To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive t...To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.展开更多
Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos gam...Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation （CGR） of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems （RIFS） in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the Dq curves, one sees that these functional protein sequences are not completely random. The Dq of all linked functional proteins studied are multifractal-like and sufficiently smooth for the Cq （analogous to specific heat） curves to be meaningful. Furthermore, the Dq curves of the measure μ based on their CCRs for different orders to link the functional protein sequences are almost identical if q 〉 0. Finally, the Ca curves of all linked functional proteins resemble a classical phase transition at a critical point.展开更多
The performance of proton exchange membrane fuel cells depends heavily on the oxygen reduction reaction(ORR)at the cathode,for which platinum-based catalysts are currently the standard.The high cost and limited availa...The performance of proton exchange membrane fuel cells depends heavily on the oxygen reduction reaction(ORR)at the cathode,for which platinum-based catalysts are currently the standard.The high cost and limited availability of platinum have driven the search for alternative catalysts.While FeN4 single-atom catalysts have shown promising potential,their ORR activity needs to be further enhanced.In contrast,dual-atom catalysts(DACs)offer not only higher metal loading but also the ability to break the ORR scaling relations.However,the diverse local structures and tunable coordination environments of DACs create a vast chemical space,making large-scale computational screening challenging.In this study,we developed a graph neural network(GNN)-based framework to predict the ORR activity of Fe-based DACs,effectively addressing the challenges posed by variations in local catalyst structures.Our model,trained on a dataset of 180 catalysts,accurately predicted the Gibbs free energy of ORR intermediates and overpotentials,and identified 32 DACs with superior catalytic activity compared to FeN4 SAC.This approach not only advances the design of high-performance DACs,but also offers a powerful computational tool that can significantly reduce the time and cost of catalyst development,thereby accelerating the commercialization of fuel cell technologies.展开更多
By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. Th...By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.展开更多
Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequen...Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.展开更多
In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hoppin...In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.展开更多
We employ the coherent thermal states(a kind of entangled states)in thermal field dynamics to establisha complete entangled state formalism expressing pseudo-classical representations of density operator for light fie...We employ the coherent thermal states(a kind of entangled states)in thermal field dynamics to establisha complete entangled state formalism expressing pseudo-classical representations of density operator for light field.Especially,the relationship between the coherent thermal state and the characteristic function and the positive Prepresentation in quantum optics theory are obtained.展开更多
A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e., coefficients S, are the com...A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e., coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum j≤7.展开更多
In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. wh...In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.展开更多
Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a ...Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.展开更多
Based on the Wigner operator in the entangled state representation we study some new important propertiesof Wigner function for bipartite entangled systems,such as size of an entangled state,upper bound of Wigner func...Based on the Wigner operator in the entangled state representation we study some new important propertiesof Wigner function for bipartite entangled systems,such as size of an entangled state,upper bound of Wigner functions,etc.These discussions demonstrate the beauty and elegance of the entangled state representation.展开更多
In Phys. Lett. A 313 （2003） 343 we have found that the self-recipràcal Hankel transformation （HT） is embodied in quantum mechanics by a transform between two entangled state representations of continuum varia...In Phys. Lett. A 313 （2003） 343 we have found that the self-recipràcal Hankel transformation （HT） is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations＇ transformation in quantum mechanics.展开更多
Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner...Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.展开更多
This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (t...This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.展开更多
In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its ...In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its acceleration response spectrum in any desired time duration is compatible with a time-scaled predefined acceleration response spectrum.For this purpose,simulated stationary acceleration time series is multiplied by the time dependent linear modulation function,then using a simple iterative scheme,it is forced to match a target acceleration response spectrum.It is shown that the generated samples have excellent conformity in low frequency,which is useful for nonlinear endurance time analysis.In the second part of this study,it is shown that this procedure can be extended to generate a set of spatially correlated endurance time excitation functions.This makes it possible to assess the performance of long structures under multi-support seismic excitation using endurance time analysis.展开更多
In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special c...In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae.展开更多
The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful ...The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order(FLO) time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform(FLO-STFT), fractional lower order Wigner-Ville distributions(FLO-WVDs), fractional lower order Cohen class time-frequency distributions(FLO-CDs), fractional lower order adaptive kernel time-frequency distributions(FLO-AKDs) and adaptive fractional lower order time-frequency auto-regressive moving average(FLO-TFARMA) model time-frequency representation method.The methods and the exiting methods based on second order statistics in SaS distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized.Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.展开更多
A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the ne...A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA（p, d, q） model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA（p, d, q） model.展开更多
The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C^n, firstly using different method and technique we der...The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C^n, firstly using different method and technique we derive the corresponding integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the two types of the bounded domains. Secondly we obtain the unified integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the general bounded domains. When functions are holomorphic, the integral formulas in this paper include formulas of Stout^([1]), Hatziafratis^([2]) and the author^([3]),and are the extension of all the integral representations for holomorphic functions in the existing papers to analytic varieties. In particular, when m = 0, firstly we gave the integral representation formulas of differentiable functions for the two types of bounded domains in C^n. Therefore they can make the concretion of Leray-Stokes formula. Secondly we obtain the unified integral representation formulas of differentiable functions for general bounded domains in C^n. So they can make the Leray-Stokes formula generalizations.展开更多
This paper introduces a new concept of ＂State Representation Methodology （SRM）＂ which is a kind of bridge condition assessment method for structural health monitoring system （SHM）. There are many methods for sys...This paper introduces a new concept of ＂State Representation Methodology （SRM）＂ which is a kind of bridge condition assessment method for structural health monitoring system （SHM）. There are many methods for system identification from the simplicity comparison of damage index to the complicated statistical pattern recognition algorithms in SHM. In these methods, modal analysis and parameters identification or many defined indices are common-used for extracting the dynamic or static characteristics of a system. However, there is a common problem： due to the complexity of a large size system with high-order nonlinear characteristics and severe environment interference, it is impossible to extract and quantify exactly these modal parameters or system parameters or indices as the feature vectors of a system in damage detection in an easy way. The SRM considered a more general theory for the non-parametric description of system state.展开更多
基金Project supported by the Foundation for Young Talents in College of Anhui Province, China (Grant Nos. gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions, China (Grant Nos. 2022AH051580 and 2022AH051586)。
文摘To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.
基金Project partially supported by the National Natural Science Foundation of China (Grant No.30570426)the Chinese Program for New Century Excellent Talents in University (Grant No.NCET-08-06867)+1 种基金Fok Ying Tung Education Foundation (Grant No.101004)Australian Research Council (Grant No.DP0559807)
文摘Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation （CGR） of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems （RIFS） in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the Dq curves, one sees that these functional protein sequences are not completely random. The Dq of all linked functional proteins studied are multifractal-like and sufficiently smooth for the Cq （analogous to specific heat） curves to be meaningful. Furthermore, the Dq curves of the measure μ based on their CCRs for different orders to link the functional protein sequences are almost identical if q 〉 0. Finally, the Ca curves of all linked functional proteins resemble a classical phase transition at a critical point.
基金This work was supported by the National Natural Science Foundation of China(No.22473001)the Natural Science Funds for Distinguished Young Scholar of Anhui Province(1908085J08)the University An-nual Scientific Research Plan of Anhui Province(2022AH010013).
文摘The performance of proton exchange membrane fuel cells depends heavily on the oxygen reduction reaction(ORR)at the cathode,for which platinum-based catalysts are currently the standard.The high cost and limited availability of platinum have driven the search for alternative catalysts.While FeN4 single-atom catalysts have shown promising potential,their ORR activity needs to be further enhanced.In contrast,dual-atom catalysts(DACs)offer not only higher metal loading but also the ability to break the ORR scaling relations.However,the diverse local structures and tunable coordination environments of DACs create a vast chemical space,making large-scale computational screening challenging.In this study,we developed a graph neural network(GNN)-based framework to predict the ORR activity of Fe-based DACs,effectively addressing the challenges posed by variations in local catalyst structures.Our model,trained on a dataset of 180 catalysts,accurately predicted the Gibbs free energy of ORR intermediates and overpotentials,and identified 32 DACs with superior catalytic activity compared to FeN4 SAC.This approach not only advances the design of high-performance DACs,but also offers a powerful computational tool that can significantly reduce the time and cost of catalyst development,thereby accelerating the commercialization of fuel cell technologies.
基金The project supported by the Natural Science Foundation of Heze University of Shandong Province of China under Grant Nos.XY07WL01 and XY05WL01the University Experimental Technology Foundation of Shandong Province of China under Grant No.S04W138
文摘By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.
文摘Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.
文摘In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.
基金the President Foundation of the Chinese Academy of Sciences
文摘We employ the coherent thermal states(a kind of entangled states)in thermal field dynamics to establisha complete entangled state formalism expressing pseudo-classical representations of density operator for light field.Especially,the relationship between the coherent thermal state and the characteristic function and the positive Prepresentation in quantum optics theory are obtained.
文摘A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e., coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum j≤7.
文摘In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.
基金Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. Y2008A23)
文摘Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.
基金Supported by the President Foundation of Chinese Academy of ScienceApecialized Research Fund for the Doctorial Progress of Higher EducationNational Natural Science Foundation of China under Grant Nos.10874174 and 10947017/A05
文摘Based on the Wigner operator in the entangled state representation we study some new important propertiesof Wigner function for bipartite entangled systems,such as size of an entangled state,upper bound of Wigner functions,etc.These discussions demonstrate the beauty and elegance of the entangled state representation.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056 and the President Foundation of the Chinese Academy of Sciences
文摘In Phys. Lett. A 313 （2003） 343 we have found that the self-recipràcal Hankel transformation （HT） is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations＇ transformation in quantum mechanics.
文摘Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.
文摘This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.
文摘In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its acceleration response spectrum in any desired time duration is compatible with a time-scaled predefined acceleration response spectrum.For this purpose,simulated stationary acceleration time series is multiplied by the time dependent linear modulation function,then using a simple iterative scheme,it is forced to match a target acceleration response spectrum.It is shown that the generated samples have excellent conformity in low frequency,which is useful for nonlinear endurance time analysis.In the second part of this study,it is shown that this procedure can be extended to generate a set of spatially correlated endurance time excitation functions.This makes it possible to assess the performance of long structures under multi-support seismic excitation using endurance time analysis.
文摘In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae.
基金supported by the National Natural Science Foundation of China(61261046,61362038)the Natural Science Foundation of Jiangxi Province(20142BAB207006,20151BAB207013)+2 种基金the Science and Technology Project of Provincial Education Department of Jiangxi Province(GJJ14738,GJJ14739)the Research Foundation of Health Department of Jiangxi Province(20175561)the Science and Technology Project of Jiujiang University(2016KJ001,2016KJ002)
文摘The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order(FLO) time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform(FLO-STFT), fractional lower order Wigner-Ville distributions(FLO-WVDs), fractional lower order Cohen class time-frequency distributions(FLO-CDs), fractional lower order adaptive kernel time-frequency distributions(FLO-AKDs) and adaptive fractional lower order time-frequency auto-regressive moving average(FLO-TFARMA) model time-frequency representation method.The methods and the exiting methods based on second order statistics in SaS distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized.Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.
基金Project supported by the National Natural Science Foundation of China (Grant No 60575038)the Natural Science Foundation of Jiangnan University, China (Grant No 20070365)the Program for Innovative Research Team of Jiangnan University, China
文摘A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA（p, d, q） model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA（p, d, q） model.
文摘The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C^n, firstly using different method and technique we derive the corresponding integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the two types of the bounded domains. Secondly we obtain the unified integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the general bounded domains. When functions are holomorphic, the integral formulas in this paper include formulas of Stout^([1]), Hatziafratis^([2]) and the author^([3]),and are the extension of all the integral representations for holomorphic functions in the existing papers to analytic varieties. In particular, when m = 0, firstly we gave the integral representation formulas of differentiable functions for the two types of bounded domains in C^n. Therefore they can make the concretion of Leray-Stokes formula. Secondly we obtain the unified integral representation formulas of differentiable functions for general bounded domains in C^n. So they can make the Leray-Stokes formula generalizations.
文摘This paper introduces a new concept of ＂State Representation Methodology （SRM）＂ which is a kind of bridge condition assessment method for structural health monitoring system （SHM）. There are many methods for system identification from the simplicity comparison of damage index to the complicated statistical pattern recognition algorithms in SHM. In these methods, modal analysis and parameters identification or many defined indices are common-used for extracting the dynamic or static characteristics of a system. However, there is a common problem： due to the complexity of a large size system with high-order nonlinear characteristics and severe environment interference, it is impossible to extract and quantify exactly these modal parameters or system parameters or indices as the feature vectors of a system in damage detection in an easy way. The SRM considered a more general theory for the non-parametric description of system state.
