In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of E...In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.展开更多
In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the max...In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the maximum distance of any pair of nodes in the support domain.The proposed method is verified and shows good performance.The results are stable and accurate with any number of nodes and an arbitrary nodal distribution.Notably,the support domain should be large enough to obtain accurate results.This method is then applied for transient analysis of curved shell structures made from functionally graded materials with complex geometries.Through several numerical examples,the accuracy of the proposed approach is demonstrated and discussed.Additionally,the influence of various factors on the dynamic behavior of the structures,including the power-law index,different materials,loading conditions,and geometrical parameters of the structures,was investigated.展开更多
In this paper, we obtain a lower semicontinuity result with respect to the strong L1-convergence of the integral functionals F（u,Ω）=Ωf（x,u（x）,εu（x））dx defined in the space SBD of special functions with boun...In this paper, we obtain a lower semicontinuity result with respect to the strong L1-convergence of the integral functionals F（u,Ω）=Ωf（x,u（x）,εu（x））dx defined in the space SBD of special functions with bounded deformation. Here Su represents the absolutely continuous part of the symmetrized distributional derivative Eu. The integrand f satisfies the standard growth assumptions of order p 〉 1 and some other conditions. Finally, by using this result,we discuss the existence of an constrained variational problem.展开更多
In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of an...In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of analytic solutions for this type of equations,and then analyze the convergence orders of the collocation solutions and give corresponding error estimates.The numerical results verify our theoretical analysis.展开更多
In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy s...In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.展开更多
The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from ...The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.展开更多
The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum f...The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.展开更多
The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum a...The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.展开更多
The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate fr...The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.展开更多
A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with...A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.展开更多
Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s res...Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.展开更多
A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresp...A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.展开更多
In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o...In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.展开更多
This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically...This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions are obtained by two powerful methods Toeplitz Matrix Method (TMM) and Product Nystr?m Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.展开更多
Exogenous neural stem cell transplantation has become one of the most promising treatment methods for chronic stroke.Recent studies have shown that most ischemia-reperfusion model rats recover spontaneously after inju...Exogenous neural stem cell transplantation has become one of the most promising treatment methods for chronic stroke.Recent studies have shown that most ischemia-reperfusion model rats recover spontaneously after injury,which limits the ability to observe long-term behavioral recovery.Here,we used a severe stroke rat model with 150 minutes of ischemia,which produced severe behavioral deficiencies that persisted at 12 weeks,to study the therapeutic effect of neural stem cells on neural restoration in chronic stroke.Our study showed that stroke model rats treated with human neural stem cells had long-term sustained recovery of motor function,reduced infarction volume,long-term human neural stem cell survival,and improved local inflammatory environment and angiogenesis.We also demonstrated that transplanted human neural stem cells differentiated into mature neurons in vivo,formed stable functional synaptic connections with host neurons,and exhibited the electrophysiological properties of functional mature neurons,indicating that they replaced the damaged host neurons.The findings showed that human fetal-derived neural stem cells had long-term effects for neurological recovery in a model of severe stroke,which suggests that human neural stem cells-based therapy may be effective for repairing damaged neural circuits in stroke patients.展开更多
Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient funct...Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f(w).展开更多
Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re...Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.展开更多
The limited capability to regenerate new neurons following injuries of the central neural system（CNS）still remains a major challenge for basic and clinical neuroscience.Neural stem cells（NSCs）could nearly have the...The limited capability to regenerate new neurons following injuries of the central neural system（CNS）still remains a major challenge for basic and clinical neuroscience.Neural stem cells（NSCs）could nearly have the potential to differentiate into all kinds of neural cells in vitro.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
In this paper, the Cauchy type integral for M-analytic function is investigated which is by definition the regular solution of the elliptic system f_x+Mf_y=0, where M is a constant m×m matrix without any real eig...In this paper, the Cauchy type integral for M-analytic function is investigated which is by definition the regular solution of the elliptic system f_x+Mf_y=0, where M is a constant m×m matrix without any real eigenvalues and f is an m×q matrix.展开更多
基金Supported by the Program of Fujian Province-HongKong
文摘In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.
基金Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study
文摘In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the maximum distance of any pair of nodes in the support domain.The proposed method is verified and shows good performance.The results are stable and accurate with any number of nodes and an arbitrary nodal distribution.Notably,the support domain should be large enough to obtain accurate results.This method is then applied for transient analysis of curved shell structures made from functionally graded materials with complex geometries.Through several numerical examples,the accuracy of the proposed approach is demonstrated and discussed.Additionally,the influence of various factors on the dynamic behavior of the structures,including the power-law index,different materials,loading conditions,and geometrical parameters of the structures,was investigated.
基金the Doctorial Programme Foundation of Education Ministry of China (No.20030288002)the National Natural Science Foundation of China(No.10771181)Natural Science Foundation of Jiangsu Higher Education Bureau.(NO.07KJD110206)
文摘In this paper, we obtain a lower semicontinuity result with respect to the strong L1-convergence of the integral functionals F（u,Ω）=Ωf（x,u（x）,εu（x））dx defined in the space SBD of special functions with bounded deformation. Here Su represents the absolutely continuous part of the symmetrized distributional derivative Eu. The integrand f satisfies the standard growth assumptions of order p 〉 1 and some other conditions. Finally, by using this result,we discuss the existence of an constrained variational problem.
基金The first author is partially supported by forefront of science and interdisciplinary innovation projects of Jilin University and NNSF(No.11071102 of China).
文摘In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of analytic solutions for this type of equations,and then analyze the convergence orders of the collocation solutions and give corresponding error estimates.The numerical results verify our theoretical analysis.
基金The project supported by the Science Foundation of Sichuan Normal University
文摘In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.
基金The project supported by the Natural Science Foundation of Sichuan Normal University
文摘The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.
基金Supported by the Natural Science Foundation of Sichuan Education Committee under Grant No.08ZA038
文摘The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.
基金supported by the Natural Science Foundation of Sichuan Normal University
文摘The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.
基金the Natural Science Foundation of Sichuan Normal University
文摘The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.
基金supported in part by the National Natural Science Foundation of China(6202530361973147)the LiaoNing Revitalization Talents Program(XLYC1907050)。
文摘A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.
文摘Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.
文摘A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.
文摘In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.
文摘This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions are obtained by two powerful methods Toeplitz Matrix Method (TMM) and Product Nystr?m Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.
文摘Exogenous neural stem cell transplantation has become one of the most promising treatment methods for chronic stroke.Recent studies have shown that most ischemia-reperfusion model rats recover spontaneously after injury,which limits the ability to observe long-term behavioral recovery.Here,we used a severe stroke rat model with 150 minutes of ischemia,which produced severe behavioral deficiencies that persisted at 12 weeks,to study the therapeutic effect of neural stem cells on neural restoration in chronic stroke.Our study showed that stroke model rats treated with human neural stem cells had long-term sustained recovery of motor function,reduced infarction volume,long-term human neural stem cell survival,and improved local inflammatory environment and angiogenesis.We also demonstrated that transplanted human neural stem cells differentiated into mature neurons in vivo,formed stable functional synaptic connections with host neurons,and exhibited the electrophysiological properties of functional mature neurons,indicating that they replaced the damaged host neurons.The findings showed that human fetal-derived neural stem cells had long-term effects for neurological recovery in a model of severe stroke,which suggests that human neural stem cells-based therapy may be effective for repairing damaged neural circuits in stroke patients.
文摘Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f(w).
文摘Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.
基金supported by National Program on Key Basic Research Project(973 Programs 2015CB755605)National Natural Science Foundation of China(81471312)
文摘The limited capability to regenerate new neurons following injuries of the central neural system（CNS）still remains a major challenge for basic and clinical neuroscience.Neural stem cells（NSCs）could nearly have the potential to differentiate into all kinds of neural cells in vitro.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金This work is supported in part by the National Natural Science Foundation of China.
文摘In this paper, the Cauchy type integral for M-analytic function is investigated which is by definition the regular solution of the elliptic system f_x+Mf_y=0, where M is a constant m×m matrix without any real eigenvalues and f is an m×q matrix.
