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An Approach to Formulation of FNLP with Complex Piecewise Linear Membership Functions 被引量:1
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作者 闻博 李宏光 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2014年第4期411-417,共7页
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
关键词 fuzzy nonlinear programming piecewise linear membership functions MODELING
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THEOREMS OF PEANO'S TYPE FOR BIVARIATE FUNCTIONS AND OPTIMAL RECOVERY OF LINEAR FUNCTIONALS
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作者 N.K. Dicheva (University of Architecture, Bulgaria) 《Analysis in Theory and Applications》 2001年第3期43-53,共11页
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
关键词 Ky THEOREMS OF PEANO’S TYPE FOR BIVARIATE functions AND OPTIMAL RECOVERY OF linear FUNCTIONALS
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ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO LINEAR MATRIX MOMENT FUNCTION ALS:THEORY AND APPLICATIONS 被引量:5
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作者 L.Jódar E.Defez E.Ponsoda 《Analysis in Theory and Applications》 1996年第1期96-115,共20页
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
关键词 ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO linear MATRIX MOMENT FUNCTION ALS 艺人 APPI
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Some inequalities for the generalized linear distortion function 被引量:2
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作者 MA Xiao-yan QIU Song-liang +1 位作者 ZHONG Gen-hong CHU Yu-ming 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2012年第1期87-93,共7页
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).
关键词 modular equation generalized linear distortion function inequality.
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A new chaotic Hopfield network with piecewise linear activation function 被引量:1
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作者 郑鹏升 唐万生 张建雄 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第3期188-192,共5页
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
关键词 Hopfield network CHAOS piecewise linear function
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A self-adaptive linear evolutionary algorithm for solving constrained optimization problems 被引量:1
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作者 Kezong TANG Jingyu YANG +1 位作者 Shang GAO Tingkai SUN 《控制理论与应用(英文版)》 EI 2010年第4期533-539,共7页
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
关键词 Multiobjective optimization Evolutionary algorithms Pareto optimal solution linear fitness function
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Statistical Thermodynamic Properties of Linear Protein Solutions
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作者 栗丽芬 梁希侠 李前忠 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2010年第2期180-184,I0001,共6页
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
关键词 Chemical potential linear protein solution Chain length Gibbs function
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A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization
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作者 Changkye Lee Sundararajan Natarajan +1 位作者 Seong-Hoon Kee Jurng-Jae Yee 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第6期1615-1634,共20页
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
关键词 Smoothed finite element method linear smoothing function topology optimization solid isotropic material with penalization(SIMP) polygonal finite element cell
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On Characterization of Poised Nodes for a Space of Bivariate Functions
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作者 Hayk Avdalyan Hakop Hakopian 《Advances in Linear Algebra & Matrix Theory》 2016年第4期89-103,共15页
There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials,... There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper. 展开更多
关键词 Bivariate Interpolation Problem Poisedness Fundamental Function Bivariate Piecewise linear Function Reductions by Basic Subproblems
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Diagnostic Measures for Functional Linear Model with Nonignorable Missing Responses
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作者 Yujian Zhu Puying Zhao 《Communications in Mathematics and Statistics》 SCIE 2024年第3期543-562,共20页
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
关键词 Case deletion Diagnostic measure Functional linear model Nonignorable nonresponse Semiparametric imputation
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Least Square Estimation for Multiple Functional Linear Model with Autoregressive Errors
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作者 Meng WANG Ming-liang SHU +2 位作者 Jian-jun ZHOU Si-xin WU Min CHEN 《Acta Mathematicae Applicatae Sinica》 2025年第1期84-98,共15页
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 ove... 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 coeficients and autoregression coeficients.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
关键词 multiple functional linear model autoregressive errors principal component analysis consistency
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Derivation of Plastic Work Rate Done per Unit Volume for Mean Yield Criterion and Its Application 被引量:8
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作者 Dewen ZHAO Yingjie XIE +1 位作者 Xiaowen WANG Xianghua LIU 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 2005年第4期433-436,共4页
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
关键词 Mean yield criterion Plastic work rate done per unit volume Functional linearization Slab forging
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FINGERPRINT-BASED KEY BINDING/RECOVERING SCHEME BASED ON FUZZY VAULT 被引量:4
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作者 Feng Quan Su Fei Cai Anni 《Journal of Electronics(China)》 2008年第3期415-421,共7页
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
关键词 BINDING Key recovering Fingerprint minutiae Fuzzy vault Multivariable linear function
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COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE 被引量:2
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作者 房艮孙 叶培新 《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期439-448,共10页
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
关键词 worst (deterministic) case stochastic case average case setting bounded linear functional error estimate
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New predictive control algorithms based on Least Squares Support Vector Machines 被引量:3
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作者 刘斌 苏宏业 褚健 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第5期440-446,共7页
Used for industrial process with different degree of nonlinearity, the two predictive control algorithms presented in this paper are based on Least Squares Support Vector Machines (LS-SVM) model. For the weakly nonlin... Used for industrial process with different degree of nonlinearity, the two predictive control algorithms presented in this paper are based on Least Squares Support Vector Machines (LS-SVM) model. For the weakly nonlinear system, the system model is built by using LS-SVM with linear kernel function, and then the obtained linear LS-SVM model is transformed into linear input-output relation of the controlled system. However, for the strongly nonlinear system, the off-line model of the controlled system is built by using LS-SVM with Radial Basis Function (RBF) kernel. The obtained nonlinear LS-SVM model is linearized at each sampling instant of system running, after which the on-line linear input-output model of the system is built. Based on the obtained linear input-output model, the Generalized Predictive Control (GPC) algorithm is employed to implement predictive control for the controlled plant in both algorithms. The simulation results after the presented algorithms were implemented in two different industrial processes model; respectively revealed the effectiveness and merit of both algorithms. 展开更多
关键词 Least Squares Support Vector Machines linear kernel function RBF kernel function Generalized predictive control
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ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS 被引量:2
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作者 顾传青 潘宝珍 吴蓓蓓 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第6期853-860,共8页
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
关键词 generalized linear functional function-valued Padé-type approximation Fredholm integral equation orthogonal polynomial determinant formula
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AN OPTIMAL FUZZY APPROXIMATOR 被引量:1
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作者 YueShihong ZhangKecun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第2期236-240,共5页
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
关键词 reproducing kernel bounded linear functional fuzzy control
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Edge method for measuring source spot-size and its principle 被引量:1
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作者 施将君 刘军 +1 位作者 刘进 李必勇 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第1期266-271,共6页
The edge method is used to measure the source spot-size. In this paper, the measuring principle and applying range are discussed. It is shown that the method can directly be used to measure the spot-size of either lig... The edge method is used to measure the source spot-size. In this paper, the measuring principle and applying range are discussed. It is shown that the method can directly be used to measure the spot-size of either light source, or low-energy x-ray source, or x-ray source with an energy higher than 250 keV. 展开更多
关键词 edge method edge spread function (ESF) linear spread function (LSF) full width at half maximum (FWHM)
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NUAT T-splines of odd bi-degree and local refinement 被引量:1
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作者 DUAN Xiao-juan WANG Guo-zhao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第4期410-421,共12页
This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces (NUAT T-splines for short) of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-... This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces (NUAT T-splines for short) of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic- trigonometric B-spline surfaces (NUAT B-spline surfaces). Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally, we prove that, for any NUAT T-spline of odd hi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix. 展开更多
关键词 odd bi-degree non-uniform algebraic-trigonometric T-spline local refinement blending function linear independence.
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Correlation functions of gauged linear σ-model 被引量:2
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作者 TIAN Gang XU GuangBo 《Science China Mathematics》 SCIE CSCD 2016年第5期823-838,共16页
This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and th... This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified r-spin curve. 展开更多
关键词 gauged linear σ-model correlation function moduli space
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