This paper presents two new theorems for multiplicative perturbations of C-regularized resolvent families, which generalize the previous related ones for the resolvent families.
In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met...In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.展开更多
Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly pertur...Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.展开更多
This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singula...This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.展开更多
Recent noteworthy developments in the field of two-dimensional（2D） correlation spectroscopy are reviewed.2D correlation spectroscopy has become a very popular tool due to its versatility and relative ease of use.The...Recent noteworthy developments in the field of two-dimensional（2D） correlation spectroscopy are reviewed.2D correlation spectroscopy has become a very popular tool due to its versatility and relative ease of use.The technique utilizes a spectroscopic or other analytical probe from a number of selections for a broad range of sample systems by employing different types of external perturbations to induce systematic variations in intensities of spectra.Such spectral intensity variations are then converted into2 D spectra by a form of correlation analysis for subsequent interpretation.Many different types of 2D correlation approaches have been proposed.In particular,2D hetero-correlation and multiple perturbation correlation analyses,including orthogonal sample design scheme,are discussed in this review.Additional references to other important developments in the field of 2D correlation spectroscopy,such as projection correlation and codistribution analysis,were also provided.展开更多
This paper presents a mixed H21H∞ control using fuzzy singularly perturbed model （FSPM） with multiple perturbation parameters. Since FSPM with multiple perturbation parameters is an extension of models with a singl...This paper presents a mixed H21H∞ control using fuzzy singularly perturbed model （FSPM） with multiple perturbation parameters. Since FSPM with multiple perturbation parameters is an extension of models with a single perturbation parameter, the theoretical results are applicable to a larger class of systems described by multiple time scale nonlinear models, such as flying aircraft and flexible space robots. The parameter-independent solution of the mixed H21H∞ controller was obtained in the form of linear matrix inequalities （LMIs）. The application of this approach to gust load alleviation of a flying vehicle verifies its effectiveness and flexibility.展开更多
文摘This paper presents two new theorems for multiplicative perturbations of C-regularized resolvent families, which generalize the previous related ones for the resolvent families.
基金supported by the National Natural Science Foundation of China (11132004 and 51078145)the Natural Science Foundation of Guangdong Province (9251064101000016)
文摘In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.
基金Project supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.
基金supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
文摘Recent noteworthy developments in the field of two-dimensional（2D） correlation spectroscopy are reviewed.2D correlation spectroscopy has become a very popular tool due to its versatility and relative ease of use.The technique utilizes a spectroscopic or other analytical probe from a number of selections for a broad range of sample systems by employing different types of external perturbations to induce systematic variations in intensities of spectra.Such spectral intensity variations are then converted into2 D spectra by a form of correlation analysis for subsequent interpretation.Many different types of 2D correlation approaches have been proposed.In particular,2D hetero-correlation and multiple perturbation correlation analyses,including orthogonal sample design scheme,are discussed in this review.Additional references to other important developments in the field of 2D correlation spectroscopy,such as projection correlation and codistribution analysis,were also provided.
基金Supported by the National High-Tech Research and Development (863) Program of China (No. 2010AA7050202)
文摘This paper presents a mixed H21H∞ control using fuzzy singularly perturbed model （FSPM） with multiple perturbation parameters. Since FSPM with multiple perturbation parameters is an extension of models with a single perturbation parameter, the theoretical results are applicable to a larger class of systems described by multiple time scale nonlinear models, such as flying aircraft and flexible space robots. The parameter-independent solution of the mixed H21H∞ controller was obtained in the form of linear matrix inequalities （LMIs）. The application of this approach to gust load alleviation of a flying vehicle verifies its effectiveness and flexibility.
