In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving th...In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.展开更多
This paper takes the synthesizing evaluation about industrial economic benefits by examples and proposes a new method named maximizing deviation method for multiindices decision. The new method can automatically deter...This paper takes the synthesizing evaluation about industrial economic benefits by examples and proposes a new method named maximizing deviation method for multiindices decision. The new method can automatically determine the weight coefficients among the multiindices and also can obtain the exact and reliable evaluation results without subjectivity.展开更多
This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviati...This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.展开更多
Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generaliz...Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.展开更多
Based on previous research work,we present a spectrum deviation method to recognize a foreshock or generalized foreshock in this paper. The criterion to determine whether an event is a foreshock is a wide spectrum for...Based on previous research work,we present a spectrum deviation method to recognize a foreshock or generalized foreshock in this paper. The criterion to determine whether an event is a foreshock is a wide spectrum for an ordinary event,however,a moderate earthquake with foreshock or generalized foreshock has the characteristics of a narrow frequency band,and it deviates to the low frequency. It may be explained by metastable extension in the rupture source or related area of the main shock or regional fragmentation damage and crack nucleation process. The calculation results of two foreshocks,the M_S4. 7 event which occurred before the Yushu M_S7. 1 earthquake on April 14,2010 and the M_S5. 3 event which occurred before the Yutian M_S7. 3 earthquake on February 12,2014,show that the spectra of foreshocks shift,and they are quite different from the nonforeshock seismic spectrum of equivalent size. Therefore,this result can verify the validity of the spectrum deviation method.展开更多
The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite ...The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.展开更多
In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analyti...In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the al- gorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.展开更多
Deviation model is an important model for through-flow analysis in axial compressors.Theoretical analysis in classical deviation models is developed under the assumption of onedimensional flow,which is controlled by t...Deviation model is an important model for through-flow analysis in axial compressors.Theoretical analysis in classical deviation models is developed under the assumption of onedimensional flow,which is controlled by the continuity equation.To consider three-dimensional characteristics in transonic flow,this study proposes an improved theoretical analysis method combining force analysis of the blade-to-blade flow with conventional analysis of the continuity equation.Influences of shock structures on transverse force,streamwise velocity and streamline curvature in the blade-to-blade flow are analyzed,and support the analytical modelling of density flow ratio between inlet and outlet conditions.Thus,a novel deviation model for transonic stages in axial compressors is proposed in this paper.The empirical coefficients are corrected based on the experimental data of a linear cascade,and the prediction accuracy is validated with the experimental data of a three-stage transonic compressor.The novel model provides accurate predictions for meridional flow fields at the design point and performance curves at design speed,and shows obvious improvements on classical models by Carter and C¸etin.展开更多
Three dimensional geophysical models were abstracted and established according to characteristics of oil and gas reservoir.Then direct current fields for different models were simulated with finite element software(fi...Three dimensional geophysical models were abstracted and established according to characteristics of oil and gas reservoir.Then direct current fields for different models were simulated with finite element software(finite element program generator) by hole-to-surface resistivity method.Numerical solution was compared with analytical one for the homogeneity earth model.And a new parameter of deviation rate was proposed by analyzing different plot curves.The results show that the relative error of solution for homogeneity earth model may attain to 0.043%.And deviation rate decreases from 18% to 1% and its anomaly range becomes wide gradually when the depth of oil and gas reservoir increases from 200 to 1 500 m.If resistivity ratio of oil and gas reservoir to sur-rounding rock decreases from 100 to 10 for the resistive oil and gas reservoir,the amplitude attenuation of deviation rate nearly reaches 8%.When there exists stratum above oil and gas reservoir,and influence of resistive stratum may be eliminated or weakened and anomaly of oil and gas reservoir can be strengthened.展开更多
We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
In this paper, the sum deviation just-in-time (JIT) sequencing problem in mixed-model production systems is studied relating with the discrete apportionment problem together with their respective mathematical formulat...In this paper, the sum deviation just-in-time (JIT) sequencing problem in mixed-model production systems is studied relating with the discrete apportionment problem together with their respective mathematical formulations. The assignment formulation for the first problem is briefly discussed followed by the existence of JIT cyclic sequences. Presenting the concise discussion on divisor methods for the discrete apportionment problem, we have proposed two mean-based divisor functions for this problem claiming that they are better than the existing divisors; hence, we found a better bound for the JIT sequencing problem. The linkage of both the problems is characterized in terms of similar type of objective functions. The problems are shown equivalent via suitable transformations and similar properties. The joint approaches for the two problems are discussed in terms of global and local deviations proposing equitably efficient solution.展开更多
The machining accuracy of workpiece is influenced by its orientation deviation, which is caused by the fixture-workpiece error. Based on the spatial coordinate theory, the orientation deviation of workpiece is measure...The machining accuracy of workpiece is influenced by its orientation deviation, which is caused by the fixture-workpiece error. Based on the spatial coordinate theory, the orientation deviation of workpiece is measured by using an on-machine verification system, which can take into account the errors resulting from fixture manufacturing, installation and adjustment, location and clamping of workpiece. According to the least square method, the model of orientation deviation is built to determine the relationship between the theoretical and actual coordinate systems. The influence of orientation deviation on machining accuracy is quantified, and it is shown that the orientation deviation only affects the dimensional precision and position precision, rather than shape precision. In the experiment, the compensation processing of realtime errors was conducted, and the perpendicularity and inclination errors of the tetragonal part were reduced by 38.46% and 47.06%, respectively.展开更多
In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise....In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).展开更多
基金supported by the National Natural Science Foundation of China(12201228,12171047)the Fundamental Research Funds for the Central Universities(3034011102)supported by National Key R&D Program of China(2020YFA0713701).
文摘In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.
文摘This paper takes the synthesizing evaluation about industrial economic benefits by examples and proposes a new method named maximizing deviation method for multiindices decision. The new method can automatically determine the weight coefficients among the multiindices and also can obtain the exact and reliable evaluation results without subjectivity.
文摘This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.
基金supported by the National Natural Science Foundation of China under Grant No.71571128the Humanities and Social Sciences Foundation of Ministry of Education of the People’s Republic of China(No.17XJA630003).
文摘Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.
基金sponsored by the National Key Technology Support Program of China entitled "Application of Digital Seismic Technology to Mid-and Short-term Prediction of Strong Earthquake"(2012BAK19B02-01)
文摘Based on previous research work,we present a spectrum deviation method to recognize a foreshock or generalized foreshock in this paper. The criterion to determine whether an event is a foreshock is a wide spectrum for an ordinary event,however,a moderate earthquake with foreshock or generalized foreshock has the characteristics of a narrow frequency band,and it deviates to the low frequency. It may be explained by metastable extension in the rupture source or related area of the main shock or regional fragmentation damage and crack nucleation process. The calculation results of two foreshocks,the M_S4. 7 event which occurred before the Yushu M_S7. 1 earthquake on April 14,2010 and the M_S5. 3 event which occurred before the Yutian M_S7. 3 earthquake on February 12,2014,show that the spectra of foreshocks shift,and they are quite different from the nonforeshock seismic spectrum of equivalent size. Therefore,this result can verify the validity of the spectrum deviation method.
文摘The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.
基金supported by the National Natural Science Foundation of China (No. 10771133)the KeyDisciplines of Shanghai Municipality (Operations Research and Cybernetics) (No. S30104)
文摘In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the al- gorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China (No. 52176039)the National Science and Technology Major Project of China (No. 2017-Ⅱ-0007-0021)
文摘Deviation model is an important model for through-flow analysis in axial compressors.Theoretical analysis in classical deviation models is developed under the assumption of onedimensional flow,which is controlled by the continuity equation.To consider three-dimensional characteristics in transonic flow,this study proposes an improved theoretical analysis method combining force analysis of the blade-to-blade flow with conventional analysis of the continuity equation.Influences of shock structures on transverse force,streamwise velocity and streamline curvature in the blade-to-blade flow are analyzed,and support the analytical modelling of density flow ratio between inlet and outlet conditions.Thus,a novel deviation model for transonic stages in axial compressors is proposed in this paper.The empirical coefficients are corrected based on the experimental data of a linear cascade,and the prediction accuracy is validated with the experimental data of a three-stage transonic compressor.The novel model provides accurate predictions for meridional flow fields at the design point and performance curves at design speed,and shows obvious improvements on classical models by Carter and C¸etin.
基金Projects(2006AA06Z105,2007AA06Z134) supported by the National High-Tech Research and Development Program of China
文摘Three dimensional geophysical models were abstracted and established according to characteristics of oil and gas reservoir.Then direct current fields for different models were simulated with finite element software(finite element program generator) by hole-to-surface resistivity method.Numerical solution was compared with analytical one for the homogeneity earth model.And a new parameter of deviation rate was proposed by analyzing different plot curves.The results show that the relative error of solution for homogeneity earth model may attain to 0.043%.And deviation rate decreases from 18% to 1% and its anomaly range becomes wide gradually when the depth of oil and gas reservoir increases from 200 to 1 500 m.If resistivity ratio of oil and gas reservoir to sur-rounding rock decreases from 100 to 10 for the resistive oil and gas reservoir,the amplitude attenuation of deviation rate nearly reaches 8%.When there exists stratum above oil and gas reservoir,and influence of resistive stratum may be eliminated or weakened and anomaly of oil and gas reservoir can be strengthened.
文摘We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
基金supported by the e-LINK project(EM ECW-ref.149674-EM-1-UK-ERAMUNDUS)financial support to carry out the work at Staffordshire University,Stafford,UK
文摘In this paper, the sum deviation just-in-time (JIT) sequencing problem in mixed-model production systems is studied relating with the discrete apportionment problem together with their respective mathematical formulations. The assignment formulation for the first problem is briefly discussed followed by the existence of JIT cyclic sequences. Presenting the concise discussion on divisor methods for the discrete apportionment problem, we have proposed two mean-based divisor functions for this problem claiming that they are better than the existing divisors; hence, we found a better bound for the JIT sequencing problem. The linkage of both the problems is characterized in terms of similar type of objective functions. The problems are shown equivalent via suitable transformations and similar properties. The joint approaches for the two problems are discussed in terms of global and local deviations proposing equitably efficient solution.
基金Supported by National Natural Science Foundation of China (No.50975200)
文摘The machining accuracy of workpiece is influenced by its orientation deviation, which is caused by the fixture-workpiece error. Based on the spatial coordinate theory, the orientation deviation of workpiece is measured by using an on-machine verification system, which can take into account the errors resulting from fixture manufacturing, installation and adjustment, location and clamping of workpiece. According to the least square method, the model of orientation deviation is built to determine the relationship between the theoretical and actual coordinate systems. The influence of orientation deviation on machining accuracy is quantified, and it is shown that the orientation deviation only affects the dimensional precision and position precision, rather than shape precision. In the experiment, the compensation processing of realtime errors was conducted, and the perpendicularity and inclination errors of the tetragonal part were reduced by 38.46% and 47.06%, respectively.
基金partially supported by the National Natural Science Foundation of China(11871382,12071361)partially supported by the National Natural Science Foundation of China(11971361,11731012)。
文摘In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).
