In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function el...In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.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
For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes...For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.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
This methodological investigation deals with measurement and valuation of ecological service functions for urban green space. Social, economic and ecological dimensions for such types of function were analyzed and a ...This methodological investigation deals with measurement and valuation of ecological service functions for urban green space. Social, economic and ecological dimensions for such types of function were analyzed and a concept “integrated ecological service functions” (IESF) was put forward for evaluation. Based upon this conceptual approach, an index system for measuring IESF for urban green space was established. With a methodological integration of fuzzy mathematics, decision making analysis and Delphi method, an AHP fuzzy evaluation techniques for IESF for urban green space, called AFIFUG method, was developed. Such a method has been directly applied to the land use strategic planning of Tianjin out ring green belt(TOGB), and its analysis results have been successfully put into operation.展开更多
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
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
Suppose X is a Banach space, and A is a closed operator. We give some equivalent conditions between A generating a local integrated cosine functions and the existence of solutions of abstract Cauchy problems.
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.
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
Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality...Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.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
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
In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b...In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.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
The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mist...The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mistake. The author wishes to correct the errors in Theorem 2 of the result part.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
This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z =...This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D + bounded by C and the open domain D outside C. (1) With f (z) assumed to be C n (n ∞-times continuously differentiable) z ∈ D + and in a neighborhood of C, f (z) and its derivatives f (n) (z) are proved uniformly continuous in the closed domain D + = [D + + C]. (2) Cauchy’s integral formulas and their derivatives z ∈ D + (or z ∈ D ) are proved to converge uniformly in D + (or in D = [D +C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f (z) and J[ f (z)]) are shown extended to hold for the complement function F(z), defined to be C n z ∈ D and about C. (4) The uniform convergence theorems for f (z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four general- ized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f (z) in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . (6) A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. (7) Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f (z) in domain D , based on the continuous numerical value of f (z) z ∈ D + = [D + + C], is presented for resolution as a conjecture.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
基金supported by the National Natural Science Foundation of China(11501127)Guangdong Natural Science Foundation(2015A030313628)+1 种基金the Training Plan for Outstanding Young Teachers in Higher Education of Guangdong(Yqgdufe1405)the Open Fund of the National Higher Education Quality Monitoring Data Center(Guangzhou)(G1613)
文摘In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.
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 the Natural Science Foundation of Department of Education of Jiangsu Province(06KJD110087) Supported by the Youth Foundation of NanJing Audit University(NSK2009/C04)
文摘For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.
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This methodological investigation deals with measurement and valuation of ecological service functions for urban green space. Social, economic and ecological dimensions for such types of function were analyzed and a concept “integrated ecological service functions” (IESF) was put forward for evaluation. Based upon this conceptual approach, an index system for measuring IESF for urban green space was established. With a methodological integration of fuzzy mathematics, decision making analysis and Delphi method, an AHP fuzzy evaluation techniques for IESF for urban green space, called AFIFUG method, was developed. Such a method has been directly applied to the land use strategic planning of Tianjin out ring green belt(TOGB), and its analysis results have been successfully put into operation.
文摘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.
文摘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.
文摘Suppose X is a Banach space, and A is a closed operator. We give some equivalent conditions between A generating a local integrated cosine functions and the existence of solutions of abstract Cauchy problems.
文摘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.
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Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.
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).
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In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.
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.
文摘The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mistake. The author wishes to correct the errors in Theorem 2 of the result part.
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.
文摘This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D + bounded by C and the open domain D outside C. (1) With f (z) assumed to be C n (n ∞-times continuously differentiable) z ∈ D + and in a neighborhood of C, f (z) and its derivatives f (n) (z) are proved uniformly continuous in the closed domain D + = [D + + C]. (2) Cauchy’s integral formulas and their derivatives z ∈ D + (or z ∈ D ) are proved to converge uniformly in D + (or in D = [D +C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f (z) and J[ f (z)]) are shown extended to hold for the complement function F(z), defined to be C n z ∈ D and about C. (4) The uniform convergence theorems for f (z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four general- ized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f (z) in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . (6) A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. (7) Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f (z) in domain D , based on the continuous numerical value of f (z) z ∈ D + = [D + + C], is presented for resolution as a conjecture.
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.