Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitr...Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.展开更多
In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by ...In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.展开更多
This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the co...This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the common equation the natural frequencies of an n th order network are correlated with the n port parameters. The equation is simple and dual in form and clear in its physical meaning. The procedure of finding the solution is simplified and standardized, and it will not cause the loss of roots. The common equation would find wide use and be systematized.展开更多
The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of...The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.展开更多
In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametri...In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.展开更多
The main purpose of this paper is to study the growth of meromorphic solutions of complex linear differential-difference equations L（z, f） =n∑i=0m∑j=0Aij（z）f^（j）（z ＋ ci） = 0 or F（z）with entire or meromorp...The main purpose of this paper is to study the growth of meromorphic solutions of complex linear differential-difference equations L（z, f） =n∑i=0m∑j=0Aij（z）f^（j）（z ＋ ci） = 0 or F（z）with entire or meromorphic coefficients, and ci, i = 0,..., n being distinct complex numbers,where there is only one dominant coefficient.展开更多
This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect...This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.展开更多
By using the variation of parameters, this paper deals with the general solution and Ulam stability of second order linear dynamic equations with variable coefficients on time scales.In particular, we also obtain the ...By using the variation of parameters, this paper deals with the general solution and Ulam stability of second order linear dynamic equations with variable coefficients on time scales.In particular, we also obtain the Ulam stability of second order linear dynamic equations with constant coefficients under different cases.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By u...In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.展开更多
The article intends to find a method to quantify traffic congestion＇s impacts on travelers to help transportation planners and policy decision makers well understand congestion situations. Three new congestion indica...The article intends to find a method to quantify traffic congestion＇s impacts on travelers to help transportation planners and policy decision makers well understand congestion situations. Three new congestion indicators, including transportation environment satisfaction （TES）, travel time satisfaction （TTS）, and traffic congestion frequency and feeling （TCFF）, are defined to estimate urban traffic congestion based on travelers＇ feelings. Data of travelers＇ attitude about congestion and trip information were collected from a survey in Shanghai, China. Based on the survey data, we estimated the value of the three indi- cators. Then, the principal components analysis was used to derive a small number of linear combinations of a set of variables to estimate the whole congestion status. A linear regression model was used to find out the significant variables which impact respondents＇ feelings. Two ordered logit models were used to select significant variables of TES and TTS. Attitudinal factor variables were also used in these models. The results show that attitudinal factor variables and cluster category variables are as important as sociodemographic variables in the models. Using the three congestion indicators, the government can collect travelers＇ feeling about traffic congestion and estimate the transportation policy that might be applied to cope with traffic congestion.展开更多
This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（H...This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.展开更多
The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and...The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.展开更多
This paper concerns the superconvergence property of the ultraweak-local discontinuous Galerkin(UWLDG)method for one-dimensional linear sixth-order equations.The crucial technique is the construction of a special proj...This paper concerns the superconvergence property of the ultraweak-local discontinuous Galerkin(UWLDG)method for one-dimensional linear sixth-order equations.The crucial technique is the construction of a special projection.We will discuss in three different situations according to the remainder of k,the highest degree of polynomials in the function space,divided by 3.We can prove the(2k-1)th-order superconvergence for the cell averages when k=0 or 2(mod 3).But if k=1(mod 3),we can only prove a(2k-2)th-order superconvergence.The same superconvergence orders can also be gained for the errors of numerical fuxes.We will also prove the superconvergence of order k+2 at some special quadrature points.Some numerical examples are given at the end of this paper.展开更多
The hydrothermal reactions of CuI, KI and bidentate amines [ 1,10 phenanthroline (phen) or ethylenediamine (en)] gave the three copper(I) halide compounds, Cu3I3(phen)2 (1), CuI(phen)2 (2) and 2 (3), which were stru...The hydrothermal reactions of CuI, KI and bidentate amines [ 1,10 phenanthroline (phen) or ethylenediamine (en)] gave the three copper(I) halide compounds, Cu3I3(phen)2 (1), CuI(phen)2 (2) and 2 (3), which were structurally characterized via singlecrystal Xray diffraction studies. Hydrogen bonds and ππ interactions are the most remarkable structural features of the title compounds. All can be described as higherdimensional supramolecular compounds connected via these secondary bondings. Moreover, the title compounds were characterized by elemental analyses, IR spectra and TGA analyses. The thirdorder nonlinear optical properties of the title compounds were also investigated and all exhibit nicer nonlinear absorption and selffocusing performance.Keywords copper(I) halide, hydrothermal synthesis, the thirdorder nonlinear optical property, supramolecular structure展开更多
In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relat...In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relative degree,and whose parameters are unknown.By generalising the application of standard direct MRAC strategy to plants described by fractional order models,we develop a fractional adaptive control scheme(FOMRAC)based on the output feedback.We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory.The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem.Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.展开更多
Despite the efficiency of trajectory piecewise-linear(TPWL)model order re-duction(MOR)for nonlinear circuits,it needs large amount of expansion points forlarge-scale nonlinear circuits.This will inevitably increase th...Despite the efficiency of trajectory piecewise-linear(TPWL)model order re-duction(MOR)for nonlinear circuits,it needs large amount of expansion points forlarge-scale nonlinear circuits.This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels.In this paper,subspaceTPWL-MOR approach is developed for the model order reduction of nonlinear cir-cuits.By breaking the high-dimensional state space into several subspaces with much lower dimensions,the subspace TPWL-MOR has very promising advantages of re-ducing the number of expansion points as well as increasing the effective region of thereduced-order model in the state space.As a result,the model size and the accuracy of the TWPL model can be greatly improved.The numerical results have shown dra-matic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.展开更多
In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential...By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.展开更多
In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings...In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings and apply it to differential inclusions.展开更多
文摘Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.
文摘In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.
文摘This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the common equation the natural frequencies of an n th order network are correlated with the n port parameters. The equation is simple and dual in form and clear in its physical meaning. The procedure of finding the solution is simplified and standardized, and it will not cause the loss of roots. The common equation would find wide use and be systematized.
基金supported by the National Natural Sci-ence Foundation of China(11501127)Natural Science Foundation of Guangdong Province(2016A030313686)+1 种基金the Training Program for Outstanding Young Teachers in University of Guangdong Province(312XCQ14564)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2013LYM0027,2014KQNCX068)
文摘The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.
文摘In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123311171119)+1 种基金the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211002)the Youth Science Foundation of Education Bureau of Jiangxi Province(Grant No.GJJ14271)
文摘The main purpose of this paper is to study the growth of meromorphic solutions of complex linear differential-difference equations L（z, f） =n∑i=0m∑j=0Aij（z）f^（j）（z ＋ ci） = 0 or F（z）with entire or meromorphic coefficients, and ci, i = 0,..., n being distinct complex numbers,where there is only one dominant coefficient.
基金supported by the National Natural Science Foundation of China (11101096)
文摘This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 11701425,11971493)。
文摘By using the variation of parameters, this paper deals with the general solution and Ulam stability of second order linear dynamic equations with variable coefficients on time scales.In particular, we also obtain the Ulam stability of second order linear dynamic equations with constant coefficients under different cases.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
基金supported by Natural Science Foundation of China（No.11171220） Support Projects of University of Shanghai for Science and Technology（No.14XPM01）
文摘In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.
基金supported by the Key Natural Science Foundation of China:Urban Transportation Planning Theory and Methods under the Information Environment, Grant No. 50738004/E0807
文摘The article intends to find a method to quantify traffic congestion＇s impacts on travelers to help transportation planners and policy decision makers well understand congestion situations. Three new congestion indicators, including transportation environment satisfaction （TES）, travel time satisfaction （TTS）, and traffic congestion frequency and feeling （TCFF）, are defined to estimate urban traffic congestion based on travelers＇ feelings. Data of travelers＇ attitude about congestion and trip information were collected from a survey in Shanghai, China. Based on the survey data, we estimated the value of the three indi- cators. Then, the principal components analysis was used to derive a small number of linear combinations of a set of variables to estimate the whole congestion status. A linear regression model was used to find out the significant variables which impact respondents＇ feelings. Two ordered logit models were used to select significant variables of TES and TTS. Attitudinal factor variables were also used in these models. The results show that attitudinal factor variables and cluster category variables are as important as sociodemographic variables in the models. Using the three congestion indicators, the government can collect travelers＇ feeling about traffic congestion and estimate the transportation policy that might be applied to cope with traffic congestion.
基金supported by the National Natural Science Foundation of China(6120300761304239+1 种基金61503392)the Natural Science Foundation of Shaanxi Province(2015JQ6213)
文摘This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.
文摘The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.
文摘This paper concerns the superconvergence property of the ultraweak-local discontinuous Galerkin(UWLDG)method for one-dimensional linear sixth-order equations.The crucial technique is the construction of a special projection.We will discuss in three different situations according to the remainder of k,the highest degree of polynomials in the function space,divided by 3.We can prove the(2k-1)th-order superconvergence for the cell averages when k=0 or 2(mod 3).But if k=1(mod 3),we can only prove a(2k-2)th-order superconvergence.The same superconvergence orders can also be gained for the errors of numerical fuxes.We will also prove the superconvergence of order k+2 at some special quadrature points.Some numerical examples are given at the end of this paper.
基金theNationalNaturalScienceFoundationofChina (No .2 97330 90 )theDoctoralProgramofHigherEducation(No.19990 18310 )
文摘The hydrothermal reactions of CuI, KI and bidentate amines [ 1,10 phenanthroline (phen) or ethylenediamine (en)] gave the three copper(I) halide compounds, Cu3I3(phen)2 (1), CuI(phen)2 (2) and 2 (3), which were structurally characterized via singlecrystal Xray diffraction studies. Hydrogen bonds and ππ interactions are the most remarkable structural features of the title compounds. All can be described as higherdimensional supramolecular compounds connected via these secondary bondings. Moreover, the title compounds were characterized by elemental analyses, IR spectra and TGA analyses. The thirdorder nonlinear optical properties of the title compounds were also investigated and all exhibit nicer nonlinear absorption and selffocusing performance.Keywords copper(I) halide, hydrothermal synthesis, the thirdorder nonlinear optical property, supramolecular structure
文摘In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relative degree,and whose parameters are unknown.By generalising the application of standard direct MRAC strategy to plants described by fractional order models,we develop a fractional adaptive control scheme(FOMRAC)based on the output feedback.We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory.The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem.Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.
文摘Despite the efficiency of trajectory piecewise-linear(TPWL)model order re-duction(MOR)for nonlinear circuits,it needs large amount of expansion points forlarge-scale nonlinear circuits.This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels.In this paper,subspaceTPWL-MOR approach is developed for the model order reduction of nonlinear cir-cuits.By breaking the high-dimensional state space into several subspaces with much lower dimensions,the subspace TPWL-MOR has very promising advantages of re-ducing the number of expansion points as well as increasing the effective region of thereduced-order model in the state space.As a result,the model size and the accuracy of the TWPL model can be greatly improved.The numerical results have shown dra-matic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.
基金Supported by Research Foundation of the Fujian Education Bureau (JA04158)the Natural Science Foundation of Fujian Province (No.2006J0209)the Foundation of Developing Science and Technology of Fuzhou University under the grant (2005-XQ-20).
文摘In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
文摘By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.
文摘In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings and apply it to differential inclusions.
