MATHEMATICAL FOUNDATION OF A NEW COMPLEXITY MEASURE

For many continuous bio-medical 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 preprocessing, such as transferring the original signal into a binary time series, is needed. C0 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.

Synchronization between two different chaotic systems with noise perturbation

This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lu¨ 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.

On Energy Gap Phenomena of the Whitney Spheres in C^(n) or CP^(n)

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.

Superconnections and an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds Dedicated to Professor Shiing-Shen Chern and Professor Yibing Shen

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.

Finite-Time Generalized Outer Synchronization Between Two Different Complex Networks

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.

Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations

这篇论文为一个非线性的抛物线的微分方程被奉献给反的问题的一个班。方程的未知系数取决于答案的坡度并且属于一套可被考虑的系数。相应直接问题的解决方案的集中连续地取决于系数集中，这被证明。把反的问题的一个伪解决方案的存在基于这结果在可被考虑的系数的适当的类上被获得。

Properties of Berwald scalar curvature

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.

An equivalence theorem of a class of Minkowski norms and its applications

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.

Harmonic 2-forms and positively curved 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.

Logarithmic vanishing theorems for effective q-ample divisors

Let X be a compact Kahler 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,ΩX^j(logD)) = 0, for i+j>n+q.