We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the f...We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.展开更多
Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suf...Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.展开更多
Aiming to ensure the consistency of quality control of Traditional Chinese Medicines(TCMs),a combination method of high-performance liquid chromatography(HPLC),ultraviolet(UV),electrochemical(EC)was developed in this ...Aiming to ensure the consistency of quality control of Traditional Chinese Medicines(TCMs),a combination method of high-performance liquid chromatography(HPLC),ultraviolet(UV),electrochemical(EC)was developed in this study to comprehensively evaluate the quality of Antiviral Mixture(AM),and Comprehensive Linear Quantification Fingerprint Method(CLQFM)was used to process the data.Quantitative analysis of three active substances in TCM was conducted.A fivewavelength fusion fingerprint(FWFF)was developed,using second-order derivatives of UV spectral data to differentiate sample levels effectively.The combination of HPLC and UV spectrophotometry,along with electrochemical fingerprinting(ECFP),successfully evaluated total active substances.Ultimately,a multidimensional profiling analytical system for TCM was developed.展开更多
Feedforward multi layer neural networks have very strong mapping capability that is based on the non linearity of the activation function, however, the non linearity of the activation function can cause the multiple ...Feedforward multi layer neural networks have very strong mapping capability that is based on the non linearity of the activation function, however, the non linearity of the activation function can cause the multiple local minima on the learning error surfaces, which affect the learning rate and solving optimal weights. This paper proposes a learning method linearizing non linearity of the activation function and discusses its merits and demerits theoretically.展开更多
This paper investigates the magnetohydrodynamic (MHD) boundary layer flow of an incompressible upper-convected Maxwell (UCM) fluid over a porous stretching surface. Similarity transformations are used to reduce th...This paper investigates the magnetohydrodynamic (MHD) boundary layer flow of an incompressible upper-convected Maxwell (UCM) fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method (STSLM). The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.展开更多
This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rul...This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.展开更多
The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the con...The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the context of the transfer matrix method of linear multibody systems closed- loop topology for computing the free vibration characteristics of elastically coupled flexible launch vehicle boosters. In this approach, the coupled system is idealized as a triple-beam system-like structure coupled by linear translational springs, where a non-uniform free-free Euler-Bemoulli beam is used. A large thrust-to-weight ratio leads to large axial accelera- tions that result in an axial inertia load distribution from nose to tail. Consequently, it causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. This scenario does not need the global dynamics equations of a system, and it has high computational efficiency and low memory requirements. The validity of the presented scenario is achieved through com- parison to other approaches published in the literature.展开更多
A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems...A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.展开更多
In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy ...In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.展开更多
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
C^1 natural element method (C^1 NEM) is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolati...C^1 natural element method (C^1 NEM) is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation (NNI), with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions (EBCs) can be imposed directly in a Galerkin scheme for partial differential equations (PDEs). In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor (SCF) are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.展开更多
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e.,...The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory(LST) for two-dimensional(2D) disturbance on one-dimensional(1D) basic flow, comparison with LST for three-dimensional(3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence(FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting(TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous' in secondary instability.展开更多
A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing ag...A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing agent TBA.In 1.2 mol/L HCl solution, Pr^(3+)reacts with TBA and forms 1:3 com- plex,the conditional stability constant(lgβ_3)of the complex determined is 15.47,and its molar absorptivity(ε_3^(630))is 1.48×10~5 L·mol^(-1)·cm^(-1).展开更多
The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solv...The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solving the damage structure analysis of hardened and softened nonlinear material.展开更多
Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical res...Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.展开更多
In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties...In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.展开更多
Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the est...Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the estimators βn* and gn*forβ and g are obtained by using class K and the least square methods. It is shown that βn* is asymptotically normal and gn* achieves the convergent rate O(n-1/3).展开更多
According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calcula...According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calculating the mole fraction of free complexing agent in the solutions from spectral data.and two linear regression formula have been introduced to determine the composition,the molar absorptivity,the conditional stability constant of the complex and the concentration of the complexing agent. This method has been used in Ho-TBA and Y-TBA systems.Ho^(3+)and Y^(3+)react with TBA and form 1: 2 complexes in HCl-NaAc buffer solution at pH 3.80.Their molar absorptivities determined are 1.03×10~8 and 1.10×10~8 cm^2·mol^(-1),and the conditional stability constants(logβ_2)are 11.37 and 11.15 respectively.After considering the pH effect in TBA complexing,their stability constants(log β_2^(ahs))are 43.23 and 43.01. respectively.The new method is adaptable to such systems where the accurate concentration of the complexing agent can not be known conveniently.展开更多
This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classica...This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.展开更多
Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability ...Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability analysis that the intersection of stability regions of the equation and the method is not empty, in addition to approaches to the boundary of the delay differential equation(DDEs) in the limiting case of step size boundary of the stability region of linear multistep methods.展开更多
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China(2019D01A05)supported by the NSFC(11571132)。
文摘We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.
基金National Natural Science Foundation of China(61973037)National 173 Program Project(2019-JCJQ-ZD-324)。
文摘Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.
基金This study was supported by the National Natural Science Foundation of China(No.81573586).
文摘Aiming to ensure the consistency of quality control of Traditional Chinese Medicines(TCMs),a combination method of high-performance liquid chromatography(HPLC),ultraviolet(UV),electrochemical(EC)was developed in this study to comprehensively evaluate the quality of Antiviral Mixture(AM),and Comprehensive Linear Quantification Fingerprint Method(CLQFM)was used to process the data.Quantitative analysis of three active substances in TCM was conducted.A fivewavelength fusion fingerprint(FWFF)was developed,using second-order derivatives of UV spectral data to differentiate sample levels effectively.The combination of HPLC and UV spectrophotometry,along with electrochemical fingerprinting(ECFP),successfully evaluated total active substances.Ultimately,a multidimensional profiling analytical system for TCM was developed.
文摘Feedforward multi layer neural networks have very strong mapping capability that is based on the non linearity of the activation function, however, the non linearity of the activation function can cause the multiple local minima on the learning error surfaces, which affect the learning rate and solving optimal weights. This paper proposes a learning method linearizing non linearity of the activation function and discusses its merits and demerits theoretically.
文摘This paper investigates the magnetohydrodynamic (MHD) boundary layer flow of an incompressible upper-convected Maxwell (UCM) fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method (STSLM). The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.
基金Project supported by the National Natural Science Foundation of China(No.11471217)
文摘This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.
基金supported by the Research Fund for the Doctoral Program of Higher Education of China(Grants 20113219110025,20133219110037)the National Natural Science Foundation of China(Grants 11102089,61304137)the Program for New Century Excellent Talents in University(NCET-10-0075)
文摘The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the context of the transfer matrix method of linear multibody systems closed- loop topology for computing the free vibration characteristics of elastically coupled flexible launch vehicle boosters. In this approach, the coupled system is idealized as a triple-beam system-like structure coupled by linear translational springs, where a non-uniform free-free Euler-Bemoulli beam is used. A large thrust-to-weight ratio leads to large axial accelera- tions that result in an axial inertia load distribution from nose to tail. Consequently, it causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. This scenario does not need the global dynamics equations of a system, and it has high computational efficiency and low memory requirements. The validity of the presented scenario is achieved through com- parison to other approaches published in the literature.
基金supported by the National Natural Science Foundation of China (No. 11071033)the Fundamental Research Funds for the Central Universities (No. 090405013)
文摘A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.
文摘In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
基金supported by the SDUST Spring Bud (2009AZZ021)Taian Science and Technology Development (20112001)
文摘C^1 natural element method (C^1 NEM) is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation (NNI), with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions (EBCs) can be imposed directly in a Galerkin scheme for partial differential equations (PDEs). In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor (SCF) are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1120214711332007+2 种基金11172203and 91216111)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120032120007)
文摘The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory(LST) for two-dimensional(2D) disturbance on one-dimensional(1D) basic flow, comparison with LST for three-dimensional(3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence(FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting(TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous' in secondary instability.
文摘A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing agent TBA.In 1.2 mol/L HCl solution, Pr^(3+)reacts with TBA and forms 1:3 com- plex,the conditional stability constant(lgβ_3)of the complex determined is 15.47,and its molar absorptivity(ε_3^(630))is 1.48×10~5 L·mol^(-1)·cm^(-1).
文摘The virtual displacement principle of elasto-plastic damage mechanics is presented. A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solving the damage structure analysis of hardened and softened nonlinear material.
基金This research was funded by Fundamental Research Grant Scheme(FRGS)under the Ministry of Higher Education Malaysia,grant number with project ref:FRGS/1/2019/STG06/UTP/03/2.
文摘Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.
文摘In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.
文摘Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the estimators βn* and gn*forβ and g are obtained by using class K and the least square methods. It is shown that βn* is asymptotically normal and gn* achieves the convergent rate O(n-1/3).
文摘According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calculating the mole fraction of free complexing agent in the solutions from spectral data.and two linear regression formula have been introduced to determine the composition,the molar absorptivity,the conditional stability constant of the complex and the concentration of the complexing agent. This method has been used in Ho-TBA and Y-TBA systems.Ho^(3+)and Y^(3+)react with TBA and form 1: 2 complexes in HCl-NaAc buffer solution at pH 3.80.Their molar absorptivities determined are 1.03×10~8 and 1.10×10~8 cm^2·mol^(-1),and the conditional stability constants(logβ_2)are 11.37 and 11.15 respectively.After considering the pH effect in TBA complexing,their stability constants(log β_2^(ahs))are 43.23 and 43.01. respectively.The new method is adaptable to such systems where the accurate concentration of the complexing agent can not be known conveniently.
文摘This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.
文摘Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability analysis that the intersection of stability regions of the equation and the method is not empty, in addition to approaches to the boundary of the delay differential equation(DDEs) in the limiting case of step size boundary of the stability region of linear multistep methods.