Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor...Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.展开更多
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.展开更多
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and th...In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.展开更多
A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integr...A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.展开更多
This article deals with evaluating the frequency response of functionally graded carbon nanotube reinforced magneto-electro-elastic(FG-CNTMEE)plates subjected to open and closed electro-magnetic circuit conditions.In ...This article deals with evaluating the frequency response of functionally graded carbon nanotube reinforced magneto-electro-elastic(FG-CNTMEE)plates subjected to open and closed electro-magnetic circuit conditions.In this regard finite element formulation has been derived.The plate kinematics adjudged via higher order shear deformation theory(HSDT)is considered for evaluation.The equations of motion are obtained with the help of Hamilton’s principle and solved using condensation technique.It is found that the convergence and accuracy of the present FE formulation is very good to address the vibration problem of FG-CNTMEE plate.For the first time,frequency response analysis of FG-CNTMEE plates considering the effect of various circuit conditions associated with parameters such as CNT distributions,volume fraction,skew angle,aspect ratio,length-to-thickness ratio and coupling fields has been carried out.The results of this article can serve as benchmark for future development and analysis of smart structures.展开更多
We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with sol...We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.展开更多
According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of va...According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained.展开更多
In this paper, by using the Nevanlinna Theory on angular domain, we establish a theorem which concerns the growth of entire function and his zero. As an application, we survey the location of zero of higher order diff...In this paper, by using the Nevanlinna Theory on angular domain, we establish a theorem which concerns the growth of entire function and his zero. As an application, we survey the location of zero of higher order differential equation, which can be regarded as an alternating but precise version of Wu and Yi.展开更多
This article deals with investigating the effect of cut-outs on the natural frequencies of magneto-electroelastic(MEE)plates incorporating finite element methods based on higher order shear deformation theory(HSDT).In...This article deals with investigating the effect of cut-outs on the natural frequencies of magneto-electroelastic(MEE)plates incorporating finite element methods based on higher order shear deformation theory(HSDT).In order to consider the influence of cut-out,the energy of the cut-out domain is subtracted from the total energy of the entire plate.The governing equations of motions are derived through incorporating Hamilton’s principle and the solution is obtained using condensation technique.The proposed numerical formulation is verified with the results of previously published literature as well as the numerical software.In addition,this research focuses on evaluating the effect of geometrical skewness and boundary conditions on the frequency response.The influence of cut-outs on the degree of coupling between magnetic,electric and elastic fields is also investigated.展开更多
In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,w...In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,where n≥2,φ(u)=|u|^(γ)sgn(u)forγ>0,ri(1≤i≤n)are positive rd-continuous functions and h∈C_(rd)(T,(0,∞)).The functionτ∈C_(rd)(T,T)satisfiesτ(t)≤t and lim_(t→∞)τ(t)=∞and f∈C(R,R).By using a generalized Riccati transformation,we give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.The obtained results are new for the corresponding higher order differential equations and difference equations.In the end,some applications and examples are provided to illustrate the importance of the main results.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
In view of a new idea on initial conditions, an open problem of nonlinear evolution equations with higher order, which was given by J. L. Lions, is solved. Effect of our results is shown on an example.
Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass a...Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass attached to a light cantilever cylinder and their corresponding deformation response spectra are estimated by utilizing a generalized single degree of freedom system. Based on the wave data recorded in the Persian Gulf region, extreme wave loading conditions corresponding to different return periods are exerted on the offshore structures. Accordingly, the effect of the higher order components of the drag force is considered and compared to the linearized state for different sea surface levels. When the fundamental period of the offshore structure is about one third of the main period of wave loading, the results indicate the linearized drag term is not capable of achieving a reliable deformation response spectrum.展开更多
In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly va...In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.展开更多
In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate ...In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.展开更多
The permanence of a nonlinear higher order discrete time system from macroeconomics is studied, and a sufficient condition is proposed for the permanence of the system described by 11(,...,)nnnnkxrxfxx---=+ where :kfR...The permanence of a nonlinear higher order discrete time system from macroeconomics is studied, and a sufficient condition is proposed for the permanence of the system described by 11(,...,)nnnnkxrxfxx---=+ where :kfRR, the initial values 01,,kxx-are real numbers and [0,1)r is constant after exploring the relationship between this equation and 1(,...,)nnnkxfxx--= for certain classes of function f. As an application a short proof is given to a known result in a simpler way than ever reported.展开更多
Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be...Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.展开更多
Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Pain...There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Painlevétest is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients.Finally the Painlevéintegrability condition of this equation is gotten.展开更多
The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order ...The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order harmonics suppression with single order diffraction gratings in extreme ultraviolet and soft x-ray. The principle of harmonic suppression with single order diffraction grating is described, and an extreme ultraviolet and soft x-ray non-harmonics grating monochromator is designed based on the single order diffraction grating. The performance is simulated by an optical design software. The emergent beams of a monochromator with different gratings are measured by a transmission grating spectrometer. The results show that the single order diffraction grating can suppress higher order harmonics effectively, and it is expected to be widely used in synchrotron radiation, diagnostics of laser induced plasma, and astrophysics.展开更多
文摘Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
基金Foundation item is supported by the NNSF of China(19971064)
文摘In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
基金supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206)Innovation Foundation of Xiamen University(XDKJCX20063019),the National Science Foundation of China (10771174)
文摘A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
文摘This article deals with evaluating the frequency response of functionally graded carbon nanotube reinforced magneto-electro-elastic(FG-CNTMEE)plates subjected to open and closed electro-magnetic circuit conditions.In this regard finite element formulation has been derived.The plate kinematics adjudged via higher order shear deformation theory(HSDT)is considered for evaluation.The equations of motion are obtained with the help of Hamilton’s principle and solved using condensation technique.It is found that the convergence and accuracy of the present FE formulation is very good to address the vibration problem of FG-CNTMEE plate.For the first time,frequency response analysis of FG-CNTMEE plates considering the effect of various circuit conditions associated with parameters such as CNT distributions,volume fraction,skew angle,aspect ratio,length-to-thickness ratio and coupling fields has been carried out.The results of this article can serve as benchmark for future development and analysis of smart structures.
基金Supported by the NNSF of China (10471107)RFDP of Higher Education of China (20060486001)
文摘We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.
文摘According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained.
文摘In this paper, by using the Nevanlinna Theory on angular domain, we establish a theorem which concerns the growth of entire function and his zero. As an application, we survey the location of zero of higher order differential equation, which can be regarded as an alternating but precise version of Wu and Yi.
文摘This article deals with investigating the effect of cut-outs on the natural frequencies of magneto-electroelastic(MEE)plates incorporating finite element methods based on higher order shear deformation theory(HSDT).In order to consider the influence of cut-out,the energy of the cut-out domain is subtracted from the total energy of the entire plate.The governing equations of motions are derived through incorporating Hamilton’s principle and the solution is obtained using condensation technique.The proposed numerical formulation is verified with the results of previously published literature as well as the numerical software.In addition,this research focuses on evaluating the effect of geometrical skewness and boundary conditions on the frequency response.The influence of cut-outs on the degree of coupling between magnetic,electric and elastic fields is also investigated.
基金supported by the Jiangxi Provincial Natural Science Foundation(20202BABL211003)the Science and Technology Project of Jiangxi Education Department(GJJ180354).
文摘In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,where n≥2,φ(u)=|u|^(γ)sgn(u)forγ>0,ri(1≤i≤n)are positive rd-continuous functions and h∈C_(rd)(T,(0,∞)).The functionτ∈C_(rd)(T,T)satisfiesτ(t)≤t and lim_(t→∞)τ(t)=∞and f∈C(R,R).By using a generalized Riccati transformation,we give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.The obtained results are new for the corresponding higher order differential equations and difference equations.In the end,some applications and examples are provided to illustrate the importance of the main results.
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 TWAS,UNESO and AMSS in Chinese AcademyThe research of the third author is partially supported by NSFC(11001239)
文摘In view of a new idea on initial conditions, an open problem of nonlinear evolution equations with higher order, which was given by J. L. Lions, is solved. Effect of our results is shown on an example.
文摘Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass attached to a light cantilever cylinder and their corresponding deformation response spectra are estimated by utilizing a generalized single degree of freedom system. Based on the wave data recorded in the Persian Gulf region, extreme wave loading conditions corresponding to different return periods are exerted on the offshore structures. Accordingly, the effect of the higher order components of the drag force is considered and compared to the linearized state for different sea surface levels. When the fundamental period of the offshore structure is about one third of the main period of wave loading, the results indicate the linearized drag term is not capable of achieving a reliable deformation response spectrum.
文摘In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.
基金the National Natural Science Foundation of China(10671184)
文摘In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.
基金the Technology Research Foundation of the State Ministry of Education (No. 02130)
文摘The permanence of a nonlinear higher order discrete time system from macroeconomics is studied, and a sufficient condition is proposed for the permanence of the system described by 11(,...,)nnnnkxrxfxx---=+ where :kfRR, the initial values 01,,kxx-are real numbers and [0,1)r is constant after exploring the relationship between this equation and 1(,...,)nnnkxfxx--= for certain classes of function f. As an application a short proof is given to a known result in a simpler way than ever reported.
文摘Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.
文摘Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
基金Supported by the Shanxi Education Department Project(Grant No.J2020398)Key Natural Science Projects of Shanxi Energy Institute(Grant No.ZZ-2018003)。
文摘There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Painlevétest is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients.Finally the Painlevéintegrability condition of this equation is gotten.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0206004)the National Natural Science Foundation of China(Grant No.11375160)the National Science Instruments Major Project of China(Grant No.2012YQ130125)
文摘The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order harmonics suppression with single order diffraction gratings in extreme ultraviolet and soft x-ray. The principle of harmonic suppression with single order diffraction grating is described, and an extreme ultraviolet and soft x-ray non-harmonics grating monochromator is designed based on the single order diffraction grating. The performance is simulated by an optical design software. The emergent beams of a monochromator with different gratings are measured by a transmission grating spectrometer. The results show that the single order diffraction grating can suppress higher order harmonics effectively, and it is expected to be widely used in synchrotron radiation, diagnostics of laser induced plasma, and astrophysics.
