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
Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph...By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph（the Theorem 2）, respectively.展开更多
A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also ...A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also the fastest among all the algorithms for the computation of chromatic polynomials.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 study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled b...In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method.展开更多
Video watermarking plays a crucial role in protecting intellectual property rights and ensuring content authenticity.This study delves into the integration of Galois Field(GF)multiplication tables,especially GF(2^(4))...Video watermarking plays a crucial role in protecting intellectual property rights and ensuring content authenticity.This study delves into the integration of Galois Field(GF)multiplication tables,especially GF(2^(4)),and their interaction with distinct irreducible polynomials.The primary aim is to enhance watermarking techniques for achieving imperceptibility,robustness,and efficient execution time.The research employs scene selection and adaptive thresholding techniques to streamline the watermarking process.Scene selection is used strategically to embed watermarks in the most vital frames of the video,while adaptive thresholding methods ensure that the watermarking process adheres to imperceptibility criteria,maintaining the video's visual quality.Concurrently,careful consideration is given to execution time,crucial in real-world scenarios,to balance efficiency and efficacy.The Peak Signal-to-Noise Ratio(PSNR)serves as a pivotal metric to gauge the watermark's imperceptibility and video quality.The study explores various irreducible polynomials,navigating the trade-offs between computational efficiency and watermark imperceptibility.In parallel,the study pays careful attention to the execution time,a paramount consideration in real-world scenarios,to strike a balance between efficiency and efficacy.This comprehensive analysis provides valuable insights into the interplay of GF multiplication tables,diverse irreducible polynomials,scene selection,adaptive thresholding,imperceptibility,and execution time.The evaluation of the proposed algorithm's robustness was conducted using PSNR and NC metrics,and it was subjected to assessment under the impact of five distinct attack scenarios.These findings contribute to the development of watermarking strategies that balance imperceptibility,robustness,and processing efficiency,enhancing the field's practicality and effectiveness.展开更多
In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatmen...In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.展开更多
Research on the independence polynomial of graphs has been very active.However,the computational complexity of determining independence polynomials for general graphs remains NP-hard.Letα(G)be the independence number...Research on the independence polynomial of graphs has been very active.However,the computational complexity of determining independence polynomials for general graphs remains NP-hard.Letα(G)be the independence number of G and i(G;k)be the number of independent sets of order k in G,then the independence polynomial is defined as I(G;x)=∑_(k=0)^(α(G))i(G;k)x^(k),i(G;0)=1.In this paper,by utilizing the transfer matrix,we obtain an analytical expression for I(CGn;x)of mono-cylindrical grid graphs CGn and present a crucial proof of it.Moreover,we also explore the Merrifield-Simmons index and other properties of CGn.展开更多
Let Abe the linear transformation on the linear space V in the field P, Vλibe the root subspace corresponding to the characteristic polynomial of the eigenvalue λi, and Wλibe the root subspace corresponding to the ...Let Abe the linear transformation on the linear space V in the field P, Vλibe the root subspace corresponding to the characteristic polynomial of the eigenvalue λi, and Wλibe the root subspace corresponding to the minimum polynomial of λi. Consider the problem of whether Vλiand Wλiare equal under the condition that the characteristic polynomial of Ahas the same eigenvalue as the minimum polynomial (see Theorem 1, 2). This article uses the method of mutual inclusion to prove that Vλi=Wλi. Compared to previous studies and proofs, the results of this research can be directly cited in related works. For instance, they can be directly cited in Daoji Meng’s book “Introduction to Differential Geometry.”展开更多
A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view...A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.展开更多
The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials...The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials and a sum analogous to Kloosterman sum mod p,an odd prime,and give two sharp asymptotic formulae for them.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
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.
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
基金Supported by the NNSF of China(10861009)Supported by the Ministry of Education Science and Technology Item of China(206156)
文摘By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph（the Theorem 2）, respectively.
基金This research is partially supported by NNSF of China.
文摘A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also the fastest among all the algorithms for the computation of chromatic polynomials.
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.
文摘In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method.
文摘Video watermarking plays a crucial role in protecting intellectual property rights and ensuring content authenticity.This study delves into the integration of Galois Field(GF)multiplication tables,especially GF(2^(4)),and their interaction with distinct irreducible polynomials.The primary aim is to enhance watermarking techniques for achieving imperceptibility,robustness,and efficient execution time.The research employs scene selection and adaptive thresholding techniques to streamline the watermarking process.Scene selection is used strategically to embed watermarks in the most vital frames of the video,while adaptive thresholding methods ensure that the watermarking process adheres to imperceptibility criteria,maintaining the video's visual quality.Concurrently,careful consideration is given to execution time,crucial in real-world scenarios,to balance efficiency and efficacy.The Peak Signal-to-Noise Ratio(PSNR)serves as a pivotal metric to gauge the watermark's imperceptibility and video quality.The study explores various irreducible polynomials,navigating the trade-offs between computational efficiency and watermark imperceptibility.In parallel,the study pays careful attention to the execution time,a paramount consideration in real-world scenarios,to strike a balance between efficiency and efficacy.This comprehensive analysis provides valuable insights into the interplay of GF multiplication tables,diverse irreducible polynomials,scene selection,adaptive thresholding,imperceptibility,and execution time.The evaluation of the proposed algorithm's robustness was conducted using PSNR and NC metrics,and it was subjected to assessment under the impact of five distinct attack scenarios.These findings contribute to the development of watermarking strategies that balance imperceptibility,robustness,and processing efficiency,enhancing the field's practicality and effectiveness.
文摘In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.
基金Supported by National Natural Science Foundation of China(Grant No.U20A20228)Huzhou Science and Technology Plan Project(Grant No.2022YZ53).
文摘Research on the independence polynomial of graphs has been very active.However,the computational complexity of determining independence polynomials for general graphs remains NP-hard.Letα(G)be the independence number of G and i(G;k)be the number of independent sets of order k in G,then the independence polynomial is defined as I(G;x)=∑_(k=0)^(α(G))i(G;k)x^(k),i(G;0)=1.In this paper,by utilizing the transfer matrix,we obtain an analytical expression for I(CGn;x)of mono-cylindrical grid graphs CGn and present a crucial proof of it.Moreover,we also explore the Merrifield-Simmons index and other properties of CGn.
文摘Let Abe the linear transformation on the linear space V in the field P, Vλibe the root subspace corresponding to the characteristic polynomial of the eigenvalue λi, and Wλibe the root subspace corresponding to the minimum polynomial of λi. Consider the problem of whether Vλiand Wλiare equal under the condition that the characteristic polynomial of Ahas the same eigenvalue as the minimum polynomial (see Theorem 1, 2). This article uses the method of mutual inclusion to prove that Vλi=Wλi. Compared to previous studies and proofs, the results of this research can be directly cited in related works. For instance, they can be directly cited in Daoji Meng’s book “Introduction to Differential Geometry.”
文摘A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.
基金Supported by NSFC(No.12126357)Natural Science Basic Research Plan in Shaanxi Province of China(No.2023-JC-QN-0058)。
文摘The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials and a sum analogous to Kloosterman sum mod p,an odd prime,and give two sharp asymptotic formulae for them.
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.
