The topic on the subspaces for the polynomially or exponentially bounded weak mild solutions of the following abstract Cauchy problem d^2/(dr^2)u(t,x)=Au(t,x);u(0,x)=x,d/(dt)u(0,x)=0,x∈X is studied, wher...The topic on the subspaces for the polynomially or exponentially bounded weak mild solutions of the following abstract Cauchy problem d^2/(dr^2)u(t,x)=Au(t,x);u(0,x)=x,d/(dt)u(0,x)=0,x∈X is studied, where A is a closed operator on Banach space X. The case that the problem is ill-posed is treated, and two subspaces Y(A, k) and H(A, ω) are introduced. Y(A, k) is the set of all x in X for which the second order abstract differential equation has a weak mild solution v( t, x) such that ess sup{(1+t)^-k|d/(dt)〈v(t,x),x^*〉|:t≥0,x^*∈X^*,|x^*‖≤1}〈+∞. H(A, ω) is the set of all x in X for which the second order abstract differential equation has a weak mild solution v(t,x)such that ess sup{e^-ωl|d/(dt)〈v(t,x),x^*)|:t≥0,x^*∈X^*,‖x^*‖≤1}〈+∞. The following conclusions are proved that Y(A, k) and H(A, ω) are Banach spaces, and both are continuously embedded in X; the restriction operator A | Y(A,k) generates a once-integrated cosine operator family { C(t) }t≥0 such that limh→0+^-1/h‖C(t+h)-C(t)‖Y(A,k)≤M(1+t)^k,arbitary t≥0; the restriction operator A |H(A,ω) generates a once- integrated cosine operator family {C(t)}t≥0 such that limh→0+^-1/h‖C(t+h)-C(t)‖H(A,ω)≤≤Me^ωt,arbitary t≥0.展开更多
In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosin...In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.展开更多
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 ...Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.展开更多
Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line (TDL) structure for nonuniform linear array (NLA) is designed according to the rule of...Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line (TDL) structure for nonuniform linear array (NLA) is designed according to the rule of minimizing the beamformer's output power while keeping the distortionless response (DR) in the direction of desired signal and keeping the constant beamwidth (CB) with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming (SOCP). The computer simulations are presented which illustrate the effectiveness of our beamformer.展开更多
This article is concerned with the oscillation of the forced second order differ- ential equation with mixed nonlinearities(a(t)(x'(t))γ)'+po(t)xγ(go(t))+n∑t=1pi(t)|x(gi(t))|αi sgn x(gi...This article is concerned with the oscillation of the forced second order differ- ential equation with mixed nonlinearities(a(t)(x'(t))γ)'+po(t)xγ(go(t))+n∑t=1pi(t)|x(gi(t))|αi sgn x(gi(t))=e(t),where γ is a quotient of odd positive integers αi〉0,i=1,2 ……n,a,e,and pi ∈ C([0,∞)R),a(t)〉0,gi:R→R are positive continuous functions on R with lim gi (t)=∞,i=0,1,……,n. Our results generalize and improve the results in a recent article by Sun and Wong[29].展开更多
A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t) + p(t)x′(t) + q(t)|x(t)|αsgnx(t) = 0, t ≥ t0,where α>1,p and q are continuous f...A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t) + p(t)x′(t) + q(t)|x(t)|αsgnx(t) = 0, t ≥ t0,where α>1,p and q are continuous functions on[t0,∞). This criterion extends and unifies some of the results obtained in [1]- [5].展开更多
This paper presents a simple and systematic approach to design second order sliding mode controller for buck converters.The second order sliding mode control(SOSMC)based on twisting algorithm has been implemented to c...This paper presents a simple and systematic approach to design second order sliding mode controller for buck converters.The second order sliding mode control(SOSMC)based on twisting algorithm has been implemented to control buck switch mode converter.The idea behind this strategy is to suppress chattering and maintain robustness and finite time convergence properties of the output voltage error to the equilibrium point under the load variations and parametric uncertainties.In addition,the influence of the twisting algorithm on the performance of closed-loop system is investigated and compared with other algorithms of first order sliding mode control such as adaptive sliding mode control(ASMC),nonsingular terminal sliding mode control(NTSMC).In comparative evaluation,the transient response of the output voltage with the step change in the load and the start-up response of the output voltage with the step change in the input voltage of buck converter were compared.Experimental results were obtained from a hardware setup constructed in laboratory.Finally,for all of the surveyed control methods,the theoretical considerations,numerical simulations,and experimental measurements from a laboratory prototype are compared for different operating points.It is shown that the proposed twisting method presents an improvement in steady state error and settling time of output voltage during load changes.展开更多
This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it's a linear bounded operator of space Ha(L)...This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it's a linear bounded operator of space Ha(L)(m, s). Then Plemelj formula and some other properties for random singular integral are proved.展开更多
In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermit...In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given.展开更多
The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t) + ↓△V(t, q(t)) = 0, where V(t, x) = -K(t, x) + W(t, x), K(t, x) is neit...The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t) + ↓△V(t, q(t)) = 0, where V(t, x) = -K(t, x) + W(t, x), K(t, x) is neither a quadratic form in x nor periodic in t and W(t, x) is superquadratic in x.展开更多
By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral dela...By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.展开更多
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an ...A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been de- rived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is 'free wave', travelling independently of the first order wave system, the other is 'phase locked waves', which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical cir- cular cylinder have been calculated, and the numerical results agree well with the experimental data.展开更多
The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predic...The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.This is a new approach,and,as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea,avoids the inaccuracies resulting from using a first order linear wave model in the simulation process.The predicted results have been systematically analyzed and compared,and the advantages of using this new approach have been convincingly substantiated.展开更多
An on-line blind source separation (BSS) algorithm is presented in this paper under the assumption that sources are temporarily correlated signals. By using only some of the observed samples in a recursive calculati...An on-line blind source separation (BSS) algorithm is presented in this paper under the assumption that sources are temporarily correlated signals. By using only some of the observed samples in a recursive calculation, the whitening matrix and the rotation matrix could be approximately obtained through the measurement of only one cost function. SimNations show goad performance of the algorithm.展开更多
The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parame...The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parametric variations. Among the most evoked control strategies adopted in this field to overcome these drawbacks presented in classical drive, it is worth mentioning the use of the second order sliding mode control(SOSMC) based on the super twisting algorithm(STA) combined with the fuzzy logic control(FSOSMC). In order to realize the optimal control performance, the FSOSMC parameters are adjusted using an optimization algorithm based on the genetic algorithm(GA). The performances of the envisaged control scheme, called G-FSOSMC, are investigated against G-SOSMC, G-PI and BBO-FSOSMC algorithms. The proposed controller scheme is efficient in reducing the torque and flux ripples, and successfully suppresses chattering. The effects of parametric uncertainties do not affect system performance.展开更多
With a new approach,the general current expressions of two typical second order catalytic reactions at microelectrodes are obtained.This allows the study of fast chemical reactions and systems where the reactants are ...With a new approach,the general current expressions of two typical second order catalytic reactions at microelectrodes are obtained.This allows the study of fast chemical reactions and systems where the reactants are present in similar concentrations.展开更多
The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold ...The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.展开更多
Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride ...Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride units, which was obtained by the reaction of 4-nitro-4'-[N-hydroxyethyl, N'-ethyl] amino azobenzene with polymethacryloyl chloride (chromophore content: 25 mol %). During thermal poling process the anhydride reacts with the epoxy group and the resulting crosslinked network structure will stabilize the second harmonic generation in the poled film. The second harmonic generation of the poled film shows a maximum with the variation of composition this is presumed to be due to the effects of the increasing of concentration, orientation order as well as orientation stability of chromophore groups during crosslinking.展开更多
基金The Natural Science Foundation of Department ofEducation of Jiangsu Province (No06KJD110087)
文摘The topic on the subspaces for the polynomially or exponentially bounded weak mild solutions of the following abstract Cauchy problem d^2/(dr^2)u(t,x)=Au(t,x);u(0,x)=x,d/(dt)u(0,x)=0,x∈X is studied, where A is a closed operator on Banach space X. The case that the problem is ill-posed is treated, and two subspaces Y(A, k) and H(A, ω) are introduced. Y(A, k) is the set of all x in X for which the second order abstract differential equation has a weak mild solution v( t, x) such that ess sup{(1+t)^-k|d/(dt)〈v(t,x),x^*〉|:t≥0,x^*∈X^*,|x^*‖≤1}〈+∞. H(A, ω) is the set of all x in X for which the second order abstract differential equation has a weak mild solution v(t,x)such that ess sup{e^-ωl|d/(dt)〈v(t,x),x^*)|:t≥0,x^*∈X^*,‖x^*‖≤1}〈+∞. The following conclusions are proved that Y(A, k) and H(A, ω) are Banach spaces, and both are continuously embedded in X; the restriction operator A | Y(A,k) generates a once-integrated cosine operator family { C(t) }t≥0 such that limh→0+^-1/h‖C(t+h)-C(t)‖Y(A,k)≤M(1+t)^k,arbitary t≥0; the restriction operator A |H(A,ω) generates a once- integrated cosine operator family {C(t)}t≥0 such that limh→0+^-1/h‖C(t+h)-C(t)‖H(A,ω)≤≤Me^ωt,arbitary t≥0.
基金This project is supported by the Natural Science Foundation of China and Science Development Foundation of the Colleges and University of Shanghai.
文摘In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.
基金Supported by the Natural Science Foundation of Hunan Province(06JJ50008) Supported by the Natural Science Foundation of Guangdong Province(7004569)
文摘Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.
基金supported by the National Nature Science Foundation of China (60472101)President Award of ChineseAcademy of Sciences(O729031511).
文摘Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line (TDL) structure for nonuniform linear array (NLA) is designed according to the rule of minimizing the beamformer's output power while keeping the distortionless response (DR) in the direction of desired signal and keeping the constant beamwidth (CB) with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming (SOCP). The computer simulations are presented which illustrate the effectiveness of our beamformer.
文摘This article is concerned with the oscillation of the forced second order differ- ential equation with mixed nonlinearities(a(t)(x'(t))γ)'+po(t)xγ(go(t))+n∑t=1pi(t)|x(gi(t))|αi sgn x(gi(t))=e(t),where γ is a quotient of odd positive integers αi〉0,i=1,2 ……n,a,e,and pi ∈ C([0,∞)R),a(t)〉0,gi:R→R are positive continuous functions on R with lim gi (t)=∞,i=0,1,……,n. Our results generalize and improve the results in a recent article by Sun and Wong[29].
文摘A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t) + p(t)x′(t) + q(t)|x(t)|αsgnx(t) = 0, t ≥ t0,where α>1,p and q are continuous functions on[t0,∞). This criterion extends and unifies some of the results obtained in [1]- [5].
文摘This paper presents a simple and systematic approach to design second order sliding mode controller for buck converters.The second order sliding mode control(SOSMC)based on twisting algorithm has been implemented to control buck switch mode converter.The idea behind this strategy is to suppress chattering and maintain robustness and finite time convergence properties of the output voltage error to the equilibrium point under the load variations and parametric uncertainties.In addition,the influence of the twisting algorithm on the performance of closed-loop system is investigated and compared with other algorithms of first order sliding mode control such as adaptive sliding mode control(ASMC),nonsingular terminal sliding mode control(NTSMC).In comparative evaluation,the transient response of the output voltage with the step change in the load and the start-up response of the output voltage with the step change in the input voltage of buck converter were compared.Experimental results were obtained from a hardware setup constructed in laboratory.Finally,for all of the surveyed control methods,the theoretical considerations,numerical simulations,and experimental measurements from a laboratory prototype are compared for different operating points.It is shown that the proposed twisting method presents an improvement in steady state error and settling time of output voltage during load changes.
基金The project is supported by the NSF of China (10271098)Education Foundation of Fujian (JB02083) Science & Technical Development Foundation of Fuzhou University (2003xy-11).
文摘This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it's a linear bounded operator of space Ha(L)(m, s). Then Plemelj formula and some other properties for random singular integral are proved.
文摘In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given.
基金Supported by National Natural Science Foundation of China (10771173)
文摘The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t) + ↓△V(t, q(t)) = 0, where V(t, x) = -K(t, x) + W(t, x), K(t, x) is neither a quadratic form in x nor periodic in t and W(t, x) is superquadratic in x.
文摘By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
文摘A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been de- rived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is 'free wave', travelling independently of the first order wave system, the other is 'phase locked waves', which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical cir- cular cylinder have been calculated, and the numerical results agree well with the experimental data.
基金The National Natural Science Foundation of China under contract No.51979165。
文摘The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.This is a new approach,and,as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea,avoids the inaccuracies resulting from using a first order linear wave model in the simulation process.The predicted results have been systematically analyzed and compared,and the advantages of using this new approach have been convincingly substantiated.
基金This project was supported by the National 863 project (2001AA422420 -02)
文摘An on-line blind source separation (BSS) algorithm is presented in this paper under the assumption that sources are temporarily correlated signals. By using only some of the observed samples in a recursive calculation, the whitening matrix and the rotation matrix could be approximately obtained through the measurement of only one cost function. SimNations show goad performance of the algorithm.
基金Project supported by the LEB Research LaboratoryDepartment of Electrical Engineering,University of Batna 2, Algeria。
文摘The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parametric variations. Among the most evoked control strategies adopted in this field to overcome these drawbacks presented in classical drive, it is worth mentioning the use of the second order sliding mode control(SOSMC) based on the super twisting algorithm(STA) combined with the fuzzy logic control(FSOSMC). In order to realize the optimal control performance, the FSOSMC parameters are adjusted using an optimization algorithm based on the genetic algorithm(GA). The performances of the envisaged control scheme, called G-FSOSMC, are investigated against G-SOSMC, G-PI and BBO-FSOSMC algorithms. The proposed controller scheme is efficient in reducing the torque and flux ripples, and successfully suppresses chattering. The effects of parametric uncertainties do not affect system performance.
文摘With a new approach,the general current expressions of two typical second order catalytic reactions at microelectrodes are obtained.This allows the study of fast chemical reactions and systems where the reactants are present in similar concentrations.
文摘The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.
文摘Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride units, which was obtained by the reaction of 4-nitro-4'-[N-hydroxyethyl, N'-ethyl] amino azobenzene with polymethacryloyl chloride (chromophore content: 25 mol %). During thermal poling process the anhydride reacts with the epoxy group and the resulting crosslinked network structure will stabilize the second harmonic generation in the poled film. The second harmonic generation of the poled film shows a maximum with the variation of composition this is presumed to be due to the effects of the increasing of concentration, orientation order as well as orientation stability of chromophore groups during crosslinking.