This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a suffi...This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.展开更多
To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an impr...To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.展开更多
To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a deriv...To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.展开更多
Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization p...Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.展开更多
In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemic...In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube, nanostar and polyomino chain.展开更多
The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the ...The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.展开更多
In this paper, a simulation model of bistable system subject to multiplicative and additive noise is built on the basis of the theory of stochastic resonance(SR). SR phenomenon appears in the system subject to multipl...In this paper, a simulation model of bistable system subject to multiplicative and additive noise is built on the basis of the theory of stochastic resonance(SR). SR phenomenon appears in the system subject to multiplicative and additive noise when a single signal transmits in the system. The output waveforms and the power spectrums at different frequencies are compared. The impact of the intensity of multiplicative and additive noise on the bistable system is discussed. It is found that this simulation model can upgrade the quality of the signal processing and the noise intensity can be effectively used for improving the effect of SR.展开更多
We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(σ(x)▽u) and multiplicative noises. Under some mild conditions on the diffusion variable σ(x) and with...We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(σ(x)▽u) and multiplicative noises. Under some mild conditions on the diffusion variable σ(x) and without any restriction on the upper growth p of nonlinearity, except that p > 2, we show the existences of random attractor in D_0^(1,2)(D_N, σ) (■∈ [2, 2p-2]) space, where D_N is an arbitrary(bounded or unbounded) domain in R^N, N ≥ 2. For this purpose, some abstract results based on the omega-limit compactness are established.展开更多
The vibrational resonance and stochastic resonance phenomena in the FitzHugh–Nagumo(FHN)neural model,driven by a high-frequency(HF)signal and a low-frequency(LF)signal and by coupled multiplicative and additive noise...The vibrational resonance and stochastic resonance phenomena in the FitzHugh–Nagumo(FHN)neural model,driven by a high-frequency(HF)signal and a low-frequency(LF)signal and by coupled multiplicative and additive noises,is investigated.For the case that the frequency of the HF signal is much higher than that of the LF signal,under the adiabatic approximation condition,the expression of the signal-to-noise ratio(SNR)with respect to the LF signal is obtained.It is shown that the SNR is a non-monotonous function of the amplitude and frequency of the HF signal.In addition,the SNR varies non-monotonically with the increasing intensities of the multiplicative and additive noise as well as with the increasing system parameters of the FHN model.The influence of the coupling strength between the multiplicative and additive noises on the SNR is discussed.展开更多
This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimiz...This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.展开更多
This paper highlights the statistical procedure used in developing models that have the ability of capturing and forecasting the traffic of mobile communication network operating in Vietnam. To build such models, we f...This paper highlights the statistical procedure used in developing models that have the ability of capturing and forecasting the traffic of mobile communication network operating in Vietnam. To build such models, we follow Box-Jenkins method to construct a multiplicative seasonal ARIMA model to represent the mean component using the past values of traffic, then incorporate a GARCH model to represent its volatility. The traffic is collected from EVN Telecom mobile communication network. Diagnostic tests and examination of forecast accuracy measures indicate that the multiplicative seasonal ARIMA/GARCH model, i.e. ARIMA (1, 0, 1) × (0, 1, 1)24/GARCH (1, 1) shows a good estimation when dealing with volatility clustering in the data series. This model can be considered to be a flexible model to capture well the characteristics of EVN traffic series and give reasonable forecasting results. Moreover, in such situations that the volatility is not necessary to be taken into account, i.e. short-term prediction, the multiplicative seasonal ARIMA/GARCH model still acts well with the GARCH parameters adjusted to GARCH (0, 0).展开更多
By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which...By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty's 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.展开更多
Short-wavelength near infrared spectroscopy (SW-NIR) is a very rapid, versatile and precise technique, which can be used in many different situations and for very types of products and chemical compounds. Extended mul...Short-wavelength near infrared spectroscopy (SW-NIR) is a very rapid, versatile and precise technique, which can be used in many different situations and for very types of products and chemical compounds. Extended multiplicative signal correction (EMSC) is a modification of the standard MSC pre-processing method that allows the separation of physical light scattering effects from chemical (vibrational) light absorbance effects in spectra. In this paper, the EMSC is applied and compared with first derivate, second derivate, MSC and SNV in combination of PLSR to obtain robust models in terms of accuracy and predict ability with a reduced calibration data set using SW-NIR spectra of moisture in marzipan. The Extended Multiplicative Signal Correction—EMSC and combination methods provide the best results in terms of prediction ability and calibration SW-NIR spectra of moisture in marzipan. The best classification results were obtained by Extended Multiplicative Signal Correction followed by second derivates.展开更多
The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at ...The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.展开更多
Sufficient conditions are presented for the asymptotic behavior of all positive solutions of the multiplicative delay Logistic equation about the positive equilibrium K. The case when r(t) =r and gj(t) = t - Tj or gj(...Sufficient conditions are presented for the asymptotic behavior of all positive solutions of the multiplicative delay Logistic equation about the positive equilibrium K. The case when r(t) =r and gj(t) = t - Tj or gj(t) = [t - kj], [.] denoting the greatest integer function,where r, Tj and kj are positive constants, j = 1, 2,... m, ale also included.展开更多
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm ...In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm for the variational model.Some numerical results are presented to illustrate the efficiency of the展开更多
Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative ...Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.展开更多
We consider a Langevin equation of active Brownian motion which contains a multiplicative as well as an additive noise term.We study the dependences of the effective diffusion coefficient Deff on both the additive and...We consider a Langevin equation of active Brownian motion which contains a multiplicative as well as an additive noise term.We study the dependences of the effective diffusion coefficient Deff on both the additive and multiplicative noises.It is found that for fixed small additive noise intensity Deff varies non-monotonously with multiplicative noise intensity,with a minimum at a moderate value of multiplicative noise,and Deff increases monotonously,however,with the multiplicative noise intensity for relatively strong additive noise;for fixed multiplicative noise intensity Deff decreases with growing additive noise intensity until it approaches a constant.An explanation is also given of the different behavior of Deff as additive and multiplicative noises approach infinity,respectively.展开更多
基金supported by the National Natural Science Foundation of China under Grants 61821004,62250056,62350710214,U23A20325,62350055the Natural Science Foundation of Shandong Province,China(ZR2021ZD14,ZR2021JQ24)+2 种基金High-level Talent Team Project of Qingdao West Coast New Area,China(RCTD-JC-2019-05)Key Research and Development Program of Shandong Province,China(2020CXGC01208)Science and Technology Project of Qingdao West Coast New Area,China(2019-32,2020-20,2020-1-4).
文摘This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.
基金supported by the National Natural Science Foundation of China(No.42174011 and No.41874001).
文摘To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.
基金supported by the National Natural Science Foundation of China(No.42174011 and No.41874001).
文摘To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.
文摘Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.
文摘In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube, nanostar and polyomino chain.
基金supported by the National Natural Science Foundation of China,Grant Nos.42174011,41874001 and 41664001Innovation Found Designated for Graduate Students of ECUT,Grant No.DHYC-202020。
文摘The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.
文摘In this paper, a simulation model of bistable system subject to multiplicative and additive noise is built on the basis of the theory of stochastic resonance(SR). SR phenomenon appears in the system subject to multiplicative and additive noise when a single signal transmits in the system. The output waveforms and the power spectrums at different frequencies are compared. The impact of the intensity of multiplicative and additive noise on the bistable system is discussed. It is found that this simulation model can upgrade the quality of the signal processing and the noise intensity can be effectively used for improving the effect of SR.
基金supported by China NSF(11271388)Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1400430)Basis and Frontier Research Project of Chongqing(cstc2014jcyj A00035)
文摘We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(σ(x)▽u) and multiplicative noises. Under some mild conditions on the diffusion variable σ(x) and without any restriction on the upper growth p of nonlinearity, except that p > 2, we show the existences of random attractor in D_0^(1,2)(D_N, σ) (■∈ [2, 2p-2]) space, where D_N is an arbitrary(bounded or unbounded) domain in R^N, N ≥ 2. For this purpose, some abstract results based on the omega-limit compactness are established.
文摘The vibrational resonance and stochastic resonance phenomena in the FitzHugh–Nagumo(FHN)neural model,driven by a high-frequency(HF)signal and a low-frequency(LF)signal and by coupled multiplicative and additive noises,is investigated.For the case that the frequency of the HF signal is much higher than that of the LF signal,under the adiabatic approximation condition,the expression of the signal-to-noise ratio(SNR)with respect to the LF signal is obtained.It is shown that the SNR is a non-monotonous function of the amplitude and frequency of the HF signal.In addition,the SNR varies non-monotonically with the increasing intensities of the multiplicative and additive noise as well as with the increasing system parameters of the FHN model.The influence of the coupling strength between the multiplicative and additive noises on the SNR is discussed.
文摘This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.
文摘This paper highlights the statistical procedure used in developing models that have the ability of capturing and forecasting the traffic of mobile communication network operating in Vietnam. To build such models, we follow Box-Jenkins method to construct a multiplicative seasonal ARIMA model to represent the mean component using the past values of traffic, then incorporate a GARCH model to represent its volatility. The traffic is collected from EVN Telecom mobile communication network. Diagnostic tests and examination of forecast accuracy measures indicate that the multiplicative seasonal ARIMA/GARCH model, i.e. ARIMA (1, 0, 1) × (0, 1, 1)24/GARCH (1, 1) shows a good estimation when dealing with volatility clustering in the data series. This model can be considered to be a flexible model to capture well the characteristics of EVN traffic series and give reasonable forecasting results. Moreover, in such situations that the volatility is not necessary to be taken into account, i.e. short-term prediction, the multiplicative seasonal ARIMA/GARCH model still acts well with the GARCH parameters adjusted to GARCH (0, 0).
基金supported in part by the National Natural Science Foundation of China(71571123,71771155)
文摘By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty's 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.
文摘Short-wavelength near infrared spectroscopy (SW-NIR) is a very rapid, versatile and precise technique, which can be used in many different situations and for very types of products and chemical compounds. Extended multiplicative signal correction (EMSC) is a modification of the standard MSC pre-processing method that allows the separation of physical light scattering effects from chemical (vibrational) light absorbance effects in spectra. In this paper, the EMSC is applied and compared with first derivate, second derivate, MSC and SNV in combination of PLSR to obtain robust models in terms of accuracy and predict ability with a reduced calibration data set using SW-NIR spectra of moisture in marzipan. The Extended Multiplicative Signal Correction—EMSC and combination methods provide the best results in terms of prediction ability and calibration SW-NIR spectra of moisture in marzipan. The best classification results were obtained by Extended Multiplicative Signal Correction followed by second derivates.
基金Project supported by the National Natural Science Foundation of China(Nos.41172116,U1261212,and 51134005)
文摘The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.
文摘Sufficient conditions are presented for the asymptotic behavior of all positive solutions of the multiplicative delay Logistic equation about the positive equilibrium K. The case when r(t) =r and gj(t) = t - Tj or gj(t) = [t - kj], [.] denoting the greatest integer function,where r, Tj and kj are positive constants, j = 1, 2,... m, ale also included.
基金Project supported by the National Natural Science Foundation of China(Nos.11126160,11201475,11371183,and 11101356)
文摘In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
基金supported by the National Natural Science Foundation of China(11101218)Natural Science Fouadation for Colleges and Universities in Jangsu Province(11KJB110009)the Scientific Research Foundation of NUPT(NY209025)
文摘In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm for the variational model.Some numerical results are presented to illustrate the efficiency of the
基金supported by the National Natural Science Foundation of China(Nos.71740021,11861034,and 61966030)the Humanities Social Science Programming Project of Ministry of Education of China(No.20YJA630059)+1 种基金the Natural Science Foundation of Jiangxi Province of China(No.20192BAB207012)the Natural Science Foundation of Qinghai Province of China(No.2019-ZJ-7086).
文摘Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.
文摘We consider a Langevin equation of active Brownian motion which contains a multiplicative as well as an additive noise term.We study the dependences of the effective diffusion coefficient Deff on both the additive and multiplicative noises.It is found that for fixed small additive noise intensity Deff varies non-monotonously with multiplicative noise intensity,with a minimum at a moderate value of multiplicative noise,and Deff increases monotonously,however,with the multiplicative noise intensity for relatively strong additive noise;for fixed multiplicative noise intensity Deff decreases with growing additive noise intensity until it approaches a constant.An explanation is also given of the different behavior of Deff as additive and multiplicative noises approach infinity,respectively.
