is employed to suppress the residual phase noise.The simulation results show that this method significantly suppresses the impact of the phase noise on the system,and the error floors can be decreased at the condition of 16 quadrature amplitude modulation(16QAM)and 32QAM.The proposed method can greatly improve the CO-OFDM system's ability to tolerate the wider laser linewidth.This method,compared to the linear interpolation sub-symbol common phase error compensation(LI-SCPEC)and Lagrange interpolation and extended Kalman filter(LRI-EKF)algorithms,has superior suppression effect.
基金The National High Technology Research and Development Program of China (863 Program) (No.2008AA01Z211)the Project of Industry-Academia-Research Demonstration Base of Education Ministry of Guangdong Province (No.2007B090200012)
文摘To reduce the number of digital predistortion coefficients, a step memory polynomial （SMP）predistorter is presented. The number of predistortion coefficients is decreased by adjusting the maximum nonlinear order for different memory orders in the traditional memory polynomial （MP）predistorter. The proposed SNIP predistorter is identified by an offline learning structure on which the coefficients can be extracted directly from the sampled input and output of a PA. Simulation results show that the SMP predistorter is not tied to a particular PA model and is, therefore, robust. The effectiveness of the SMP predistorter is demonstrated by simulations and experiments on an MP model, a parallel Wiener model, a Wiener-Hammerstein model, a sparsedelay memory polynomial model and a real PA which is fabricated based on the Freescale LDMOSFET MRF21030. Compared with the traditional MP predistorter, the SMP predistorter can reduce the number of coefficients by 60%.
基金The National Natural Science Foundation of China(No60472026)
文摘A two-dimensional （2-D） polynomial regression model is set up to approximate the time-frequency response of slowly time-varying orthogonal frequency-division multiplexing （OFDM） systems. With this model the estimation of the OFDM time-frequency response is turned into the optimization of some time-invariant model parameters. A new algorithm based on the expectation-maximization （EM） method is proposed to obtain the maximum-likelihood （ML） estimation of the polynomial model parameters over the 2-D observed data. At the same time, in order to reduce the complexity and avoid the computation instability, a novel recursive approach （RPEMTO） is given to calculate the values of the parameters. It is further shown that this 2-D polynomial EM-based algorithm for time-varying OFDM （PEMTO） can be simplified mathematically to handle the one-dimensional sequential estimation. Simulations illustrate that the proposed algorithms achieve a lower bit error rate （BER） than other blind algorithms.
文摘The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.
基金supported by the National Natural Science Foundation of China(No.41404053)Special Project for MeteoScientific Research in the Public Interest(No.GYHY201306073)+1 种基金Natural Science Foundation of Jiangsu Province(No.BK20140994),Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.14KJB170012)Training Program of Innovation and Entrepreneurship for Undergraduates of NUIST(No.201510300178)
文摘We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To obtain the pure anomaly field,the main field and the induced field of the ionospheric and magnetospheric fields were removed from measured data.We also compared the SS model anomalies and the data obtained with Kriging interpolation（KI）.The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0-1990.0 to 2000.0.The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity.The anomalous distributions in the X-,Y-,and Z-direction and F are mainly negative.The 3DTP model anomalies suggest that the intensity in the X-direction increases from-100 nT to 0 nT with longitude,whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative.The intensity in the Z-direction and F are very similar and in most areas it is about-50 nT and higher in western Tibet.The SS model anomalies overall reflect the actual distribution of the magnetic field anomalies;however,because of the uneven distribution of measurements,it yields several big anomalies.Owing to the added altitude term,the 3DTP model offers higher precision and is consistent with KI.
基金The National Natural Science Foundation of China(No.60702028)the National High Technology Research and Development Program of China(863Program)(No.2007AA01Z268)
文摘Based on the frequency domain training sequences, the polynomial-based carrier frequency offset （CFO） estimation in multiple-input multiple-output （ MIMO ） orthogonal frequency division multiplexing （ OFDM ） systems is extensively investigated. By designing the training sequences to meet certain conditions and exploiting the Hermitian and real symmetric properties of the corresponding matrices, it is found that the roots of the polynomials corresponding to the cost functions are pairwise and that both meger CFO and fractional CFO can be estimated by the direct polynomial rooting approach. By analyzing the polynomials corresponding to the cost functions and their derivatives, it is shown that they have a common polynomial factor and the former can be expressed in a quadratic form of the common polynomial factor. Analytical results further reveal that the derivative polynomial rooting approach is equivalent to the direct one in estimation at the same signal-to-noise ratio（SNR） value and that the latter is superior to the former in complexity. Simulation results agree well with analytical results.
