The Husimi function(Q-function)of a quantum state is the distribution function of the density operator in the coherent state representation.It is widely used in theoretical research,such as in quantum optics.The Wehrl...The Husimi function(Q-function)of a quantum state is the distribution function of the density operator in the coherent state representation.It is widely used in theoretical research,such as in quantum optics.The Wehrl entropy is the Shannon entropy of the Husimi function,and is nonzero even for pure states.This entropy has been extensively studied in mathematical physics.Recent research also suggests a significant connection between the Wehrl entropy and manybody quantum entanglement in spin systems.We investigate the statistical interpretation of the Husimi function and the Wehrl entropy,taking the system of N spin-1/2 particles as an example.Due to the completeness of coherent states,the Husimi function and Wehrl entropy can be explained via the positive operator-valued measurement(POVM)theory,although the coherent states are not a set of orthonormal basis.Here,with the help of the Bayes’theorem,we provide an alternative probabilistic interpretation for the Husimi function and the Wehrl entropy.This interpretation is based on direct measurements of the system,and thus does not require the introduction of an ancillary system as in the POVM theory.Moreover,under this interpretation the classical correspondences of the Husimi function and the Wehrl entropy are just phase-space probability distribution function of N classical tops,and its associated entropy,respectively.Therefore,this explanation contributes to a better understanding of the relationship between the Husimi function,Wehrl entropy,and classical-quantum correspondence.The generalization of this statistical interpretation to continuous-variable systems is also discussed.展开更多
High entropy materials(HEMs)are the promising electrocatalysts for anion exchange membrane electrolyser(AEMs)and proton exchange membrane fuel cells(PEMFCs)due to the intriguing cocktail effect,wide design space,tailo...High entropy materials(HEMs)are the promising electrocatalysts for anion exchange membrane electrolyser(AEMs)and proton exchange membrane fuel cells(PEMFCs)due to the intriguing cocktail effect,wide design space,tailorable electronic structure,and entropy stabilization effect.The precise fabrication of HEMs with functional nanostructures provides a crucial avenue to optimize the adsorption strength and catalytic activity for electrocatalysis.This review comprehensively summarizes the development of HEMs,focusing on the principles and strategies of structural design,and the catalytic mechanism towards hydrogen evolution reaction,oxygen evolution reaction and oxygen reduction reaction for the development of high-performance electrocatalysts.The complexity inherent in the interactions between different elements,the changes in the d-band center and the Gibbs free energies during the catalytic progress,as well as the coordination environment of the active sites associated with the unique crystal structure to improve the catalytic performance are discussed.We also provide a perspective on the challenges and future development direction of HEMs in electrocatalysis.This review will contribute to the design and development of HEMs-based catalysts for the next generation of electrochemical applications.展开更多
This paper describes and explores a maximum-entropy approach to continuous minimax problem, which is applicable in many fields, such as transportation planning and game theory. It illustrates that the maximum entropy ...This paper describes and explores a maximum-entropy approach to continuous minimax problem, which is applicable in many fields, such as transportation planning and game theory. It illustrates that the maximum entropy approcach has easy framework and proves that every accumulation of {x_k} generated by maximum-entropy programming is -optimal solution of initial continuous minimax problem. The paper also explains BFGS or TR method for it. Two numerical exam.ples for continuous minimax problem are展开更多
Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a var...Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.展开更多
Based on KKT complementary condition in optimization theory, an unconstrained non-differential optimization model for support vector machine is proposed. An adjustable entropy function method is given to deal with the...Based on KKT complementary condition in optimization theory, an unconstrained non-differential optimization model for support vector machine is proposed. An adjustable entropy function method is given to deal with the proposed optimization problem and the Newton algorithm is used to figure out the optimal solution. The proposed method can find an optimal solution with a relatively small parameter p, which avoids the numerical overflow in the traditional entropy function methods. It is a new approach to solve support vector machine. The theoretical analysis and experimental results illustrate the feasibility and efficiency of the proposed algorithm.展开更多
Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the...Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method （LSMEQFM） and that with constraint condition （LSMEQFMCC） are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples （10 samples）; LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples; with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples （10 samples）.展开更多
Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorith...Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.展开更多
In this article, we introduce the concept of entropy functional for continuous systems on compact metric spaces, and prove some of its properties. We also extract the Kolmogorov entropy from the entropy functional.
this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)...this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)f is the L_(p) projection body of a log-concave function f.Our results give a partial answer to this problem.展开更多
Let f be a continuous anti-unimodal solution of a p-order Frigenbaum's dunctioal equation.A criterion is given to determine whether or not the topological entropy of j is zero.And a continuous anti-unimodal soluti...Let f be a continuous anti-unimodal solution of a p-order Frigenbaum's dunctioal equation.A criterion is given to determine whether or not the topological entropy of j is zero.And a continuous anti-unimodal solution of 4-order equation with positive topological eotrpy is constructed.展开更多
Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore...Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers （TFNs）, the entropies of any two TFNs which can not be always the same type, also, have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets （TFSs） with same sizes of support intervals and different heights, the relationship of their entropies lies on their height. Finally, we point it out a mistake that Chen＇s assertion that the entropy of resultant fuzzy set of elevation operation is directly to that of the original one while elevation factor just acts as a propartional factor. These results should contribute to the analysis and design of a fuzzy system.展开更多
The deep learning model is overfitted and the accuracy of the test set is reduced when the deep learning model is trained in the network intrusion detection parameters, due to the traditional loss function convergence...The deep learning model is overfitted and the accuracy of the test set is reduced when the deep learning model is trained in the network intrusion detection parameters, due to the traditional loss function convergence problem. Firstly, we utilize a network model architecture combining Gelu activation function and deep neural network;Secondly, the cross-entropy loss function is improved to a weighted cross entropy loss function, and at last it is applied to intrusion detection to improve the accuracy of intrusion detection. In order to compare the effect of the experiment, the KDDcup99 data set, which is commonly used in intrusion detection, is selected as the experimental data and use accuracy, precision, recall and F1-score as evaluation parameters. The experimental results show that the model using the weighted cross-entropy loss function combined with the Gelu activation function under the deep neural network architecture improves the evaluation parameters by about 2% compared with the ordinary cross-entropy loss function model. Experiments prove that the weighted cross-entropy loss function can enhance the model’s ability to discriminate samples.展开更多
High-entropy alloys(HEA)are novel materials obtained by introducing chemical disorder through mixing multiple-principal components,performing rather attractive features together with charming and exceptional propertie...High-entropy alloys(HEA)are novel materials obtained by introducing chemical disorder through mixing multiple-principal components,performing rather attractive features together with charming and exceptional properties in comparison with traditional alloys.However,the trade-off relationship is still present between strength and ductility in HEAs,significantly limiting the practical and wide application of HEAs.Moreover,the preparation of HEAs by trial-and-error method is time-consuming and resource-wasting,hindering the high-speed and high-quality development of HEAs.Herein,the primary objective of this work is to summarize the latest advancements in HEAs,focusing on methods for predicting phase structures and the factors influencing mechanical properties.Additionally,strengthening and toughening strategies for HEAs are highlighted,thus maximizing their application potential.Besides,challenges and future investigation direction of HEAs are also identified and proposed.展开更多
High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface compl...High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface complexity and tendency for elemental segregation,which results in discrepancies between bulk and surface compositions,pose challenges for direct investigation via density functional theory.To address this,Monte Carlo simulations combined with molecular dynamics were employed to model surface segregation across a broad range of elements,including Cu,Ag,Au,Pt,Pd,and Al.The analysis revealed a trend in surface segregation propensity following the order Ag>Au>Al>Cu>Pd>Pt.To capture the correlation between surface site characteristics and the free energy of multi-dentate CO_(2)reduction intermediates,a graph neural network was designed,where adsorbates were transformed into pseudo-atoms at their centers of mass.This model achieved mean absolute errors of 0.08–0.15 eV for the free energies of C_(2)intermediates,enabling precise site activity quantification.Results indicated that increasing the concentration of Cu,Ag,and Al significantly boosts activity for CO and C_(2)formation,whereas Au,Pd,and Pt exhibit negative effects.By screening stable composition space,promising HEA bulk compositions for CO,HCOOH,and C_(2)products were predicted,offering superior catalytic activity compared to pure Cu catalysts.展开更多
A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main p...A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)=αHγ e -βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α, β, and γ in the function are expressed in terms of the mean , variance V= (H-)2 and bias B= (H-)3 ; and (3) with , V and B estimated from observed data, the n -year return-period wave height H n is computed in accordance with the formula 11-F(H n)=n , where F(H n) is defined as F(H n)=∫ H n 0f(H) d H. Examples of estimating the 50 and 100-year return period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.展开更多
基金supported by the National Key Research and Development Program of China[Grant No.2022YFA1405300(PZ)]the Innovation Program for Quantum Science and Technology(Grant No.2023ZD0300700)。
文摘The Husimi function(Q-function)of a quantum state is the distribution function of the density operator in the coherent state representation.It is widely used in theoretical research,such as in quantum optics.The Wehrl entropy is the Shannon entropy of the Husimi function,and is nonzero even for pure states.This entropy has been extensively studied in mathematical physics.Recent research also suggests a significant connection between the Wehrl entropy and manybody quantum entanglement in spin systems.We investigate the statistical interpretation of the Husimi function and the Wehrl entropy,taking the system of N spin-1/2 particles as an example.Due to the completeness of coherent states,the Husimi function and Wehrl entropy can be explained via the positive operator-valued measurement(POVM)theory,although the coherent states are not a set of orthonormal basis.Here,with the help of the Bayes’theorem,we provide an alternative probabilistic interpretation for the Husimi function and the Wehrl entropy.This interpretation is based on direct measurements of the system,and thus does not require the introduction of an ancillary system as in the POVM theory.Moreover,under this interpretation the classical correspondences of the Husimi function and the Wehrl entropy are just phase-space probability distribution function of N classical tops,and its associated entropy,respectively.Therefore,this explanation contributes to a better understanding of the relationship between the Husimi function,Wehrl entropy,and classical-quantum correspondence.The generalization of this statistical interpretation to continuous-variable systems is also discussed.
基金supported by the Guangdong Basic and Applied Basic Research Fund Project(2022A1515140061,No.11000-2344014)Startup Foundation for Postdoctor by Dongguan University of Technology(No.11000-221110149)the High-level Talents Program(contract number 2023JC10L014)of the Department of Science and Technology of Guangdong Province。
文摘High entropy materials(HEMs)are the promising electrocatalysts for anion exchange membrane electrolyser(AEMs)and proton exchange membrane fuel cells(PEMFCs)due to the intriguing cocktail effect,wide design space,tailorable electronic structure,and entropy stabilization effect.The precise fabrication of HEMs with functional nanostructures provides a crucial avenue to optimize the adsorption strength and catalytic activity for electrocatalysis.This review comprehensively summarizes the development of HEMs,focusing on the principles and strategies of structural design,and the catalytic mechanism towards hydrogen evolution reaction,oxygen evolution reaction and oxygen reduction reaction for the development of high-performance electrocatalysts.The complexity inherent in the interactions between different elements,the changes in the d-band center and the Gibbs free energies during the catalytic progress,as well as the coordination environment of the active sites associated with the unique crystal structure to improve the catalytic performance are discussed.We also provide a perspective on the challenges and future development direction of HEMs in electrocatalysis.This review will contribute to the design and development of HEMs-based catalysts for the next generation of electrochemical applications.
基金The Project was supported by National Natural Science Foundation of china.
文摘This paper describes and explores a maximum-entropy approach to continuous minimax problem, which is applicable in many fields, such as transportation planning and game theory. It illustrates that the maximum entropy approcach has easy framework and proves that every accumulation of {x_k} generated by maximum-entropy programming is -optimal solution of initial continuous minimax problem. The paper also explains BFGS or TR method for it. Two numerical exam.ples for continuous minimax problem are
基金This workis financially supported by the National Natural Science Foundation of China (Grant No.40490263 andNo.40276006)
文摘Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.
基金the National Natural Science Foundation of China (60574075)
文摘Based on KKT complementary condition in optimization theory, an unconstrained non-differential optimization model for support vector machine is proposed. An adjustable entropy function method is given to deal with the proposed optimization problem and the Newton algorithm is used to figure out the optimal solution. The proposed method can find an optimal solution with a relatively small parameter p, which avoids the numerical overflow in the traditional entropy function methods. It is a new approach to solve support vector machine. The theoretical analysis and experimental results illustrate the feasibility and efficiency of the proposed algorithm.
文摘Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method （LSMEQFM） and that with constraint condition （LSMEQFMCC） are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples （10 samples）; LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples; with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples （10 samples）.
基金State Natural Science Foundation of China (49974021).
文摘Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.
文摘In this article, we introduce the concept of entropy functional for continuous systems on compact metric spaces, and prove some of its properties. We also extract the Kolmogorov entropy from the entropy functional.
基金The National Natural Science Foundation of China(11701373)The Shanghai Sailing Program(17YF1413800)。
文摘this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)f is the L_(p) projection body of a log-concave function f.Our results give a partial answer to this problem.
文摘Let f be a continuous anti-unimodal solution of a p-order Frigenbaum's dunctioal equation.A criterion is given to determine whether or not the topological entropy of j is zero.And a continuous anti-unimodal solution of 4-order equation with positive topological eotrpy is constructed.
基金The National Natural Science Foundation of China(No.60474022)
文摘Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers （TFNs）, the entropies of any two TFNs which can not be always the same type, also, have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets （TFSs） with same sizes of support intervals and different heights, the relationship of their entropies lies on their height. Finally, we point it out a mistake that Chen＇s assertion that the entropy of resultant fuzzy set of elevation operation is directly to that of the original one while elevation factor just acts as a propartional factor. These results should contribute to the analysis and design of a fuzzy system.
文摘The deep learning model is overfitted and the accuracy of the test set is reduced when the deep learning model is trained in the network intrusion detection parameters, due to the traditional loss function convergence problem. Firstly, we utilize a network model architecture combining Gelu activation function and deep neural network;Secondly, the cross-entropy loss function is improved to a weighted cross entropy loss function, and at last it is applied to intrusion detection to improve the accuracy of intrusion detection. In order to compare the effect of the experiment, the KDDcup99 data set, which is commonly used in intrusion detection, is selected as the experimental data and use accuracy, precision, recall and F1-score as evaluation parameters. The experimental results show that the model using the weighted cross-entropy loss function combined with the Gelu activation function under the deep neural network architecture improves the evaluation parameters by about 2% compared with the ordinary cross-entropy loss function model. Experiments prove that the weighted cross-entropy loss function can enhance the model’s ability to discriminate samples.
基金supported by the National Natural Science Foundation of China(Nos.52375451,52005396)Shandong Provincial Natural Science Foundation,China(Nos.ZR2023YQ052,ZR2023ME087)+6 种基金Shandong Provincial Technological SME Innovation Capability Promotion Project,China(No.2023TSGC0375)Young Taishan Scholars Program of Shandong Province,China(No.tsqn202306041)Guangdong Basic and Applied Basic Research Foundation,China(No.2023 A1515010044)Shandong Provincial Youth Innovation Team,China(No.2022KJ038)Open Project of State Key Laboratory of Solid Lubrication,China(No.LSL-22-11)Young Talent Fund of University Association for Science and Technology in Shaanxi,China(No.20210414)Qilu Youth Scholar Project Funding of Shandong University,China。
文摘High-entropy alloys(HEA)are novel materials obtained by introducing chemical disorder through mixing multiple-principal components,performing rather attractive features together with charming and exceptional properties in comparison with traditional alloys.However,the trade-off relationship is still present between strength and ductility in HEAs,significantly limiting the practical and wide application of HEAs.Moreover,the preparation of HEAs by trial-and-error method is time-consuming and resource-wasting,hindering the high-speed and high-quality development of HEAs.Herein,the primary objective of this work is to summarize the latest advancements in HEAs,focusing on methods for predicting phase structures and the factors influencing mechanical properties.Additionally,strengthening and toughening strategies for HEAs are highlighted,thus maximizing their application potential.Besides,challenges and future investigation direction of HEAs are also identified and proposed.
文摘High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface complexity and tendency for elemental segregation,which results in discrepancies between bulk and surface compositions,pose challenges for direct investigation via density functional theory.To address this,Monte Carlo simulations combined with molecular dynamics were employed to model surface segregation across a broad range of elements,including Cu,Ag,Au,Pt,Pd,and Al.The analysis revealed a trend in surface segregation propensity following the order Ag>Au>Al>Cu>Pd>Pt.To capture the correlation between surface site characteristics and the free energy of multi-dentate CO_(2)reduction intermediates,a graph neural network was designed,where adsorbates were transformed into pseudo-atoms at their centers of mass.This model achieved mean absolute errors of 0.08–0.15 eV for the free energies of C_(2)intermediates,enabling precise site activity quantification.Results indicated that increasing the concentration of Cu,Ag,and Al significantly boosts activity for CO and C_(2)formation,whereas Au,Pd,and Pt exhibit negative effects.By screening stable composition space,promising HEA bulk compositions for CO,HCOOH,and C_(2)products were predicted,offering superior catalytic activity compared to pure Cu catalysts.
基金ThisworkisfinanciallysupportedbythePh.D.FoundationoftheMinistryoftheEducationofChina (No .2 0 0 0 4 2 30 8)
文摘A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)=αHγ e -βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α, β, and γ in the function are expressed in terms of the mean , variance V= (H-)2 and bias B= (H-)3 ; and (3) with , V and B estimated from observed data, the n -year return-period wave height H n is computed in accordance with the formula 11-F(H n)=n , where F(H n) is defined as F(H n)=∫ H n 0f(H) d H. Examples of estimating the 50 and 100-year return period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.
