This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance system...This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.展开更多
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan...Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.展开更多
We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic in...We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic integrals,these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones.We present a practical application of p-DOBIs for deriving the Picard–Fuchs operator.Then we establish the expression of generalized dispersion relation,which enables us to obtain the dispersion relation representation of arbitrary banana integrals.Moreover,we propose a hypothesis for generalized dispersion relation and p-DOBIs,which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.展开更多
Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. T...Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.展开更多
In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and ...In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and reduce the time of numerical computation greatly. Based on the new form, an analytical formula of diffraction field in the far zone has been presented for the polygonal aperture illuminated by a uniform plane wave.展开更多
The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integ...The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.展开更多
We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant in...We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant integrals, symmetric integral, and Skorohod integral with respect to two-parameter Wiener processes.展开更多
Integral Imaging(II)是一种能够记录和显示全真三维场景的图像技术.该技术采用微透镜阵列记录空间场景,空间任意一点的深度信息只需通过一次成像即可直接获得.本文研究结合多基线立体匹配算法采用II直接获取物体空间信息的方法.其结果...Integral Imaging(II)是一种能够记录和显示全真三维场景的图像技术.该技术采用微透镜阵列记录空间场景,空间任意一点的深度信息只需通过一次成像即可直接获得.本文研究结合多基线立体匹配算法采用II直接获取物体空间信息的方法.其结果既可为下一代基于II的三维电视图像的数据处理提供应用基础,同时也可望应用于开发新型的深度测量工具.展开更多
Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were appli...Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.展开更多
Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds...Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.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
In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion i...In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.展开更多
In this paper,we introduce and study the concept of McShane delta integral on time scales.We discuss the relationship between McShane delta integral and Henstock delta integral,and prove a dominated convergence theore...In this paper,we introduce and study the concept of McShane delta integral on time scales.We discuss the relationship between McShane delta integral and Henstock delta integral,and prove a dominated convergence theorems for the McShane delta integral.展开更多
In this paper, a class of singular integral equations with complex translations is discussed. By using the Plemelj projection method the authors reduce them to the boundary value problem of analytic functions in A(+)(...In this paper, a class of singular integral equations with complex translations is discussed. By using the Plemelj projection method the authors reduce them to the boundary value problem of analytic functions in A(+)(H) over cap(0) with upper translation and the boundary value problem of analytic functions in A-(H) over cap(0) with lower translation, which are solved here.展开更多
By elastic-plastic finite deformation finite element analysis (FEA), the conservation of J-integral is investigated in detail for a welded joint with an overmatchingweld in plane stress case. It is indicated that J-in...By elastic-plastic finite deformation finite element analysis (FEA), the conservation of J-integral is investigated in detail for a welded joint with an overmatchingweld in plane stress case. It is indicated that J-integral is path dependent under various conditions at least in the cases studied in this paper. Meanwhile, the above conclusions are verified by the hybrid method results in which combined Moire interferometry with FEA.展开更多
Algorithm for Laplace ′s integral is given when the inverse image function has high order discontinui ty. The multi-node technique of B-spline is used to describe the interruption point, cusp and non-smooth point of...Algorithm for Laplace ′s integral is given when the inverse image function has high order discontinui ty. The multi-node technique of B-spline is used to describe the interruption point, cusp and non-smooth point of the inverse image function. The difference quotient and de Boor algorithm are used to derive the image function of the Lapl ace′s integral under non-uniform partition. And a set of practical formula is got when the partition is quasi-uniform. The scheme enables the image function to be approximated within any prescribed tolerance. Experiments also show that g ood result is achieved. It is much faster than that of Simpsons rule, and much s impler than that of Berge method, the traditional efficient method. It is no lon ger to find the zero points and coefficients of Gauss-Laguerre or Gauss-Legend re polynomials. The image function of Laplace′s integral can also be computed while the inverse image function is hyper-function with high order discontinuity.展开更多
In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such si...In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq（R3） for all q 1. The condition on the integral kernels is known to be optimal.展开更多
This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s...This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s),u(s))dB(s)+∫_(0)^(t)h(t,s)dξ(s).by Here d B(s)denotes the Brownian motion It?type differential,ξdenotes the singular control(singular in time t with respect to Lebesgue measure)and u denotes the regular control(absolutely continuous with respect to Lebesgue measure).Such systems may for example be used to model harvesting of populations with memory,where X(t)represents the population density at time t,and the singular control processξrepresents the harvesting effort rate.The total income from the harvesting is represented by J(u, ξ) = E[∫_(0)^(t) f_(0)(t,X(t), u(t))dt + ∫_(0)^(t)f_(1)(t,X(t))dξ(t) + g(X(T))] for the given functions f0,f1 and g,where T>0 is a constant denoting the terminal time of the harvesting.Note that it is important to allow the controls to be singular,because in some cases the optimal controls are of this type.Using Hida-Malliavin calculus,we prove sufficient conditions and necessary conditions of optimality of controls.As a consequence,we obtain a new type of backward stochastic Volterra integral equations with singular drift.Finally,to illustrate our results,we apply them to discuss optimal harvesting problems with possibly density dependent prices.展开更多
基金the National Natural Science Foundation of China(Grant No.12072090).
文摘This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.
基金supported by the NSF of Hebei Province(A2022208007)the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)。
文摘Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
基金supported by the National Natural Science Foundation of China(Grant No.12175318)the Natural Science Foundation of Guangdong Province of China(Grant No.2022A1515011922).
文摘We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic integrals,these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones.We present a practical application of p-DOBIs for deriving the Picard–Fuchs operator.Then we establish the expression of generalized dispersion relation,which enables us to obtain the dispersion relation representation of arbitrary banana integrals.Moreover,we propose a hypothesis for generalized dispersion relation and p-DOBIs,which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.
文摘Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.
文摘In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and reduce the time of numerical computation greatly. Based on the new form, an analytical formula of diffraction field in the far zone has been presented for the polygonal aperture illuminated by a uniform plane wave.
基金Supported by the Natural Science Foundation of Shandong Province（ZR2010AL019） Supported by the Education Science Foundation of Shandong Province（2010JZ123）
文摘The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.
文摘We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant integrals, symmetric integral, and Skorohod integral with respect to two-parameter Wiener processes.
文摘Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.
基金the Bilateral Science and Technology Collaboration Program of Australia 1998 the Natural Science Foundation of China (No. 1
文摘Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.
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.
基金partially supported by NNSF of China (60534080)the firstauthor is supported in part by the National Science Foundation (DMS0504783)
文摘In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp （f） of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.
文摘In this paper,we introduce and study the concept of McShane delta integral on time scales.We discuss the relationship between McShane delta integral and Henstock delta integral,and prove a dominated convergence theorems for the McShane delta integral.
文摘In this paper, a class of singular integral equations with complex translations is discussed. By using the Plemelj projection method the authors reduce them to the boundary value problem of analytic functions in A(+)(H) over cap(0) with upper translation and the boundary value problem of analytic functions in A-(H) over cap(0) with lower translation, which are solved here.
文摘By elastic-plastic finite deformation finite element analysis (FEA), the conservation of J-integral is investigated in detail for a welded joint with an overmatchingweld in plane stress case. It is indicated that J-integral is path dependent under various conditions at least in the cases studied in this paper. Meanwhile, the above conclusions are verified by the hybrid method results in which combined Moire interferometry with FEA.
文摘Algorithm for Laplace ′s integral is given when the inverse image function has high order discontinui ty. The multi-node technique of B-spline is used to describe the interruption point, cusp and non-smooth point of the inverse image function. The difference quotient and de Boor algorithm are used to derive the image function of the Lapl ace′s integral under non-uniform partition. And a set of practical formula is got when the partition is quasi-uniform. The scheme enables the image function to be approximated within any prescribed tolerance. Experiments also show that g ood result is achieved. It is much faster than that of Simpsons rule, and much s impler than that of Berge method, the traditional efficient method. It is no lon ger to find the zero points and coefficients of Gauss-Laguerre or Gauss-Legend re polynomials. The image function of Laplace′s integral can also be computed while the inverse image function is hyper-function with high order discontinuity.
基金Supported by the NSFC (10771054, 10971141, 11071200)the NFS of Beijing (1092004)the NFS of Fujian Province (2010J01013)
文摘In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq（R3） for all q 1. The condition on the integral kernels is known to be optimal.
基金the financial support provided by the Swedish Research Council grant(2020-04697)the Norwegian Research Council grant(250768/F20),respectively。
文摘This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s),u(s))dB(s)+∫_(0)^(t)h(t,s)dξ(s).by Here d B(s)denotes the Brownian motion It?type differential,ξdenotes the singular control(singular in time t with respect to Lebesgue measure)and u denotes the regular control(absolutely continuous with respect to Lebesgue measure).Such systems may for example be used to model harvesting of populations with memory,where X(t)represents the population density at time t,and the singular control processξrepresents the harvesting effort rate.The total income from the harvesting is represented by J(u, ξ) = E[∫_(0)^(t) f_(0)(t,X(t), u(t))dt + ∫_(0)^(t)f_(1)(t,X(t))dξ(t) + g(X(T))] for the given functions f0,f1 and g,where T>0 is a constant denoting the terminal time of the harvesting.Note that it is important to allow the controls to be singular,because in some cases the optimal controls are of this type.Using Hida-Malliavin calculus,we prove sufficient conditions and necessary conditions of optimality of controls.As a consequence,we obtain a new type of backward stochastic Volterra integral equations with singular drift.Finally,to illustrate our results,we apply them to discuss optimal harvesting problems with possibly density dependent prices.
