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
In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomialsG（z）=（f^n（f^m（z）-1）∏j=1^d f（z＋cj）^vj）^（k）-α（z）,H（z）=（f^n（f（z）-1）^m∏j=1^d f（z...In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomialsG（z）=（f^n（f^m（z）-1）∏j=1^d f（z＋cj）^vj）^（k）-α（z）,H（z）=（f^n（f（z）-1）^m∏j=1^d f（z＋cj）^vj）^（k）-α（z）,where f is transcendental entire function of finite order, cj（j = 1,2,…,d）, n,m,d, and vj（j = 1, 2,… , d） are integers, and obtain some theorems, which extended and improved many previous results.展开更多
In this paper,we mainly investigate the forms of entire solutions for certain Fermattype partial differential-difference equations in C^(2)by using Nevanlinna’s theory of several complex variables.
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
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
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 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
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
In this paper,the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with variable coefficients and mixed conditions.This method is using a simple ...In this paper,the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with variable coefficients and mixed conditions.This method is using a simple computational manner to obtain a quite acceptable approximate solution.The main characteristic behind this method lies in the fact that,on the one hand,the problem will be reduced to a system of algebraic equations.On the other hand,the efficiency and accuracy of the Bernstein polynomials method for solving these equations are high.The existence and uniqueness of the solution have been proved.Moreover,an estimation of the error bound for this method will be shown by preparing some theorems.Finally,some numerical experiments are presented to show the excellent behavior and high accuracy of this algorithm in comparison with some other well-known methods.展开更多
Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines...Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.展开更多
On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear ...On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].展开更多
Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely...Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.展开更多
Let P be a complex polynomial of the form P (z)=(λz-a)mΠj=1n-m(z-zj),where|zj|≥1,1≤j≤n-m.The aim of this paper is to obtain generalisation of a result due to Zargar and Manzoor and a result due to Mir,Nazir and W...Let P be a complex polynomial of the form P (z)=(λz-a)mΠj=1n-m(z-zj),where|zj|≥1,1≤j≤n-m.The aim of this paper is to obtain generalisation of a result due to Zargar and Manzoor and a result due to Mir,Nazir and Wani.We shall also obtain an interesting bound which contains the zeros of the second derivative of P (z).展开更多
A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have...A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.展开更多
In this paper,the method of polynomial particular solutions is used to solve nonlinear Poisson-type partial differential equations in one,two,and three dimensions.The condition number of the coefficient matrix is redu...In this paper,the method of polynomial particular solutions is used to solve nonlinear Poisson-type partial differential equations in one,two,and three dimensions.The condition number of the coefficient matrix is reduced through the implementation of multiple scale technique,ultimately yielding a stable numerical solution.The methodological process can be divided into two main parts:first,identifying the corresponding polynomial particular solutions for the linear differential operator terms in the governing equations,and second,employing these polynomial particular solutions as basis function to iteratively solve the remaining nonlinear terms within the governing equations.Additionally,we investigate the potential improvement in numerical accuracy for equations with singularities in the analytical solution by shifting the computational domain a certain distance.Numerical experiments are conducted to assess both the accuracy and stability of the proposed method.A comparison of the obtained results with those produced by other numerical methods demonstrates the accuracy,stability,and efficiency of the proposed method in handling nonlinear Poisson-type partial differential equations.展开更多
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supported by National Natural Science Foundation of China(11171184)
文摘In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomialsG（z）=（f^n（f^m（z）-1）∏j=1^d f（z＋cj）^vj）^（k）-α（z）,H（z）=（f^n（f（z）-1）^m∏j=1^d f（z＋cj）^vj）^（k）-α（z）,where f is transcendental entire function of finite order, cj（j = 1,2,…,d）, n,m,d, and vj（j = 1, 2,… , d） are integers, and obtain some theorems, which extended and improved many previous results.
基金Supported by the National Natural Science Foundation of China(Grant No.11971344).
文摘In this paper,we mainly investigate the forms of entire solutions for certain Fermattype partial differential-difference equations in C^(2)by using Nevanlinna’s theory of several complex variables.
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 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Supported by the Shiraz University of Technology,Shiraz,Iran.
文摘In this paper,the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with variable coefficients and mixed conditions.This method is using a simple computational manner to obtain a quite acceptable approximate solution.The main characteristic behind this method lies in the fact that,on the one hand,the problem will be reduced to a system of algebraic equations.On the other hand,the efficiency and accuracy of the Bernstein polynomials method for solving these equations are high.The existence and uniqueness of the solution have been proved.Moreover,an estimation of the error bound for this method will be shown by preparing some theorems.Finally,some numerical experiments are presented to show the excellent behavior and high accuracy of this algorithm in comparison with some other well-known methods.
基金supported by Science and Technology Project of Yunnan Provincial Transportation Department(Grant No.25 of 2018)the National Natural Science Foundation of China(Grant No.52279107)The authors are grateful for the support by the China Scholarship Council(CSC No.202206260203 and No.201906690049).
文摘Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.
基金Supported by the National Natural Science Foundation of China(12261023,11861023)the Foundation of Science and Technology project of Guizhou Province of China([2018]5769-05)。
文摘On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].
基金supported by the National Natural Science Foundation of China(12131015,12071422).
文摘Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.
文摘Let P be a complex polynomial of the form P (z)=(λz-a)mΠj=1n-m(z-zj),where|zj|≥1,1≤j≤n-m.The aim of this paper is to obtain generalisation of a result due to Zargar and Manzoor and a result due to Mir,Nazir and Wani.We shall also obtain an interesting bound which contains the zeros of the second derivative of P (z).
文摘A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.
基金supported by the Science and Technology Research Project of Education Department of Jiangxi Province,Philippine Council for Industry,Energy,and Emerging Technology Research and Development(Grant Nos.GJJ2200605)the National Natural Science Foundation of China(11461026)Jiangxi Provincial Natural Science Foundation(20282BA8201016).
文摘In this paper,the method of polynomial particular solutions is used to solve nonlinear Poisson-type partial differential equations in one,two,and three dimensions.The condition number of the coefficient matrix is reduced through the implementation of multiple scale technique,ultimately yielding a stable numerical solution.The methodological process can be divided into two main parts:first,identifying the corresponding polynomial particular solutions for the linear differential operator terms in the governing equations,and second,employing these polynomial particular solutions as basis function to iteratively solve the remaining nonlinear terms within the governing equations.Additionally,we investigate the potential improvement in numerical accuracy for equations with singularities in the analytical solution by shifting the computational domain a certain distance.Numerical experiments are conducted to assess both the accuracy and stability of the proposed method.A comparison of the obtained results with those produced by other numerical methods demonstrates the accuracy,stability,and efficiency of the proposed method in handling nonlinear Poisson-type partial differential equations.
