In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type in...In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type integral and Cauchy principal value integral on the Curve of Parabola at infinity. At the end, we discuss the Riemann boundary value problems for sectionally holomorphic functions with the Curve of Parabola as their jump curve and obtain the explicit form.展开更多
By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s + 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s+...By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s + 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s+2ho(hmbn-1 -hnbm-1) ∈ ExtA^s+6,t+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 7, n ≥ m + 2 ≥ 5, q = 2(p- 1), 0 ≤ s 〈 p - 2, t= (s + 2 + (s + 2)p + p^m + p^n)q. The advantage of this method is to extend the range of s without much complicated argument as in [1].展开更多
In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△)(p 〉1). We first derive the representation of isometries between the unit spheres of comple...In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△)(p 〉1). We first derive the representation of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces lp(Γ)and lp(△) can be extended to be a linear isometry on the whole space.展开更多
In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry ...In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole space.展开更多
The boundary control problem of a cantilever Euler-Bernoulli beam with input time delay is considered.In order to exponentially stabilize the system, a feedback controller is adopted.And we study the well-posedness an...The boundary control problem of a cantilever Euler-Bernoulli beam with input time delay is considered.In order to exponentially stabilize the system, a feedback controller is adopted.And we study the well-posedness and exponential stability of the closed-loop system.The approach used in this paper is done by several steps.Firstly, the well-posedness of this system is proved by semi-group theory.Secondly, the asymptotical expression of eigenvalue is investigated by spectral analysis.Thirdly, the exponential stability of the system is studied by multiplier technology.Finally, numerical simulations on the dynamical behavior of the system are given to support the results obtained.展开更多
Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean and fluc...Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean and fluc- tuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in the frequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance axe demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.展开更多
The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence th...The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained, which extend the related results for this class of equations on a finite interval with a finite. number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.展开更多
The instability of a hypersonic boundary layer on a cone is investigated by bicoherence spectrum analysis.The experiment is conducted at Mach number 6 in a hypersonic wind tunnel.The time series signals of instantaneo...The instability of a hypersonic boundary layer on a cone is investigated by bicoherence spectrum analysis.The experiment is conducted at Mach number 6 in a hypersonic wind tunnel.The time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface along streamwise direction to investigate the development of the unstable disturbances.The bicoherence spectrum analysis based on wavelet transform is employed to investigate the nonlinear interactions of the instability of Mack modes in hypersonic laminar boundary layer transition.The results show that wavelet bicoherence is a powerful tool in studying the unstable mode nonlinear interaction of hypersonic laminar-turbulent transition.The first mode instability gives rise to frequency shifts to higher unstable modes at the early stage of hypersonic laminar-turbulent transition.The modulations subsequently lead to the second mode instability occurrence.The second mode instability governs the last stage of instability and final breakdown to turbulence with multi-scale disturbances growth.展开更多
The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equippi...The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution it,as given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.展开更多
Let E be a Riesz space with a disjoint system {u_i :i∈I}. We denote by E_i the principal band generated by u_i(i∈I). A necessary and sufficient condition is found in this paper under which sup{X_i:i∈I} exists in E ...Let E be a Riesz space with a disjoint system {u_i :i∈I}. We denote by E_i the principal band generated by u_i(i∈I). A necessary and sufficient condition is found in this paper under which sup{X_i:i∈I} exists in E for every x_i∈E (i∈I).展开更多
A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and...A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.展开更多
In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce th...In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function space L2 on the boundary manifold. Then an easy example of several variables, the version of torus in C2, is stated. For the noncommutative classical group L1, the characteristic boundary of a kind of bounded symmetric domain in C4, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem on L1, if so, the solution is given explicitly.展开更多
In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space. The disjoint supercyclic properties of weig...In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space. The disjoint supercyclic properties of weighted translations on locally compact discrete groups, the di rec t sums of finite classical weighted backward shifts, and the bilateral backward opera tor weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space l^2 (Z) never satisfy the d-Supercyclicity Criterion by a simple proof.展开更多
Inspired by Cardano's method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor (DSDT) is revisited from a new view- point. This decomposition simplifies the cubic tenso...Inspired by Cardano's method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor (DSDT) is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.展开更多
Let U^n be the unit polydisc of C^n and φ(φ,…,φ) a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0*(U^n) if and only if φ ...Let U^n be the unit polydisc of C^n and φ(φ,…,φ) a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0*(U^n) if and only if φ ∈β0*(U^n) for every ι=1,2,... ,n, and also gives a sufficient and necessary condition for the composition operator Cφto be compact on the little Bloch space β0* (U^n).展开更多
Let Q be the quaternion division algebra over real field F.Denote by H_n(Q)the set of all n×n hermitian matrices over Q.We characterize the additive maps from H_n(Q) into H_m(Q)that preserve rank-1 matrices when ...Let Q be the quaternion division algebra over real field F.Denote by H_n(Q)the set of all n×n hermitian matrices over Q.We characterize the additive maps from H_n(Q) into H_m(Q)that preserve rank-1 matrices when the rank of the image of I_n is equal to n. Let Q_R be the quaternion division algebra over the field of real number R.The additive maps from H_n(Q_R) into H_m(Q_R)that preserve rank-1 matrices are also given.展开更多
The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-diffe...The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.展开更多
文摘In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type integral and Cauchy principal value integral on the Curve of Parabola at infinity. At the end, we discuss the Riemann boundary value problems for sectionally holomorphic functions with the Curve of Parabola as their jump curve and obtain the explicit form.
基金supported by the National Natural Science Foundation of China (10501045, 10771105)the NCET and the Fund of the Personnel Division of Nankai University.
文摘By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s + 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s+2ho(hmbn-1 -hnbm-1) ∈ ExtA^s+6,t+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 7, n ≥ m + 2 ≥ 5, q = 2(p- 1), 0 ≤ s 〈 p - 2, t= (s + 2 + (s + 2)p + p^m + p^n)q. The advantage of this method is to extend the range of s without much complicated argument as in [1].
基金supported by Higher Educational Science and Technology Program Foundation of Shandong Province(J11LA02)Young and Middle-Aged Scientists Research Foundation of Shandong Province(BS2010SF004)Higher Educational Science and Technology Program Foundation of Shandong Province(J10LA53)
文摘In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△)(p 〉1). We first derive the representation of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces lp(Γ)and lp(△) can be extended to be a linear isometry on the whole space.
基金Supported by NSFC (10871101)the Doctoral Programme Foundation of Institution of Higher Education (20060055010)
文摘In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole space.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61174080)
文摘The boundary control problem of a cantilever Euler-Bernoulli beam with input time delay is considered.In order to exponentially stabilize the system, a feedback controller is adopted.And we study the well-posedness and exponential stability of the closed-loop system.The approach used in this paper is done by several steps.Firstly, the well-posedness of this system is proved by semi-group theory.Secondly, the asymptotical expression of eigenvalue is investigated by spectral analysis.Thirdly, the exponential stability of the system is studied by multiplier technology.Finally, numerical simulations on the dynamical behavior of the system are given to support the results obtained.
基金Supported by the National Natural Science Foundation of China under Grant No 10472081, the New Century Excellent Talent Project (NCET) of the Ministry of Education of China, and Plan of Tianjin Science and Technology Development under Grant No 06TXTJJC13800.
文摘Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean and fluc- tuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in the frequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance axe demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.
文摘The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained, which extend the related results for this class of equations on a finite interval with a finite. number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.
基金Supported by the National Natural Science Foundation of China under Grant No 10832001the Opening Subject of State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences.
文摘The instability of a hypersonic boundary layer on a cone is investigated by bicoherence spectrum analysis.The experiment is conducted at Mach number 6 in a hypersonic wind tunnel.The time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface along streamwise direction to investigate the development of the unstable disturbances.The bicoherence spectrum analysis based on wavelet transform is employed to investigate the nonlinear interactions of the instability of Mack modes in hypersonic laminar boundary layer transition.The results show that wavelet bicoherence is a powerful tool in studying the unstable mode nonlinear interaction of hypersonic laminar-turbulent transition.The first mode instability gives rise to frequency shifts to higher unstable modes at the early stage of hypersonic laminar-turbulent transition.The modulations subsequently lead to the second mode instability occurrence.The second mode instability governs the last stage of instability and final breakdown to turbulence with multi-scale disturbances growth.
文摘The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution it,as given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.
文摘Let E be a Riesz space with a disjoint system {u_i :i∈I}. We denote by E_i the principal band generated by u_i(i∈I). A necessary and sufficient condition is found in this paper under which sup{X_i:i∈I} exists in E for every x_i∈E (i∈I).
文摘A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.
文摘In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function space L2 on the boundary manifold. Then an easy example of several variables, the version of torus in C2, is stated. For the noncommutative classical group L1, the characteristic boundary of a kind of bounded symmetric domain in C4, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem on L1, if so, the solution is given explicitly.
基金supported by the Research Project of Tianjin Municipal Education Commission(2017KJ124)
文摘In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space. The disjoint supercyclic properties of weighted translations on locally compact discrete groups, the di rec t sums of finite classical weighted backward shifts, and the bilateral backward opera tor weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space l^2 (Z) never satisfy the d-Supercyclicity Criterion by a simple proof.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044)the China Postdoctoral Science Foundation(No.2015M570035)
文摘Inspired by Cardano's method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor (DSDT) is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
文摘Let U^n be the unit polydisc of C^n and φ(φ,…,φ) a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0*(U^n) if and only if φ ∈β0*(U^n) for every ι=1,2,... ,n, and also gives a sufficient and necessary condition for the composition operator Cφto be compact on the little Bloch space β0* (U^n).
文摘Let Q be the quaternion division algebra over real field F.Denote by H_n(Q)the set of all n×n hermitian matrices over Q.We characterize the additive maps from H_n(Q) into H_m(Q)that preserve rank-1 matrices when the rank of the image of I_n is equal to n. Let Q_R be the quaternion division algebra over the field of real number R.The additive maps from H_n(Q_R) into H_m(Q_R)that preserve rank-1 matrices are also given.
基金Supported by the NSF of China(4080502090511009+2 种基金107020506070401560877001)
文摘The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.