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Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Kunfeng Liang Zhijun Liu Xinru Bao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第3期3033-3049,共17页
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna... Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed. 展开更多
关键词 Population balance equation CRYSTALLIZATION peridynamic differential operator Euler’s first-order explicit method
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Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method
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作者 LIN Youliang LI Wu +1 位作者 LIU Gang HUANG Dong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2024年第1期178-185,共8页
Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)oper... Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison. 展开更多
关键词 fuzzy decision making CLUSTERING density operator multi-attribute decision making(MADM)
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Symplectic partitioned Runge-Kutta method based onthe eighth-order nearly analytic discrete operator and its wavefield simulations 被引量:3
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作者 张朝元 马啸 +1 位作者 杨磊 宋国杰 《Applied Geophysics》 SCIE CSCD 2014年第1期89-106,117,118,共20页
We propose a symplectic partitioned Runge-Kutta (SPRK) method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this te... We propose a symplectic partitioned Runge-Kutta (SPRK) method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete (NAD) operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction (LWC) method and the eighth-order staggered-grid (SG)method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research. 展开更多
关键词 SYMPLECTIC partitioned RUNGE-KUTTA method NEARLY ANALYTIC DISCRETE operator Numerical dispersion Wavefield simulation
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Method based on fuzzy linguistic scale and FIOWGA operator for decision-making problems 被引量:3
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作者 徐泽水 达庆利 《Journal of Southeast University(English Edition)》 EI CAS 2003年第1期88-91,共4页
In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing... In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness. 展开更多
关键词 fuzzy linguistic scale triangular fuzzy numbers FIOWGA operator
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Three methods for generating monotonic OWA operator weights with given orness level 被引量:1
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作者 刘新旺 《Journal of Southeast University(English Edition)》 EI CAS 2004年第3期369-373,共5页
Based on the properties of ordered weighted averaging (OWA) operator and regular increasing monotone (RIM) quantifier, three methods for generating monotonic OWA operator weights are proposed. They are geometric OWA o... Based on the properties of ordered weighted averaging (OWA) operator and regular increasing monotone (RIM) quantifier, three methods for generating monotonic OWA operator weights are proposed. They are geometric OWA operator weights, equidifferent OWA operator weights and the modified RIM quantifier OWA weights. Compared with most of the common OWA methods for generating weights, the methods proposed in this paper are more intuitive and efficient in computation. And as there are more than one solution in most cases, the decision maker can set some initial condition and chooses the appropriate solution in the real decision process, which increases the flexibility of decision making to some extent. All these three OWA methods for generating weights are illustrated by numerical examples. 展开更多
关键词 ordered weighted averaging operator orness measure fuzzy quantifier
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Some OWA operator weights determination methods with RIM quantifier
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作者 刘新旺 《Journal of Southeast University(English Edition)》 EI CAS 2007年第S1期76-82,共7页
Based on the quantifier guided method,an ordered weighted averaging(OWA)weights generating method under given orness level with regular increasing monotone(RIM)quantifiers is proposed.Then the RIM quantifier based OWA... Based on the quantifier guided method,an ordered weighted averaging(OWA)weights generating method under given orness level with regular increasing monotone(RIM)quantifiers is proposed.Then the RIM quantifier based OWA weights generating method is modified to make the generated weights be monotonic,which can be used to express the decision maker's consistent preference information.Finally,both of these weights generating methods are extended to their generic forms,so that they can generate the OWA weights for any ordinary elements set with any given aggregated value. 展开更多
关键词 ordered weighted averaging operator orness measure aggregation weights
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A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem 被引量:38
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作者 Timon Rabczuk Huilong Ren Xiaoying Zhuang 《Computers, Materials & Continua》 SCIE EI 2019年第4期31-55,共25页
A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the ... A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems. 展开更多
关键词 Nonlocal operator method Variational principle Nonlocal operators Hourglass mode
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ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Ioannis K.ARGYROS Santhosh GEORGE 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1318-1324,共7页
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is... In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping. 展开更多
关键词 nonlinear ill-posed equations iterative regularization m-accretive operator Newton type method
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GALERKIN-PETROV METHODS OF TOEPLITZ OPERATORS ON DIRICHLET SPACE 被引量:1
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作者 王晓峰 曹广福 《Acta Mathematica Scientia》 SCIE CSCD 2007年第2期308-316,共9页
The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that s... The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry. 展开更多
关键词 Galerkin-Petrov methods polynomial collocation analytic element collocation Toeplitz operators Dirichlet space
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Multilevel Iteration Methods for Solving Linear Operator Equations of the First Kind 被引量:2
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作者 罗兴钧 《Northeastern Mathematical Journal》 CSCD 2008年第1期1-9,共9页
In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergen... In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework. 展开更多
关键词 operator equations of the first kind ill-posed problem multilevel iteration method Tikhonov regularization
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Generalized ordered weighted averaging operators based methods for MADM in intuitionistic fuzzy set setting 被引量:4
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作者 Wang Shuqi Li Dengfeng Wu Zhiqian 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第6期1247-1254,共8页
Multiattribute decision making(MADM) problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy(IF) sets, are investigated.Firstly, the relative degrees of membership and th... Multiattribute decision making(MADM) problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy(IF) sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example. 展开更多
关键词 multiattribute decision making intuitionistic fuzzy set ordered weighted averaging operator fuzzy set.
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REGULARIZATION METHODS FOR NONLINEAR ILL-POSED PROBLEMS WITH ACCRETIVE OPERATORS 被引量:2
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作者 王吉安 李景 刘振海 《Acta Mathematica Scientia》 SCIE CSCD 2008年第1期141-150,共10页
This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussio... This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussion on the convergence rates of regular solutions. 展开更多
关键词 REGULARIZATION ill-posed problems nonlinear accretive operator convergence rates
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On the Stable Method Computing Values of Unbounded Operators 被引量:1
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作者 Nguyen Van Kinh 《Open Journal of Optimization》 2020年第4期129-137,共9页
Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a... Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method. 展开更多
关键词 The Stable method Ill-Posed Problem REGULARIZATION Tikhonov method Unbounded Linear operator
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Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian 被引量:1
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作者 范洪义 陈俊华 袁洪春 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第9期145-149,共5页
For classical Hamiltonian with general form H = 1/2∑ijMijpipj+1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (... For classical Hamiltonian with general form H = 1/2∑ijMijpipj+1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived. 展开更多
关键词 invariant eigen-operator method method normal coordinates
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WEIGHTED L_p-APPROXIMATION OF DERIVATIVES BY THE METHOD OF BETA OPERATORS 被引量:1
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作者 宋儒瑛 《Acta Mathematica Scientia》 SCIE CSCD 1999年第S1期575-582,共8页
The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropria... The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropriate weighted Lp-metric by the rate of Ditzian and Totik's r-th order weighted modulus of Smoothness. 展开更多
关键词 Beta operators weighted modulus of smoothness weighted K-functional
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ADJOINT OPERATOR METHOD AND NORMAL FORMS OF HIGHER ORDER FOR NONLINEAR DYNAMICAL SYSTEM
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作者 张伟 陈予恕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第5期449-461,共13页
Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical... Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied. 展开更多
关键词 nonlinear dynamical system adjoint operator method normal forms of order 3 and 4 degenerate bifurcation of codimension 3 universal unfolding
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Using the Fractional Order Method to Generalize Strengthening Buffer Operator and Weakening Buffer Operator 被引量:2
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作者 Lifeng Wu Sifeng Liu Yingjie Yang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第6期1074-1078,共5页
To reveal the relationship between a weakening buffer operator and strengthening buffer operator, the traditional integer order buffer operator is extended to one that is fractional order. Fractional order buffer oper... To reveal the relationship between a weakening buffer operator and strengthening buffer operator, the traditional integer order buffer operator is extended to one that is fractional order. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also results in small adjustments of the buffer effect.The effectiveness of the grey model(GM(1,1)) with the fractional order buffer operator is validated by six cases. 展开更多
关键词 Fractional order grey system theory strengthening buffer operator (SBO) weakening buffer operator (WBO)
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Optical Operator Method Studied via Fresnel Operator Decomposition and Coherent State Representation
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作者 MA Shan-Jun HU Li-Yun FAN Hong-Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第5期1295-1298,共4页
We find that the mapping from classical optical transformations to the optical operator method can be realized by using the coherent state representation and the technique of integration within an ordered product of o... We find that the mapping from classical optical transformations to the optical operator method can be realized by using the coherent state representation and the technique of integration within an ordered product of operators. The optical Fresnel operator derived in (Commun. Theor. Phys. (Beijing, China) 38 (2002) 147) can unify those frequently used optical operators. Various decompositions of Fresnel operator into the exponential canonical operators are obtained. 展开更多
关键词 optical operator method optical Fresnel operator IWOP technique
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Optical Operator Method in Two-Mode Case and Entangled Fresnel Operator's Decomposition
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作者 马善钧 胡利云 范洪义 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第5期907-912,共6页
Based on the entangled Fresnel operator (EFO) proposed in [Commun. Theor. Phys. 46 (2006) 559], the optical operator method studied by the IWOP technique (Ma et al., Commun. Theor. Phys. 49 (2008) 1295) is ext... Based on the entangled Fresnel operator (EFO) proposed in [Commun. Theor. Phys. 46 (2006) 559], the optical operator method studied by the IWOP technique (Ma et al., Commun. Theor. Phys. 49 (2008) 1295) is extended to the two-mode case, which gives the decomposition of the entangled Fresnel operator, corresponding to the decomposition of ray transfer matrix [A, B, C, D]. The EFO can unify those optical operators in two-mode case. Various decompositions of EFO into the exponential canonical operators are obtained. The entangled state representation is useful in the research. 展开更多
关键词 optical operator method entangled Fresnel operator IWOP technique
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The TBD method for dim targets based on multi-level crossover and matching operator 被引量:1
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作者 张海英 段鸿 廖明宏 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2011年第1期57-61,共5页
In order to improve the tracking performance in this paper following TBD(Track before Detection) framework multi-level crossover and matching operator is presented.In data association stage the greedy principle is ado... In order to improve the tracking performance in this paper following TBD(Track before Detection) framework multi-level crossover and matching operator is presented.In data association stage the greedy principle is adopted to handle time complexity in DPA and at the same time crossover mathing operator is given to construct candidate trajectory.In addition the corresponding strategy is introduced in preprocessing and postprocessing to remove clutter and suppress false alarm rate.By the experimental comparison and analysis it can be found that the method is more perfer to strengthen the tracking performance of targets with SNR < 2.0 dB. 展开更多
关键词 track before detection high order correlation filter crossover operator dynamie programming
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