Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs...Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.展开更多
Background: Routine lung function testing requires expensive equipment, or requires maximum expiratory effort. The airflow perturbation device (APD) is a light handheld device, allowing for serial measures of respirat...Background: Routine lung function testing requires expensive equipment, or requires maximum expiratory effort. The airflow perturbation device (APD) is a light handheld device, allowing for serial measures of respiratory resistance noninvasively and effortlessly. Methods: In a convenience sample of 398 patients undergoing pulmonary function testing, we compared routine spirometric indices (forced expired volume in 1 second (FEV1), peak expiratory flow (PEF)), and airways resistance (Raw-272 patients), to measures of respiratory resistance measured with the APD including inspiratory (IR), expiratory (ER) and averaged (AR) resistance. Results: Measures of lung function were significantly correlated (p 0.001). On regression analysis, between 7% - 17% of the variance (R2) for FEV1, PEF, and Raw was explained by APD measurements. Approximately 2/3 of the variance in FEV1 was explained by PEF measurements. Conclusions: APD measurements of lung function correlate with conventional measures. Future studies should be directed at exploring the use of the APD device in serial measures of lung function in patients with lung disease.展开更多
In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is ...In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space Xθ(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed.展开更多
The problem of real-time photorealistic imaging is discussed. New techniques for specifying free forms without their approximation by polygons are considered. Free forms based on the perturbation functions have an adv...The problem of real-time photorealistic imaging is discussed. New techniques for specifying free forms without their approximation by polygons are considered. Free forms based on the perturbation functions have an advantage of spline representation of surfaces, that is, a high degree of smoothness, and an advantage of arbitrary form for a small number of perturbation functions. Transformations of geometric objects are described for set-theoretic operations, projections, offsetting, and metamorphosis. We propose a GPU solution to render freeform objects at high frame rates.展开更多
We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and ...We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states （DOS） of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field, atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO-TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.展开更多
In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitio...In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality （LMI） framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.展开更多
A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter fa...A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n） （the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.展开更多
A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is give...A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.展开更多
The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for n...The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.展开更多
Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semi...Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.展开更多
This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to t...This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.展开更多
This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. T...This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. The convergence of the HPSTM solutions to the exact solutions is shown. As a novel application of homotopy perturbation sumudu transform method, the presented work showed some essential difference with existing similar application four classical examples also highlighted the significance of this work.展开更多
A novel collaborative beamforming algorithm is proposed in a wireless communication system with multiple transmitters and one receiver. All transmitters take part in the collaboration and the weighted message is trans...A novel collaborative beamforming algorithm is proposed in a wireless communication system with multiple transmitters and one receiver. All transmitters take part in the collaboration and the weighted message is transmitted simultaneously. In order to maximize the beamforming gain, the transmitters use one bit feedback information to adjust the phase offset. It tracks the direction in which the signal strength at the receiver can increase. The directional search and perturbation theory is used to achieve the phase alignment. The feasibility of the proposed algorithm is proved both experimentally and theoretically. Simulation results show that the proposed algorithm can improve the convergent speed of the phase alignment.展开更多
In the present paper, the singular perturbations for the higher-order scalar nonlinear boundary value problem epsilon(2)y(n)=f(t,epsilon y,y',...,y((n-2)),epsilon y((n-1)), t is an element of[0,1] H1(y(0,epsilon),...In the present paper, the singular perturbations for the higher-order scalar nonlinear boundary value problem epsilon(2)y(n)=f(t,epsilon y,y',...,y((n-2)),epsilon y((n-1)), t is an element of[0,1] H1(y(0,epsilon),...,y((n-3))(0,epsilon),epsilon y((n-2))(0,epsilon),epsilon y((n-1))(0,epsilon),epsilon)=0, H2(y(0,epsilon),y((n-1))(0,epsilon),y(1,epsilon)...,y((n-1))(1,epsilon),epsilon=0 are studied, where epsilon > 0 is a small parameter, n greater than or equal to 2. Under some mild assumptions, we prove the existence and local uniqueness of the perturbed solution and give out the uniformly valid asymptotic expansions up to its nth-order derivative function by employing the Banach/Picard fixed-point theorem. Then the existing results are extended and improved.展开更多
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second_order Volterra functional differential equation was considered first...By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second_order Volterra functional differential equation was considered first. Then, by constructing the right_side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second_order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.展开更多
Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough s...Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.展开更多
Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools ar...Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.展开更多
The newly developed single trajectory quadrature method is applied to a two-dimensional example. Theresults based on different versions of new perturbation expansion and the new Green's function deduced from thism...The newly developed single trajectory quadrature method is applied to a two-dimensional example. Theresults based on different versions of new perturbation expansion and the new Green's function deduced from thismethod are compared with each other, also compared with the result from the traditional perturlbation theory. As thefirst application to higher-dimensional non-separable potential thc obtained result further confirms the applicability andpotential of this new method.展开更多
In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, ...In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.展开更多
The newly developed single trajectory quadrature method is applied to a two-dimensional example. The results based on different versions of new perturbation expansion and the new Green's function deduced from this...The newly developed single trajectory quadrature method is applied to a two-dimensional example. The results based on different versions of new perturbation expansion and the new Green's function deduced from this method are compared with each other, also compared with the result from the traditional perturbation theory. As the first application to higher-dimensional non-separable potential the obtained result further confirms the applicability and potential of this new method.展开更多
文摘Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.
文摘Background: Routine lung function testing requires expensive equipment, or requires maximum expiratory effort. The airflow perturbation device (APD) is a light handheld device, allowing for serial measures of respiratory resistance noninvasively and effortlessly. Methods: In a convenience sample of 398 patients undergoing pulmonary function testing, we compared routine spirometric indices (forced expired volume in 1 second (FEV1), peak expiratory flow (PEF)), and airways resistance (Raw-272 patients), to measures of respiratory resistance measured with the APD including inspiratory (IR), expiratory (ER) and averaged (AR) resistance. Results: Measures of lung function were significantly correlated (p 0.001). On regression analysis, between 7% - 17% of the variance (R2) for FEV1, PEF, and Raw was explained by APD measurements. Approximately 2/3 of the variance in FEV1 was explained by PEF measurements. Conclusions: APD measurements of lung function correlate with conventional measures. Future studies should be directed at exploring the use of the APD device in serial measures of lung function in patients with lung disease.
文摘In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space Xθ(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed.
文摘The problem of real-time photorealistic imaging is discussed. New techniques for specifying free forms without their approximation by polygons are considered. Free forms based on the perturbation functions have an advantage of spline representation of surfaces, that is, a high degree of smoothness, and an advantage of arbitrary form for a small number of perturbation functions. Transformations of geometric objects are described for set-theoretic operations, projections, offsetting, and metamorphosis. We propose a GPU solution to render freeform objects at high frame rates.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50971101 and 51074127)the Research Fund of the State Key Laboratory of Solidification Processing(NPU)of China(Grant No.SKLSP201010)
文摘We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states （DOS） of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field, atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO-TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.
文摘In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality （LMI） framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.
基金The project partly supported by the National Natural Science Foundation of China(19925414,10474045)
文摘A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n） （the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.
基金Supported by National Natural Science Foundation of China(11071075, 11171113)National Natural Science Foundation of China-subsidized by CAS Knowledge Innovation Project (30921064,90820307)+1 种基金Shang Natural Science Foundation(10ZR1409200)Division of Computational Science,E-institute of Shanghai Jiaotong University(E03004)
文摘A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.
文摘The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.
基金supported by the National Natural Science Foundation of China(60674018)
文摘Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.
基金partially supported by Ministerio de Educación y Ciencia,Spain,and FEDER,Projects MTM2013-43014-P and MTM 2016-75140-P
文摘This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.
文摘This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. The convergence of the HPSTM solutions to the exact solutions is shown. As a novel application of homotopy perturbation sumudu transform method, the presented work showed some essential difference with existing similar application four classical examples also highlighted the significance of this work.
基金supported by the National Natural Science Foundation of China(6130115561571003)+2 种基金the Ministry of Education(MCM20130111)the Funds for the Central Universities(ZYGX2014J001)the State Grid Power(W2015000333)
文摘A novel collaborative beamforming algorithm is proposed in a wireless communication system with multiple transmitters and one receiver. All transmitters take part in the collaboration and the weighted message is transmitted simultaneously. In order to maximize the beamforming gain, the transmitters use one bit feedback information to adjust the phase offset. It tracks the direction in which the signal strength at the receiver can increase. The directional search and perturbation theory is used to achieve the phase alignment. The feasibility of the proposed algorithm is proved both experimentally and theoretically. Simulation results show that the proposed algorithm can improve the convergent speed of the phase alignment.
文摘In the present paper, the singular perturbations for the higher-order scalar nonlinear boundary value problem epsilon(2)y(n)=f(t,epsilon y,y',...,y((n-2)),epsilon y((n-1)), t is an element of[0,1] H1(y(0,epsilon),...,y((n-3))(0,epsilon),epsilon y((n-2))(0,epsilon),epsilon y((n-1))(0,epsilon),epsilon)=0, H2(y(0,epsilon),y((n-1))(0,epsilon),y(1,epsilon)...,y((n-1))(1,epsilon),epsilon=0 are studied, where epsilon > 0 is a small parameter, n greater than or equal to 2. Under some mild assumptions, we prove the existence and local uniqueness of the perturbed solution and give out the uniformly valid asymptotic expansions up to its nth-order derivative function by employing the Banach/Picard fixed-point theorem. Then the existing results are extended and improved.
文摘By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second_order Volterra functional differential equation was considered first. Then, by constructing the right_side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second_order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
基金supported by the National Natural Science Foundation of China (Grant No 60571058)the Specialized Research Fund for the Doctoral Program of Higher Education Institutions of China (Grant No 20070701010)
文摘Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.
文摘Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
基金The project partly supported by National Natural Science Foundation of China under Grant No. 19947001
文摘The newly developed single trajectory quadrature method is applied to a two-dimensional example. Theresults based on different versions of new perturbation expansion and the new Green's function deduced from thismethod are compared with each other, also compared with the result from the traditional perturlbation theory. As thefirst application to higher-dimensional non-separable potential thc obtained result further confirms the applicability andpotential of this new method.
文摘In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.
文摘The newly developed single trajectory quadrature method is applied to a two-dimensional example. The results based on different versions of new perturbation expansion and the new Green's function deduced from this method are compared with each other, also compared with the result from the traditional perturbation theory. As the first application to higher-dimensional non-separable potential the obtained result further confirms the applicability and potential of this new method.
