Lung image registration plays an important role in lung analysis applications,such as respiratory motion modeling.Unsupervised learning-based image registration methods that can compute the deformation without the req...Lung image registration plays an important role in lung analysis applications,such as respiratory motion modeling.Unsupervised learning-based image registration methods that can compute the deformation without the requirement of supervision attract much attention.However,it is noteworthy that they have two drawbacks:they do not handle the problem of limited data and do not guarantee diffeomorphic(topologypreserving)properties,especially when large deformation exists in lung scans.In this paper,we present an unsupervised few-shot learning-based diffeomorphic lung image registration,namely Dlung.We employ fine-tuning techniques to solve the problem of limited data and apply the scaling and squaring method to accomplish the diffeomorphic registration.Furthermore,atlas-based registration on spatio-temporal(4D)images is performed and thoroughly compared with baseline methods.Dlung achieves the highest accuracy with diffeomorphic properties.It constructs accurate and fast respiratory motion models with limited data.This research extends our knowledge of respiratory motion modeling.展开更多
We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other...We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other.In particular,the moduli space of nice point arrangements with same combinatorics in CPl is connected.It generalizes the result on point arrangements in CP3 to point arrangements in CPl for any l.展开更多
This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and i...This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables E<sub>mn</sub> (E-tensor, inverse densitized tetrad of the metric) and 16 variables A<sub>mn</sub> (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.展开更多
The boundary charge which constitutes the Virasoro algebra in (2-+ 1)-dirnensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion ...The boundary charge which constitutes the Virasoro algebra in (2-+ 1)-dirnensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.展开更多
We call a group A-simple,if it has no non-trivial normal abelian subgroup.We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are A-simple.
A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedbac...A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.展开更多
The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian,...The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respec-tively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived fromthis Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishingNoether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relationof this vanishing Noether current.展开更多
The volume of hippocampal subfields is closely related with early diagnosis of Alzheimer's disease.Due to the anatomical complexity of hippocampal subfields,automatic segmentation merely on the content of MR image...The volume of hippocampal subfields is closely related with early diagnosis of Alzheimer's disease.Due to the anatomical complexity of hippocampal subfields,automatic segmentation merely on the content of MR images is extremely difficult.We presented a method which combines multi-atlas image segmentation with extreme learning machine based bias detection and correction technique to achieve a fully automatic segmentation of hippocampal subfields.Symmetric diffeomorphic registration driven by symmetric mutual information energy was implemented in atlas registration,which allows multi-modal image registration and accelerates execution time.An exponential function based label fusion strategy was proposed for the normalized similarity measure case in segmentation combination,which yields better combination accuracy.The test results show that this method is effective,especially for the larger subfields with an overlap of more than 80%,which is competitive with the current methods and is of potential clinical significance.展开更多
Let B(E,F) be the set of all bounded linear operators from a Banach space E into another Banach space F,B^+(E, F) the set of all double splitting operators in B(E, F)and GI(A) the set of generalized inverses of A ∈ B...Let B(E,F) be the set of all bounded linear operators from a Banach space E into another Banach space F,B^+(E, F) the set of all double splitting operators in B(E, F)and GI(A) the set of generalized inverses of A ∈ B^+(E, F). In this paper we introduce an unbounded domain ?(A, A^+) in B(E, F) for A ∈ B^+(E, F) and A^+∈GI(A), and provide a necessary and sufficient condition for T ∈ ?(A, A^+). Then several conditions equivalent to the following property are proved: B = A+(IF+(T-A)A^+)^(-1) is the generalized inverse of T with R(B)=R(A^+) and N(B)=N(A^+), for T∈?(A, A^+), where IF is the identity on F. Also we obtain the smooth(C~∞) diffeomorphism M_A(A^+,T) from ?(A,A^+) onto itself with the fixed point A. Let S = {T ∈ ?(A, A^+) : R(T)∩ N(A^+) ={0}}, M(X) = {T ∈ B(E,F) : TN(X) ? R(X)} for X ∈ B(E,F)}, and F = {M(X) : ?X ∈B(E, F)}. Using the diffeomorphism M_A(A^+,T) we prove the following theorem: S is a smooth submanifold in B(E,F) and tangent to M(X) at any X ∈ S. The theorem expands the smooth integrability of F at A from a local neighborhoold at A to the global unbounded domain ?(A, A^+). It seems to be useful for developing global analysis and geomatrical method in differential equations.展开更多
This paper gives an estimate of excess functions of rays on complete non-compact manifolds. By using this estimation, the authors can get the results in [3] as corollaries, which asserts that a complete manifold is di...This paper gives an estimate of excess functions of rays on complete non-compact manifolds. By using this estimation, the authors can get the results in [3] as corollaries, which asserts that a complete manifold is diffeomorphic to Rn under some curvature and pinching conditions. At last, they obtain a refinement of them with extra Ricci condition.展开更多
We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O(1/√n).
In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. ...In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.展开更多
Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. I...Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented.展开更多
The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian...The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian,respectively.For Einstein's GR in the stationary,axisymmetric black holes,the mass formula in vacuum can be derived from this Noether current although it definitely vanishes.This indicates that the mass formula of black holes is a vanishing Noether charge in this case.The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.展开更多
The global robust output regulation problem of the singular nonlinear system is investigated. Motivated by the input-output linearization of the normal affine nonlinear system, a global diffeomorphism map is designed ...The global robust output regulation problem of the singular nonlinear system is investigated. Motivated by the input-output linearization of the normal affine nonlinear system, a global diffeomorphism map is designed under the assumption that the singular nonlinear system has a strong relative degree. The global diffeomorphism map transfers the singular nonlinear system into a new singular nonlinear system with a special structure. Attaching an internal model to the new singular nonlinear system yields an augmented singular nonlinear system and the global robust stabilization solution of the augmented system implies the global robust output regulation solution of the original singular nonlinear system. Then the global stabilization problem is solved by some appropriate assumptions and the solvability conditions of the global robust output regulation problem are established. Finally, a simulation example is given to illustrate the design approach.展开更多
Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
Let T:X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f:X → R^d is a Hlder continuous function with ∫_X^(fdm) = 0.If the components of f are cohomologously i...Let T:X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f:X → R^d is a Hlder continuous function with ∫_X^(fdm) = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2:=σ~2 (f ) such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π( m*( 1√ nS f n ),N (0,σ~2 ) ≤A√n, where m*(1√ n S^fn)denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.展开更多
In this paper, a non-variational version of a max-min principle is proposed, andan existence and uniqueness result is obtained for the nonlinear two-point boundaryvalue problenl u' + g(t.u) = f(t),u(0) = u(2...In this paper, a non-variational version of a max-min principle is proposed, andan existence and uniqueness result is obtained for the nonlinear two-point boundaryvalue problenl u' + g(t.u) = f(t),u(0) = u(2π) = 0展开更多
In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normaliza...In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normalization of analytically integrable differential systems. Then we present a new result on the equivalent characterization of the existence of the first integrals of an analytic differential systems near a nonhyperbolic singularity. Finally we pose some open problems on this subject.展开更多
基金the National Natural Science Foundation of China(No.61801413)the Natural Science Foundation of Fujian Province(Nos.2019J05123 and 2017J05110)。
文摘Lung image registration plays an important role in lung analysis applications,such as respiratory motion modeling.Unsupervised learning-based image registration methods that can compute the deformation without the requirement of supervision attract much attention.However,it is noteworthy that they have two drawbacks:they do not handle the problem of limited data and do not guarantee diffeomorphic(topologypreserving)properties,especially when large deformation exists in lung scans.In this paper,we present an unsupervised few-shot learning-based diffeomorphic lung image registration,namely Dlung.We employ fine-tuning techniques to solve the problem of limited data and apply the scaling and squaring method to accomplish the diffeomorphic registration.Furthermore,atlas-based registration on spatio-temporal(4D)images is performed and thoroughly compared with baseline methods.Dlung achieves the highest accuracy with diffeomorphic properties.It constructs accurate and fast respiratory motion models with limited data.This research extends our knowledge of respiratory motion modeling.
基金supported by National Natural Science Foundation of China(Grant No.10731030)Program of Shanghai Subject Chief Scientist (PSSCS) of Shanghai
文摘We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other.In particular,the moduli space of nice point arrangements with same combinatorics in CPl is connected.It generalizes the result on point arrangements in CP3 to point arrangements in CPl for any l.
文摘This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables E<sub>mn</sub> (E-tensor, inverse densitized tetrad of the metric) and 16 variables A<sub>mn</sub> (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.
文摘The boundary charge which constitutes the Virasoro algebra in (2-+ 1)-dirnensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.
基金the author Rong at Capital Normal University,which was partially supported by NSFC Grant 11821101,Beijing Natural Science Foundation Z19003,and a research fund from Capital Normal University.
文摘We call a group A-simple,if it has no non-trivial normal abelian subgroup.We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are A-simple.
文摘A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.
文摘The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respec-tively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived fromthis Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishingNoether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relationof this vanishing Noether current.
基金Supported by the National Natural Science Foundation of China(Nos.60971133,61271112)
文摘The volume of hippocampal subfields is closely related with early diagnosis of Alzheimer's disease.Due to the anatomical complexity of hippocampal subfields,automatic segmentation merely on the content of MR images is extremely difficult.We presented a method which combines multi-atlas image segmentation with extreme learning machine based bias detection and correction technique to achieve a fully automatic segmentation of hippocampal subfields.Symmetric diffeomorphic registration driven by symmetric mutual information energy was implemented in atlas registration,which allows multi-modal image registration and accelerates execution time.An exponential function based label fusion strategy was proposed for the normalized similarity measure case in segmentation combination,which yields better combination accuracy.The test results show that this method is effective,especially for the larger subfields with an overlap of more than 80%,which is competitive with the current methods and is of potential clinical significance.
文摘Let B(E,F) be the set of all bounded linear operators from a Banach space E into another Banach space F,B^+(E, F) the set of all double splitting operators in B(E, F)and GI(A) the set of generalized inverses of A ∈ B^+(E, F). In this paper we introduce an unbounded domain ?(A, A^+) in B(E, F) for A ∈ B^+(E, F) and A^+∈GI(A), and provide a necessary and sufficient condition for T ∈ ?(A, A^+). Then several conditions equivalent to the following property are proved: B = A+(IF+(T-A)A^+)^(-1) is the generalized inverse of T with R(B)=R(A^+) and N(B)=N(A^+), for T∈?(A, A^+), where IF is the identity on F. Also we obtain the smooth(C~∞) diffeomorphism M_A(A^+,T) from ?(A,A^+) onto itself with the fixed point A. Let S = {T ∈ ?(A, A^+) : R(T)∩ N(A^+) ={0}}, M(X) = {T ∈ B(E,F) : TN(X) ? R(X)} for X ∈ B(E,F)}, and F = {M(X) : ?X ∈B(E, F)}. Using the diffeomorphism M_A(A^+,T) we prove the following theorem: S is a smooth submanifold in B(E,F) and tangent to M(X) at any X ∈ S. The theorem expands the smooth integrability of F at A from a local neighborhoold at A to the global unbounded domain ?(A, A^+). It seems to be useful for developing global analysis and geomatrical method in differential equations.
文摘This paper gives an estimate of excess functions of rays on complete non-compact manifolds. By using this estimation, the authors can get the results in [3] as corollaries, which asserts that a complete manifold is diffeomorphic to Rn under some curvature and pinching conditions. At last, they obtain a refinement of them with extra Ricci condition.
基金Supported by NSF of China (10571174)the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese Scholarsthe Scientific Research Foundation of Ministry of Human and Resources and Social Security of China for Returned Overseas Scholars
文摘We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O(1/√n).
文摘In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.
基金Supported by the National Natural Science Foundation of China(11671070,11501051)NSF of Heilongjiang Province of China(QC2016008)the Project of Science and Technology of Jilin Provincial Education Department(JJKH2090547KJ)
文摘Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented.
文摘The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian,respectively.For Einstein's GR in the stationary,axisymmetric black holes,the mass formula in vacuum can be derived from this Noether current although it definitely vanishes.This indicates that the mass formula of black holes is a vanishing Noether charge in this case.The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.
基金supported by the National Natural Science Foundation of China(61374035)the Fundamental Research Funds for the Central Universities(20720150177)
文摘The global robust output regulation problem of the singular nonlinear system is investigated. Motivated by the input-output linearization of the normal affine nonlinear system, a global diffeomorphism map is designed under the assumption that the singular nonlinear system has a strong relative degree. The global diffeomorphism map transfers the singular nonlinear system into a new singular nonlinear system with a special structure. Attaching an internal model to the new singular nonlinear system yields an augmented singular nonlinear system and the global robust stabilization solution of the augmented system implies the global robust output regulation solution of the original singular nonlinear system. Then the global stabilization problem is solved by some appropriate assumptions and the solvability conditions of the global robust output regulation problem are established. Finally, a simulation example is given to illustrate the design approach.
文摘Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
基金supported by the National Natural Science Foundation of China(10571174)the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese ScholarsScientific Research Foundation of Ministry of Human Resources and Social Security for Returned Overseas Chinese Scholars
文摘Let T:X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f:X → R^d is a Hlder continuous function with ∫_X^(fdm) = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2:=σ~2 (f ) such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π( m*( 1√ nS f n ),N (0,σ~2 ) ≤A√n, where m*(1√ n S^fn)denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.
文摘In this paper, a non-variational version of a max-min principle is proposed, andan existence and uniqueness result is obtained for the nonlinear two-point boundaryvalue problenl u' + g(t.u) = f(t),u(0) = u(2π) = 0
基金supported by the NNSF of China Grant 11271252the RFDP of Higher Education of China grant 20110073110054the FP7-PEOPLE-2012-IRSES-316338 of Europe
文摘In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normalization of analytically integrable differential systems. Then we present a new result on the equivalent characterization of the existence of the first integrals of an analytic differential systems near a nonhyperbolic singularity. Finally we pose some open problems on this subject.