The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a ...The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a bivariate function by given scattered data has been obtained in a simple analytical form as a special case.展开更多
By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f（t, u） ...By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f（t, u） is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.展开更多
The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stoc...The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.展开更多
As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially...As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China's weather data is applied to illustrate the validity of our model.展开更多
This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common...This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.展开更多
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Erro...In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.展开更多
In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectru...This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.展开更多
Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasi...Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.展开更多
In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce ...In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.展开更多
The thermodynamic properties of linear protein solutions are discussed by a statistical me-chanics theory with a lattice model. The numerical results show that the Gibbs function of the solution decreases, and the pro...The thermodynamic properties of linear protein solutions are discussed by a statistical me-chanics theory with a lattice model. The numerical results show that the Gibbs function of the solution decreases, and the protein chemical potential is enhanced with increase of the protein concentration for dilute solutions. The influences of chain length and temperature on the Gibbs function of the solution as well as the protein chemical potential are analyzed.As an application of the theory, the chemical potentials of some mutants of type I antifreeze proteins are computed and discussed.展开更多
In this paper, some properties of solutions of linear differential equations f^（k）＋A（z）f = 0 and f（k）＋ A（z）f = F（z） are discussed. Our results are a generalization of the original results.
The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basi...The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.展开更多
Assessing the influence of individual observations of the functional linear models is important and challenging,especially when the observations are subject to missingness.In this paper,we introduce three case-deletio...Assessing the influence of individual observations of the functional linear models is important and challenging,especially when the observations are subject to missingness.In this paper,we introduce three case-deletion diagnostic measures to identify influential observations in functional linear models when the covariate is functional and observations on the scalar response are subject to nonignorable missingness.The nonignorable missing data mechanism is modeled via an exponential tilting semiparametric functional model.A semiparametric imputation procedure is developed to mitigate the effects of missing data.Valid estimations of the functional coefficients are based on functional principal components analysis using the imputed dataset.A smoothed bootstrap samplingmethod is introduced to estimate the diagnostic probability for each proposed diagnostic measure,which is helpful to unveil which observations have the larger influence on estimation and prediction.Simulation studies and a real data example are conducted to illustrate the finite performance of the proposed methods.展开更多
For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How ...For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.展开更多
To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the s...To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.展开更多
In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estima...In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means展开更多
Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be a...Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known, and at the same time, it can be applied to solving the approximating solution of the given equation.展开更多
In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate ...In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate done per unit volume were derived. A generalized worked example of slab forging was analyzed by the criterion and its corresponding plastic work rate done per unit volume. Then, the precision of the solution was compared with those by Mises and Twin shear stress yield criterions, respectively. It turned out that the calculated results by MY criterion were in good agreement with those by Mises criterion.展开更多
This letter proposes fingerprint-based key binding/recovering with fuzzy vault. Fingerprint minutiae data and the cryptographic key are merged together by a multivariable linear function. First, the minutiae data are ...This letter proposes fingerprint-based key binding/recovering with fuzzy vault. Fingerprint minutiae data and the cryptographic key are merged together by a multivariable linear function. First, the minutiae data are bound by a set of random data through the linear function. The number of the function’s variables is determined by the required number of matched minutiae. Then, a new key de- rived from the random data is used to encrypt the cryptographic key. Lastly, the binding data are protected using fuzzy vault scheme. The proposed scheme provides the system with the flexibility to use changeable number of minutiae to bind/recover the protected key and a unified method regardless of the length of the key.展开更多
文摘The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a bivariate function by given scattered data has been obtained in a simple analytical form as a special case.
基金. Supported by National Natural Science Foundation of China （Grant No. 10871116）, Natural Science Foundation of Shandong Province of China （Grant No. ZR2010AM005） and the Doctoral Program Foundation of Education Ministry of China （Grant No. 200804460001）Acknowledgements The authors would like to thank the referees for their valuable comments.
文摘By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f（t, u） is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.
基金Project supported by the Natural Science Foundation of China(10371009) and Research Fund for the Doctoral Program Higher Education.
文摘The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.
基金supported by National Nature Science Foundation of China(No.11861074,No.11371354 and N0.11301464)Key Laboratory of Random Complex Structures and Data Science,Chinese Academy of Sciences,Beijing 100190,China(No.2008DP173182)Applied Basic Research Project of Yunnan Province(No.2019FB138).
文摘As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China's weather data is applied to illustrate the validity of our model.
基金supported by National Natural Science Foundation of China(No.61374065)the Research Fund for the Taishan Scholar Project of Shandong Province
文摘This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.
文摘In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.
基金Supported by the National Natural Science Foundation of China(11071069, 11171307)the Natural Science Foundation of Hunan Province(09JJ6003)
文摘In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
基金Project partially supported by the China Postdoctoral Science Foundation (Grant No. 20060400705)Tianjin University Research Foundation (Grant No. TJU-YFF-08B06)
文摘This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.
文摘Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.
基金supported by the National Natural Science Foundation of China(No.60803049,60472060)
文摘In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.
基金This work was supported by the National Natural Science Foundation of China （No.10764003 and No.30560039）.
文摘The thermodynamic properties of linear protein solutions are discussed by a statistical me-chanics theory with a lattice model. The numerical results show that the Gibbs function of the solution decreases, and the protein chemical potential is enhanced with increase of the protein concentration for dilute solutions. The influences of chain length and temperature on the Gibbs function of the solution as well as the protein chemical potential are analyzed.As an application of the theory, the chemical potentials of some mutants of type I antifreeze proteins are computed and discussed.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123211171119)+1 种基金the Youth Science Foundation of Education Bureau of Jiangxi Province(Grant No.GJJ12207)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211009)
文摘In this paper, some properties of solutions of linear differential equations f^（k）＋A（z）f = 0 and f（k）＋ A（z）f = F（z） are discussed. Our results are a generalization of the original results.
基金support by Basic Science Research Program through the National Research Foundation(NRF)funded by Korea Ministry of Education(No.2016R1A6A1A0312812).
文摘The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.
基金supported by the General Project of National Natural Science Foundation of China(Grant No.12071416).
文摘Assessing the influence of individual observations of the functional linear models is important and challenging,especially when the observations are subject to missingness.In this paper,we introduce three case-deletion diagnostic measures to identify influential observations in functional linear models when the covariate is functional and observations on the scalar response are subject to nonignorable missingness.The nonignorable missing data mechanism is modeled via an exponential tilting semiparametric functional model.A semiparametric imputation procedure is developed to mitigate the effects of missing data.Valid estimations of the functional coefficients are based on functional principal components analysis using the imputed dataset.A smoothed bootstrap samplingmethod is introduced to estimate the diagnostic probability for each proposed diagnostic measure,which is helpful to unveil which observations have the larger influence on estimation and prediction.Simulation studies and a real data example are conducted to illustrate the finite performance of the proposed methods.
基金supported by the National Natural Science Foundation of China(No.12271370)。
文摘For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.
基金Project supported by the National Natural Science Foundation of China (No. 10271074)
文摘To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.
文摘In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means
基金Project supported by the National Natural Science Foundation of China(Grant No.10271074)
文摘Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known, and at the same time, it can be applied to solving the approximating solution of the given equation.
基金This research was supported by the National Natural Sci—ence Foundation of China(Grant No.50474015)
文摘In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate done per unit volume were derived. A generalized worked example of slab forging was analyzed by the criterion and its corresponding plastic work rate done per unit volume. Then, the precision of the solution was compared with those by Mises and Twin shear stress yield criterions, respectively. It turned out that the calculated results by MY criterion were in good agreement with those by Mises criterion.
基金Supported by the National Natural Science Foundation of China (No.60472069)
文摘This letter proposes fingerprint-based key binding/recovering with fuzzy vault. Fingerprint minutiae data and the cryptographic key are merged together by a multivariable linear function. First, the minutiae data are bound by a set of random data through the linear function. The number of the function’s variables is determined by the required number of matched minutiae. Then, a new key de- rived from the random data is used to encrypt the cryptographic key. Lastly, the binding data are protected using fuzzy vault scheme. The proposed scheme provides the system with the flexibility to use changeable number of minutiae to bind/recover the protected key and a unified method regardless of the length of the key.
