For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; ...For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.展开更多
From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430...From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.展开更多
In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimens...In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.展开更多
This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors.The two networks can be undirected or directed,and they may also cont...This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors.The two networks can be undirected or directed,and they may also contain isolated nodes and clusters.By using suitable controllers,sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory.Finally,numerical examples are examined to illustrate the effectiveness of the analytical results.The effect of control parameters on the synchronization time is also numerically demonstrated.展开更多
This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochast...This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.展开更多
This paper presents a self-contained proof of Special Termination of MMP (Minimal Model Program). By refining the assumptions and simplifying the argument, it offers a more accessible approach compared to the original...This paper presents a self-contained proof of Special Termination of MMP (Minimal Model Program). By refining the assumptions and simplifying the argument, it offers a more accessible approach compared to the original proof in BCHM (Birkar-Cascini-Hacon-McKernan).展开更多
This article presents an algebraic proof of the invariance of plurigenera for families of smooth projective varieties under deformations.While Siu’s original proof relied on analytic tools such as multiplier ideal sh...This article presents an algebraic proof of the invariance of plurigenera for families of smooth projective varieties under deformations.While Siu’s original proof relied on analytic tools such as multiplier ideal sheaves and L2-extension theorems,our approach reformulates these techniques within the framework of algebraic geometry,emphasizing multiplier ideals,Castelnuovo-Mumford regularity,and Nadel vanishing theorem.Key steps include establishing the surjectivity of restriction maps for pluricanonical sections via careful analysis of base ideals and asymptotic multiplier ideals.This work aligns with recent efforts to translate Siu’s results into algebraic settings and provides a foundation for extending the invariance theorem to singular varieties.展开更多
In this paper,we prove several convergence theorems for the mean curvature flow of n-dimensional closed submanifolds in the unit sphere S^(n+k)under integral curvature pinching conditions.In particular,we prove that i...In this paper,we prove several convergence theorems for the mean curvature flow of n-dimensional closed submanifolds in the unit sphere S^(n+k)under integral curvature pinching conditions.In particular,we prove that if the L^(n)-norm of the second fundamental form of the initial submanifold is small enough,then the mean curvature flow either shrinks to a round point in finite time,or converges to a totally geodesic submanifold as the time tends to infinity.As a consequence of the smooth convergence theorems,we obtain several differentiable sphere theorems for certain submanifolds in S^(n+k).展开更多
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible ...This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.展开更多
We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature.As a consequence,Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds.For(α,β)-metrics on ma...We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature.As a consequence,Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds.For(α,β)-metrics on manifold of dimension greater than 2,if the mean Landsberg curvature and the Berwald scalar curvature both vanish,then the Berwald curvature also vanishes.展开更多
In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifo...In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifolds of dimension n 4 with vanishing Landsberg curvatures must be Berwald manifolds.展开更多
Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigi...Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.展开更多
In this paper,we establish an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds by using the Mathai-Quillen’s superconnection formalism,in which no extra vector field is involved.Furthermore,we prove a more ...In this paper,we establish an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds by using the Mathai-Quillen’s superconnection formalism,in which no extra vector field is involved.Furthermore,we prove a more general Lichnerowicz formula in this direction through a geometric localization procedure.展开更多
We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality,then it is definite.We also discuss some new insights for compact Riemannian 4-manifolds...We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality,then it is definite.We also discuss some new insights for compact Riemannian 4-manifolds with positive sectional curvature.展开更多
Let X be a compact K?hler manifold and D be a simple normal crossing divisor. If D is the support of some effective q-ample divisor, we show H^i(X, ?_X^j (log D)) = 0, for i + j > n + q.
文摘For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.
文摘From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.
基金Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61203304,61203055 and 10901145the Fundamental Research Funds for the Central Universities under Grant Nos.2011QNA26,2010LKSX04,and 2010LKSX01
文摘This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors.The two networks can be undirected or directed,and they may also contain isolated nodes and clusters.By using suitable controllers,sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory.Finally,numerical examples are examined to illustrate the effectiveness of the analytical results.The effect of control parameters on the synchronization time is also numerically demonstrated.
基金supported by the National Natural Science Foundation of China (Grant No. 10901145)
文摘This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.
文摘This paper presents a self-contained proof of Special Termination of MMP (Minimal Model Program). By refining the assumptions and simplifying the argument, it offers a more accessible approach compared to the original proof in BCHM (Birkar-Cascini-Hacon-McKernan).
文摘This article presents an algebraic proof of the invariance of plurigenera for families of smooth projective varieties under deformations.While Siu’s original proof relied on analytic tools such as multiplier ideal sheaves and L2-extension theorems,our approach reformulates these techniques within the framework of algebraic geometry,emphasizing multiplier ideals,Castelnuovo-Mumford regularity,and Nadel vanishing theorem.Key steps include establishing the surjectivity of restriction maps for pluricanonical sections via careful analysis of base ideals and asymptotic multiplier ideals.This work aligns with recent efforts to translate Siu’s results into algebraic settings and provides a foundation for extending the invariance theorem to singular varieties.
基金supported by National Natural Science Foundation of China(Grant Nos.11531012,12071424,12171423 and 12471051)。
文摘In this paper,we prove several convergence theorems for the mean curvature flow of n-dimensional closed submanifolds in the unit sphere S^(n+k)under integral curvature pinching conditions.In particular,we prove that if the L^(n)-norm of the second fundamental form of the initial submanifold is small enough,then the mean curvature flow either shrinks to a round point in finite time,or converges to a totally geodesic submanifold as the time tends to infinity.As a consequence of the smooth convergence theorems,we obtain several differentiable sphere theorems for certain submanifolds in S^(n+k).
基金NNSF of China Grant No.10671211Hu'nan Provincial NSF Grant No.07JJ3005the Scientific and Technical Research Council (TUBITAK) of Turkey
文摘This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11871126,11501067,11571184).
文摘We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature.As a consequence,Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds.For(α,β)-metrics on manifold of dimension greater than 2,if the mean Landsberg curvature and the Berwald scalar curvature both vanish,then the Berwald curvature also vanishes.
基金supported by National Natural Science Foundation of China (Grant Nos. 11221091, 11271062, 11501067, 11571184, 11871126 and 11931007)China Scholarship Council Visiting Scholar Program+1 种基金the Fundamental Research Funds for the General UniversitiesNankai Zhide Foundation。
文摘In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifolds of dimension n 4 with vanishing Landsberg curvatures must be Berwald manifolds.
基金supported by the National Natural Science Foundation of China(No.12271069)the Natural Science Foundation of Chongqing(No.cstc2021jcyj-msxm X0443)+1 种基金the Chongqing“Zhitongche”foundation for doctors(No.CSTB2022BSXM-JCX0101)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJQN202201138)。
文摘Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.
基金supported by National Natural Science Foundation of China(Grant Nos.11221091,11271062,11501067,11571184,11871126 and 11931007)Natural Science Foundation of Chongqing+2 种基金China(Grant No.CSTB2022NSCQ-MSX0397)the Fundamental Research Funds for the Central Universities and Nankai Zhide Foundationthe Chern Institute of Mathematics Visiting Scholars Program。
文摘In this paper,we establish an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds by using the Mathai-Quillen’s superconnection formalism,in which no extra vector field is involved.Furthermore,we prove a more general Lichnerowicz formula in this direction through a geometric localization procedure.
文摘We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality,then it is definite.We also discuss some new insights for compact Riemannian 4-manifolds with positive sectional curvature.
文摘Let X be a compact K?hler manifold and D be a simple normal crossing divisor. If D is the support of some effective q-ample divisor, we show H^i(X, ?_X^j (log D)) = 0, for i + j > n + q.
