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THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS
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作者 宁正元 王秀丽 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1301-1317,共17页
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
关键词 integral functional Q-minima ω-minima Ekeland’s variational principle Hlder continuous
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A Lower Semicontinuity Result for Some Integral Functionals in the Space SBD
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作者 Zhong-xue Lu Xiao-ping Yang Min-ling Zheng 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2008年第2期297-304,共8页
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
关键词 SBD space integral functionals lower semicontinuity
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Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints 被引量:3
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作者 Wei Zhao Yanjun Liu Lei Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第3期617-627,共11页
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
关键词 Adaptive control backstepping design integral barrier Lyapunov function(iBLF) states observer
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Numerical Treatments of Functional Fredholm Integral Equation in 2D with Discontinuous Kernels
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作者 Abeer M. Al-Bugami 《Journal of Applied Mathematics and Physics》 2023年第11期3702-3711,共10页
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
关键词 Functional integral Equation TMM PNM Hammerstion
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Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time 被引量:5
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第9期445-448,共4页
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
关键词 functional integrals quantum fluctuations noncommutative space-time
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Functional Integrals and Collective Excitations in Boson-Fermion Model 被引量:5
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期769-772,共4页
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
关键词 functional integrals excitation spectrum boson-fermion model
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Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling 被引量:5
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第4X期653-656,共4页
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
关键词 functional integrals free energy sine-Gordon-Thirring model
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Functional Integrals and Excitation Energy in Three-Band Hubbard Model 被引量:4
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第3期567-570,共4页
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
关键词 functional integrals Green's functions excitation energy Hubbard model
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Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model 被引量:4
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期893-896,共4页
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
关键词 functional integrals variational-cumulant expansion sine-Gordon Thirring model
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ON THE DISTRIBUTION OF VALUES AND DEFICIENT FUNCTION OF A GENERAL RANDOM INTEGRAL FUNCTION 被引量:2
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作者 田范基 《Acta Mathematica Scientia》 SCIE CSCD 2001年第3期363-368,共6页
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
关键词 random integral function deficient function order of growth
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AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES 被引量:1
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作者 陈泽乾 孙牧 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期739-747,共9页
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
关键词 Sectorial operator H^∞ Functional calculus area integral function square function L^p space
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SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS 被引量:3
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作者 LI Cheng ZHENG Yanping CHEN Zhongzhong 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2007年第5期23-27,共5页
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
关键词 Fibre reinforced composite Accurate boundary conditions Mapping functions Complex hole shape integral equations
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AREA INTEGRAL FUNCTIONS AND H∞ FUNCTIONAL CALCULUS FOR SECTORIAL OPERATORS ON HILBERT SPACES
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作者 陈泽乾 孙牧 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期989-997,共9页
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
关键词 sectorial operator H∞ functional calculus area integral function squarefunction Hilbert space
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Functional Integral Approach to Transition Temperature of a Homogeneous ImperfectBose Gas
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作者 HUGuang-Xi DAIXian-Xi +1 位作者 DAIJi-Xin WilliamE.Evenson 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第6期895-898,共4页
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
关键词 bose gas functional integral transition temperature
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ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du))+integral from n=■Q to (G(x,u))
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作者 严树森 《Acta Mathematica Scientia》 SCIE CSCD 1989年第2期231-240,共10页
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
关键词 ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to x u Du ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n Q to x u
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THE CAUCHY TYPE INTEGRAL FOR M-ANALYTIC FUNCTION AND ITS APPLICATION
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作者 林伟 戴道清 《Acta Mathematica Scientia》 SCIE CSCD 1990年第2期149-166,共18页
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
关键词 PR THE CAUCHY TYPE integral FOR M-ANALYTIC FUNCTION AND ITS APPLICATION
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THE INTEGRAL AS A FUNCTlON OF THE UPPER LIMIT AND DEPENDING ON A PARAMETER TO SOLVE DRAWING THROUGH IDLING ROLLS
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作者 赵德文 赵志业 张强 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第1期93-100,共8页
The relocity and sirain-rate .field which are different from Avilzur's have beenestablished in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler, an... The relocity and sirain-rate .field which are different from Avilzur's have beenestablished in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler, an analylical upper-bound solution todrawing stress through idling rolls has been obtained in this paper. 展开更多
关键词 drawing through idling rolls integral as a function of theupper limit. integration depending on a parameter analyticalsolution
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FRACTIONAL INTEGRALS OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES
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作者 Wang Shiming 《Analysis in Theory and Applications》 1993年第1期82-96,共15页
In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the... In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n. 展开更多
关键词 TH FRACTIONAL integralS OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES
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On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions
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作者 Muawya Elsheikh Hamid Alshaikh Hamed Elmuiz Mohammed Eldirdiri Sheima 《Applied Mathematics》 2016年第18期2285-2295,共11页
In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce... In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties. 展开更多
关键词 Fuzzy Numbers AP-Henstock integrals of Interval-Valued Functions AP-Henstock integrals of Fuzzy-Number-Valued Functions
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On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions
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作者 Muawya Elsheikh Hamid Alshaikh Hamed Elmuiz 《Journal of Applied Mathematics and Physics》 2016年第4期779-786,共8页
In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.
关键词 Fuzzy Numbers Henstock-Stieltjes (HS) integrals of Interval-Valued Functions Henstock-Stieltjes (HS) integrals of Fuzzy-Number-Valued Functions
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