Boundedness of the period maps and global Torelli theorem

Recently, we proved the Griffiths conjecture on the boundedness of the period maps, and then used it to prove global Torelli theorem on the Torelli space under certain natural conditions. This paper serves as a review of these results and an introduction to the main ideas behind the proofs.

Deformations of complex orbifolds and the period maps

We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard arguments.Then we consider the period map for a family of complex Kahler orbifolds.We prove that the period map is holomorphic,horizontal and consistent with our Kodaira-Spencer map.

关于“Structure of the set of periods for the Lorenz map”一文的注记

在“ＳｔｒｕｃｔｕｒｅｏｆｔｈｅｓｅｔｏｆＰｅｏｒｉｄｓｆｏｒｔｈｅＬｏｒｅｎｚｍａｐ”一文中，ＪＬｌｉｂｒｅ得到了，对于Ｌｏｒｅｎｚ映射，著名的Ｓａｒｋｏｖｓｋｉｉ定理仍然成立．即若ｎ∈Ｐ（ｆ）且ｎ＞＞ｋ（ｋ＞１），则ｋ∈Ｐ（ｆ）．然而，ＪＬｌｉｂｒｅ的文中该结论的主要依据有部分错误．本文改正了这些错误，给出了一些引理，并由此证明该结论仍然成立．

Noise destroys the coexistence of periodic orbits of a piecewise linear map

The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5(P-5) and period-6(P-6) in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc<τ<τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ>τc(τc and τc are critical values),only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ<τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.

Partial and complete periodic synchronization in coupled discontinuous map lattices

The partial and complete periodic synchronization in coupled discontinuous map lattices consisting of both discontinuous and non-invertible maps are discussed. We classify three typical types of periodic synchronization states, which give rise to different spatiotemporal patterns including static partial periodic synchronization, dynamically periodic synchronization, and complete periodic synchronization patterns. A special prelude dynamics of partial and complete periodic synchronization motion, which is shown by five separated concave curves in the time series plots of the order parameters,is observed. The detailed analysis shows that the special prelude dynamics is induced by the competition between two synchronized clusters, and the analytical expression for the corresponding order parameter is obtained.

General expansion for period maps of Riemann surfaces

In this paper,we get the full expansion for period map from the moduli space Mg of curves to the coarse moduli space Ag of g-dimensional principally polarized abelian varieties in Bers coordinates.This generalizes fully the famous Rauch's variational formula.As applications,we compute the curvature of Siegel metric at point [X] with Π([X]) =√ -1 Ig and the Christoffel symbols of L2-induced Bergman metric on Mg.

On the Judgement of Full-Period Sequences and a Novel Congruential Map with Double Modulus on Z(p^n)

This paper studies the judgement problem of full-period maps on Z(p^n) and proposes a novel congruential map with double modulus on Z(p^n). The full-period properties of the sequences generated by the novel map are studied completely. We prove some theorems including full-period judgement theorem on Z(p^n) and validate them by some numerical experiments. In the experiments, full-period sequences are generated by a full-period map on Z(p^n). By the binarization, full-period sequences are transformed into binary sequences. Then, we test the binary sequences with the NIST SP 800-22 software package and make the poker test. The passing rates of the statistical tests are high in NIST test and the sequences pass the poker test. So the randomness and statistic characteristics of the binary sequences are good. The analysis and experiments show that these full-period maps can be applied in the pseudo-random number generation(PRNG), cryptography, spread spectrum communications and so on.

Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable

To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with the differential Chay model,this paper fits a discontinuous map of a slow control variable of the Chay model based on simulation results.The procedure of period adding bifurcation scenario from period k to period k + 1 bursting(k = 1,2,3,4) involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map.Moreover,dynamics of the border-collision bifurcation are identified in the discontinuous map,which is employed to understand the experimentally observed period increment sequence.The simple discontinuous map is of practical importance in the modeling of collective behaviours of neural populations like synchronization in large neural circuits.

Periodic Windows in Weakly Coupled Map Lattices

<Abstract>The periodic windows in weakly coupled map lattices with both diffusive and gradient couplings are studied. By using the mode analysis method,which reduces the behavior of the coupled systems to a few numbers of independent modes,we theoretically analyze the detailed structures of the periodic windows.We find that the gradient coupling greatly enlarges the width of the periodic windows,compared with the diffusive coupling.

PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES

It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.

THE ASYMPTOTIC PERIODICITY OF PIECEWISE MONOTONE SELFMAPS OF THE INTERVAL

Let f : I → I be a piecewise monotone interval map. The critical point set C(f) of f consists of all the preimages of its turning points. It is proved that the complex dynamical behaviors of f are all concentrated on the derived set of C(f). f is asymptotically periodic if and only if the derived set of C(f) is countable.

Bifurcation analysis of the logistic map via two periodic impulsive forces

The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincare′ map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map.

THE ASYMPTOTIC PERIODICITY OF LORENZ MAPS

A Lorenz map f: I - I is a one dimensional piecewise monotone map witha single discontinuity c. Let be the collection of all the preimages of c.Authors prove that if C’(f) is countable then there exists M such that Card(ω(x))≤ Mfor all x ∈ I. If C’(f) is uncountable then ω(z) is uncountable for some x∈I. So f isasymptotically periodic if and only if C’(f) is countable.

Effects of Colored Noise on Periodic Orbits in a One-Dimensional Map

噪音能导致反的加倍时期的转变和混乱。在逻辑地图的不同周期的序列，周期的轨道上的有颜色的噪音的效果被调查。这被发现轨道的动态行为，由指数地相关的有颜色的噪音导致了，在他们的动态行为上的噪音紧张的转变，和效果的合并是不同的与噪音的关联时间的效果不同。显著地，也就是，噪音能导致新周期的轨道二条新轨道出现在时期--在分叉参数值=的四个序列 3.5 ，在时期的四条新轨道--在=的八个序列 3.55 ，并且在时期的三条新轨道--在=的六个序列 3.846 分别地。而且，新轨道的动态行为清楚地显示出 resonancelike 反应到有颜色的噪音。

Second Descendible Self-Mapping with Closed Periodic Points Set

Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point of the set orb (y,f) is a isolated point of the set w (z,f);3) For any z ε R(f), the set w (z,f) is finite;4) For any z ε R(f), the set w' (z,f) is finite. The consult give another condition of f with closed periodic set other than [1].

基于渐近均匀化方法的准周期梁结构等效刚度数值实现方法研究

相比周期梁结构,准周期梁结构沿轴向梯度变化,具有更大的设计自由度,能够获得更好的结构性能。由于其非均质性,一般将其均匀化为具有等效性质的均质梁结构,但现有工作很少涉及准周期梁结构等效性质的计算。本文针对由周期梁结构映射而成的准周期梁结构,通过引入雅可比矩阵,基于渐近均匀化方法推导的单胞方程及其等效性质计算列式,并建立了其单胞方程及等效刚度的有限元求解列式。该方法可以处理沿轴向变形的任意微单胞构型,数值算例验证了其正确性和有效性。

FFT和MEM在冲击回波法识别混凝土缺陷尺寸中的对比研究

针对冲击回波法识别混凝土缺陷尺寸的两种信号分析方法,通过理论分析与现场模型试验,研究了FFT(快速傅里叶变换)和MEM(最大熵法)在冲击回波信号处理中的应用,结果表明:FFT算法简单快速,但分析过程添加的窗函数会导致频谱泄露和分辨率降低;MEM算法可以对已知数据外的信号进行合理估计,具有较高的分辨率,更加符合实际工程的要求;频谱图和卓越周期图可以携带缺陷信息,缺陷在FFT计算结果中体现为峰值提前,在MEM计算结果中体现为峰值延后;等值线图可以更加直观地识别缺陷位置,MEM的计算结果比FFT计算结果精度更高。

元素周期表中的电子亲和势及砷电子亲和势的测量示例

基于先前对原子的电子亲和势和原子负离子的分析工作[J.Phys.Chem.Ref.Data 51,021502(2022)],本篇综述提供了一个关于原子的电子亲和势的简要概述.本文简要描述和对比了三种常用的测量电子亲和势的实验方法,以凸显它们各自的优缺点.为了阐明目前研究中所使用的慢电子速度成像法的特点,本文对砷元素(As)的电子亲和势以及其负离子(As-)的激发态进行了测量.测得As元素的电子亲和势为6488.61(5)cm^(-1)或0.804485(6)eV.实验清晰地分辨了As-的精细结构,其激发态^(3)P_(1)能量比基态^(3)P_(2)的能量高出1029.94(18)cm^(-1)或0.12770(3)eV;激发态^(3)P_(0)能量比基态^(3)P_(2)的能量高出1343.04(55)cm^(-1)或0.16652(7)eV.

基于Logistic-map的长周期混沌序列发生器

利用无周期的混沌映射生成长周期伪随机序列具有巨大的优越性,但有限字长效应会使混沌序列出现动力学特征退化,从而出现短周期现象,导致混沌序列安全性显著降低。分析了采用整数类型实现Logistic型混沌序列对周期特性的影响,指出整数型Logitstic-map序列不具备长周期特性,提出了一种利用m序列加扰Logistic-map的长周期混沌序列发生器的实现方案,并对输出序列特性进行了仿真分析。该方案易于实现,降低了长周期对整数位数的要求,输出序列的周期得到明显扩展,随机性、相关性和线性复杂度良好。

顾及分类与定量误差订正的数值预报降水统计后处理方法

采用统计后处理方法的数值预报降水是延长水文预报有效预见期的重要途径,已有统计后处理方法不能同时订正预报降水的分类和定量误差,且对预报降水有效预见期的影响关注不足。提出耦合经验分位数映射模型(EQM)和伯努利-元高斯模型(BMGD)的统计后处理方法EQM-BMGD,建立用于有效预见期评价的综合精度指标,应用于汉江流域。研究结果表明:EQM-BMGD集成了2种单一方法的优势,并输出了更高精度的预报降水;订正后面平均预报降水各预见期晴雨预报准确率(O P)和绝对平均误差(E MA)的增益均超过了10%,预见期222~228 h的O P仍接近0.7且E MA低于0.7 mm/(6 h),有效预见期延长18~66 h;在栅格尺度上,所有栅格在预见期96~102 h的O P和E MA增益分别超过10%和20%,除西南少数栅格外,O P超过0.8同时E MA控制在1.0 mm/(6 h)以下,北部部分栅格有效预见期延长了18~54 h。EQM-BMGD被证实能够兼顾分类和定量误差的削减,丰富了数值预报降水统计后处理方法的选择。