Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergenc...Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.展开更多
In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the ...In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter ~ is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.展开更多
The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and math...The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.展开更多
Combining Adomian decomposition method （ADM） with Pade approximants, we solve two differentiaidifference equations （DDEs）： the relativistic Toda lattice equation and the modified Volterra lattice equation. With t...Combining Adomian decomposition method （ADM） with Pade approximants, we solve two differentiaidifference equations （DDEs）： the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.展开更多
In this paper,we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padéapproximant.The virial expansion is ...In this paper,we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padéapproximant.The virial expansion is a high-temperature and low-density expansion and in practice,often,only the first several virial coefficients can be obtained.For Bose gases,we determine the BEC phase transition from a truncated virial expansion.For Fermi gases,we recover the low-temperature and high-density result from the virial expansion.展开更多
For the generalized inverse function-valued Pade approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued po...For the generalized inverse function-valued Pade approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form.展开更多
The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, t...The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, to simplify computation of the function-valued Padé approximants, an efficient Pfaffian formula for the determinants was extended from the matrix form to the function-valued form. As an important application, a Pfaffian formula of [4/4] type Padé approximant was established.展开更多
In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.
In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches ...In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.展开更多
Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . W...Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence πβ,fn,m , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.展开更多
Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergence for multiva...Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants,she gives in[2]a de Montessus de Bollore type theorem.In this paper,we will discuss the zero set of a real multivariate polynomial,and present a convergence theorem in measure of multivariate Pade approximant.The proof technique used in this paper is quite different from that used in the univariate case.展开更多
Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which i...Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which is nearest to X in a certain matrix norm. The problem is first solved with regard to four common norms: The Frobenius norm, the Schatten p-norm, the trace norm, and the spectral norm. Then the solution is extended to any unitarily invariant matrix norm. The proof is based on a subtle combination of Ky Fan dominance theorem, a modified pinching principle, and Mirsky minimum-norm theorem.展开更多
The Asymptotic Numerical Method (ANM) is a family of algorithms for path following problems, where each step is based on the computation of truncated vector series [1]. The Vector Padé approximants were introduce...The Asymptotic Numerical Method (ANM) is a family of algorithms for path following problems, where each step is based on the computation of truncated vector series [1]. The Vector Padé approximants were introduced in the ANM to improve the domain of validity of vector series and to reduce the number of steps needed to obtain the entire solution path [1,2]. In this paper and in the framework of the ANM, we define and build a new type of Vector Padé approximant from a truncated vector series by extending the definition of the Padé approximant of a scalar series without any orthonormalization procedure. By this way, we define a new class of Vector Padé approximants which can be used to extend the domain of validity in the ANM algorithms. There is a connection between this type of Vector Padé approximant and Vector Padé type approximant introduced in [3, 4]. We show also that the Vector Padé approximants introduced in the previous works [1,2], are special cases of this class. Applications in 2D nonlinear elasticity are presented.展开更多
When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out...When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output（MIMO） feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output（SISO） systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.展开更多
This article represents a pioneering study centered on the corrosion kinetics of untreated and thermally processed mechano-synthesized Al_(x)Cr_(y)Ni_(z) two-dimensional decagonal quasicrystalline structure and crysta...This article represents a pioneering study centered on the corrosion kinetics of untreated and thermally processed mechano-synthesized Al_(x)Cr_(y)Ni_(z) two-dimensional decagonal quasicrystalline structure and crystalline approximants.It sheds light on the distinguished corrosion behavior of untreated and heat-treated mechano-synthesized Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2)alloys,including a wide diversity of miscellaneous intermetallic phases.A comprehensive characterization was performed to analyze crystallographic structure and thermal characteristics of Al_(x)Cr_(y)Ni_(z) powder particles.Electrochemical evaluations of the mechano-synthesized Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2) specimens and their heat-treated counterparts were conducted under cyclic potentiodynamic polarization tests with 0.1 mol/L Na_(2)SO_(4)(pH=2) and 3.5%NaCl(pH=8.5) electrolytes at room temperature,respectively.Al_(72)Cr_(15)Ni_(13) two-dimensional decagonal quasicrystalline phase was attained following 6 h mechanosynthesis and subsequent annealing treatment at 1035℃.There is no evidence of quasicrystal formation in the Al_(86)Cr_(12)Ni_(2) alloy system after 6 h mechano-synthesis and successive thermal processing at 445 and 570℃.In this study,we conducted the first investigation into electrochemical performance of both Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2) intermetallics.Both Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2) alloys develop a protective passive film in 0.1 mol/L Na_(2)SO_(4) electrolyte.It was determined that 6 h mechano-synthesized Al_(72)Cr_(15)Ni_(13) sample,subjected to annealing at 1035℃,stands out in the Al-Cr-Ni alloy systems for applications necessitating exceptional corrosion resistance,passivation behavior,and minimal susceptibility to pitting corrosion when compared to other tested counterparts.This alloy is characterized by a corrosion current density of 3.73μA/cm^(2) and a corrosion potential of-0.16 V(vs.Ag/AgCl),revealing a remarkably stable passive film up to a current density of 0.02 A/cm^(2) and a potential of 2.41 V(vs.Ag/AgCl)within 0.1 mol/L Na_(2)SO_(4) medium.Likewise,it exhibited a drastically diminished corrosion current density of 11.65μA/cm^(2) and a reduced corrosion potential of-0.27 V(vs.Ag/AgCl)within 3.5%NaCl electrolyte,attributed to the formation of two-dimensional decagonal quasicrystalline phase and hexagonalδ-Al_(3)Ni_(2) crystalline approximant at 1035℃.It also encompassed a re-passivation current density and potential of 50.35μA/cm^(2)and-0.04 V(vs.Ag/AgCl),respectively,within the latter solution.Its corrosion mechanism may be ascribed to a two-step surface precipitation process:initially,Al dissolves into a hydroxide,succeeded by the formation and precipitation of Al oxides,such as NaAlO_(2) and Al_(2)O_(3)·xH_(2)O.展开更多
The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)metho...The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)methods.This paper reviews INLA algorithm and provides a systematic review of six key books that explore the theoretical foundations,practical implementations,and diverse applications of INLA.These six books cover spatial and spatio-temporal modelling,general Bayesian inference,SPDE-based spatial analysis,geospatial health data,regression modelling,and dynamic time series.In addition,these books highlight the versatility of INLA method in handling complex models while maintaining high computational efficiency.This paper begins with an introduction to the INLA method and algorithm,followed by a systematic review of six key publications in the field.展开更多
Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular s...Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular set functions attracts much attention since the 1970s.A large body of work has been done using approximation algorithms.When the dimension of the independent variable of the set function changes from one tok,it is called ak-submodular set function.Thek-submodular set function,a generalization of the classical submodular set function,arises in diverse fields with varied applications.In many practical scenarios,quantifying the degree of closeness to submodularity becomes essential,leading to concepts such as approximately submodular set functions and the diminishing-return(DR) ratio.This paper investigates ak-dimensional set function under matroid constraints,which may lack full submodularity.Instead,we focus on an approximately non-ksubmodular set function characterized by its DR ratio.Employing a greedy algorithmic approach,we derive an approximation guarantee for this problem.Notably,when the DR ratio is set to one,our results align with existing findings in the literature.Experimental results demonstrate the superiority of our algorithm over the baselines.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approxima...To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approximates the densest k-subgraphs of the entire graph through four steps:partitioning the large-scale dynamic graph,constructing a partial set of the densest k-subgraphs,heuristically merging the subgraph sets,and finally extracting the densest k-subgraphs.This approach significantly reduces the computational time for large-scale dynamic graphs while simultaneously improving the quality of the resulting subgraphs.This algorithm is applicable to various definitions of“density”and can accommodate diverse requirements on the number of edges.When integrated with existing static densest subgraph detection algorithms,it achieves scalability and computational efficiency.Theoretical analysis demonstrates that the optimal density of the densest k-subgraphs extracted by the proposed algorithm reaches 0.9.To evaluate the performance of the algorithm,experiments were conducted on four billion-scale datasets:Friendster,Orkut,YouTube,and DBLP.The results indicate that the proposed algorithm outperforms static methods in both runtime efficiency and subgraph quality on large-scale dynamic graphs.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
文摘Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11072168 and 10872141)
文摘In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter ~ is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.
基金Project supported by the National Key Basic Research Project of China (Grant No 2004CB318000)the National Natural Science Foundation of China (Grant Nos 10771072 and 10735030)Shanghai Leading Academic Discipline Project of China (Grant No B412)
文摘The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.
基金supported by the National Natural Science Foundation of China under Grant No. 10735030Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0734
文摘Combining Adomian decomposition method （ADM） with Pade approximants, we solve two differentiaidifference equations （DDEs）： the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.
基金supported in part by The Fundamental Research Funds for the Central Universities under Grant No.2020JKF306Special Funds for theoretical physics Research Program of the NSFC under Grant No.11947124,and NSFC under Grant Nos.11575125 and 11675119。
文摘In this paper,we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padéapproximant.The virial expansion is a high-temperature and low-density expansion and in practice,often,only the first several virial coefficients can be obtained.For Bose gases,we determine the BEC phase transition from a truncated virial expansion.For Fermi gases,we recover the low-temperature and high-density result from the virial expansion.
文摘For the generalized inverse function-valued Pade approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form.
文摘The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, to simplify computation of the function-valued Padé approximants, an efficient Pfaffian formula for the determinants was extended from the matrix form to the function-valued form. As an important application, a Pfaffian formula of [4/4] type Padé approximant was established.
文摘In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.
基金This research is suported by National Science foundation Grant.
文摘In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.
文摘Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence πβ,fn,m , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.
基金Supported by National Science Foundation of China for Youth
文摘Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants,she gives in[2]a de Montessus de Bollore type theorem.In this paper,we will discuss the zero set of a real multivariate polynomial,and present a convergence theorem in measure of multivariate Pade approximant.The proof technique used in this paper is quite different from that used in the univariate case.
文摘Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which is nearest to X in a certain matrix norm. The problem is first solved with regard to four common norms: The Frobenius norm, the Schatten p-norm, the trace norm, and the spectral norm. Then the solution is extended to any unitarily invariant matrix norm. The proof is based on a subtle combination of Ky Fan dominance theorem, a modified pinching principle, and Mirsky minimum-norm theorem.
文摘The Asymptotic Numerical Method (ANM) is a family of algorithms for path following problems, where each step is based on the computation of truncated vector series [1]. The Vector Padé approximants were introduced in the ANM to improve the domain of validity of vector series and to reduce the number of steps needed to obtain the entire solution path [1,2]. In this paper and in the framework of the ANM, we define and build a new type of Vector Padé approximant from a truncated vector series by extending the definition of the Padé approximant of a scalar series without any orthonormalization procedure. By this way, we define a new class of Vector Padé approximants which can be used to extend the domain of validity in the ANM algorithms. There is a connection between this type of Vector Padé approximant and Vector Padé type approximant introduced in [3, 4]. We show also that the Vector Padé approximants introduced in the previous works [1,2], are special cases of this class. Applications in 2D nonlinear elasticity are presented.
基金financial support from the honour program of the Department of Electrical Engineering,Faculty of Engineering,Chulalongkorn University
文摘When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output（MIMO） feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output（SISO） systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.
文摘This article represents a pioneering study centered on the corrosion kinetics of untreated and thermally processed mechano-synthesized Al_(x)Cr_(y)Ni_(z) two-dimensional decagonal quasicrystalline structure and crystalline approximants.It sheds light on the distinguished corrosion behavior of untreated and heat-treated mechano-synthesized Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2)alloys,including a wide diversity of miscellaneous intermetallic phases.A comprehensive characterization was performed to analyze crystallographic structure and thermal characteristics of Al_(x)Cr_(y)Ni_(z) powder particles.Electrochemical evaluations of the mechano-synthesized Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2) specimens and their heat-treated counterparts were conducted under cyclic potentiodynamic polarization tests with 0.1 mol/L Na_(2)SO_(4)(pH=2) and 3.5%NaCl(pH=8.5) electrolytes at room temperature,respectively.Al_(72)Cr_(15)Ni_(13) two-dimensional decagonal quasicrystalline phase was attained following 6 h mechanosynthesis and subsequent annealing treatment at 1035℃.There is no evidence of quasicrystal formation in the Al_(86)Cr_(12)Ni_(2) alloy system after 6 h mechano-synthesis and successive thermal processing at 445 and 570℃.In this study,we conducted the first investigation into electrochemical performance of both Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2) intermetallics.Both Al_(72)Cr_(15)Ni_(13) and Al_(86)Cr_(12)Ni_(2) alloys develop a protective passive film in 0.1 mol/L Na_(2)SO_(4) electrolyte.It was determined that 6 h mechano-synthesized Al_(72)Cr_(15)Ni_(13) sample,subjected to annealing at 1035℃,stands out in the Al-Cr-Ni alloy systems for applications necessitating exceptional corrosion resistance,passivation behavior,and minimal susceptibility to pitting corrosion when compared to other tested counterparts.This alloy is characterized by a corrosion current density of 3.73μA/cm^(2) and a corrosion potential of-0.16 V(vs.Ag/AgCl),revealing a remarkably stable passive film up to a current density of 0.02 A/cm^(2) and a potential of 2.41 V(vs.Ag/AgCl)within 0.1 mol/L Na_(2)SO_(4) medium.Likewise,it exhibited a drastically diminished corrosion current density of 11.65μA/cm^(2) and a reduced corrosion potential of-0.27 V(vs.Ag/AgCl)within 3.5%NaCl electrolyte,attributed to the formation of two-dimensional decagonal quasicrystalline phase and hexagonalδ-Al_(3)Ni_(2) crystalline approximant at 1035℃.It also encompassed a re-passivation current density and potential of 50.35μA/cm^(2)and-0.04 V(vs.Ag/AgCl),respectively,within the latter solution.Its corrosion mechanism may be ascribed to a two-step surface precipitation process:initially,Al dissolves into a hydroxide,succeeded by the formation and precipitation of Al oxides,such as NaAlO_(2) and Al_(2)O_(3)·xH_(2)O.
基金supported by the National Natural Science Foundation of China[grant number 12001266]the Humanities and Social Science Projects ofMinistry of Education of China[grant number 19YJCZH166]supported by the National Natural Science Foundation of China[grant numbers 12271168 and 12531013].
文摘The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)methods.This paper reviews INLA algorithm and provides a systematic review of six key books that explore the theoretical foundations,practical implementations,and diverse applications of INLA.These six books cover spatial and spatio-temporal modelling,general Bayesian inference,SPDE-based spatial analysis,geospatial health data,regression modelling,and dynamic time series.In addition,these books highlight the versatility of INLA method in handling complex models while maintaining high computational efficiency.This paper begins with an introduction to the INLA method and algorithm,followed by a systematic review of six key publications in the field.
基金Supported by the Natural Science Foundation of Shandong Province (No.ZR2023MA031)the Natural Science Foundation of China (No.12201619)。
文摘Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular set functions attracts much attention since the 1970s.A large body of work has been done using approximation algorithms.When the dimension of the independent variable of the set function changes from one tok,it is called ak-submodular set function.Thek-submodular set function,a generalization of the classical submodular set function,arises in diverse fields with varied applications.In many practical scenarios,quantifying the degree of closeness to submodularity becomes essential,leading to concepts such as approximately submodular set functions and the diminishing-return(DR) ratio.This paper investigates ak-dimensional set function under matroid constraints,which may lack full submodularity.Instead,we focus on an approximately non-ksubmodular set function characterized by its DR ratio.Employing a greedy algorithmic approach,we derive an approximation guarantee for this problem.Notably,when the DR ratio is set to one,our results align with existing findings in the literature.Experimental results demonstrate the superiority of our algorithm over the baselines.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金The National Natural Science Foundation of China(No.62172443).
文摘To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approximates the densest k-subgraphs of the entire graph through four steps:partitioning the large-scale dynamic graph,constructing a partial set of the densest k-subgraphs,heuristically merging the subgraph sets,and finally extracting the densest k-subgraphs.This approach significantly reduces the computational time for large-scale dynamic graphs while simultaneously improving the quality of the resulting subgraphs.This algorithm is applicable to various definitions of“density”and can accommodate diverse requirements on the number of edges.When integrated with existing static densest subgraph detection algorithms,it achieves scalability and computational efficiency.Theoretical analysis demonstrates that the optimal density of the densest k-subgraphs extracted by the proposed algorithm reaches 0.9.To evaluate the performance of the algorithm,experiments were conducted on four billion-scale datasets:Friendster,Orkut,YouTube,and DBLP.The results indicate that the proposed algorithm outperforms static methods in both runtime efficiency and subgraph quality on large-scale dynamic graphs.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
