Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical state.We propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier transform.With this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical states.Then,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state.Due to computational complexity,calculations are not performed for higher dimensional models.However,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal.Finally,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.

Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.

Potential sliding zone recognition method for the slow-moving landslide based on the Hurst exponent

The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the threat of secondary disasters,the small baseline subsets(SBAS)technology is applied to process 59 synthetic aperture radar(SAR)images captured from Sentinel-1A satellite.Firstly,the time series deformation of the Zhongbao landslide along the radar line of sight(LOS)direction is calculated by SBAS technology.Then,the projection transformation is conducted to determine the slope displacement.Furthermore,the Hurst exponent of the surface deformation along the two directions is calculated to quantify the hidden deformation development trend and identify the unstable deformation areas.Given the suddenness of the Zhongbao landslide failure,the multi-temporal interferometric synthetic aperture radar(InSAR)technology is the ideal tool to obtain the surface deformation history without any monitoring equipment.The obtained deformation process indicates that the Zhongbao landslide is generally stable with slow creep deformation before failure.Moreover,the Hurst exponent distribution on the landslide surface in different time stages reveals more deformation evolution information of the Zhongbao landslide,with partially unstable areas detected before the failure.Two potential unstable areas after the Zhongbao landslide disaster are revealed by the Hurst exponent distribution and verified by the GNSS monitoring results and deformation mechanism discussion.The method combining SBASInSAR and Hurst exponent proposed in this study could help prevent and control secondary landslide disasters.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT

In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p＆q-Laplacian type involving the critical Sobolev exponent：{-△pu-△qu=│u│^p＊-2u＋μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^＊=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ （0, μ0）, the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.

EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS

The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions.

MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.

p-LAPLACE EQUATIONS WITH MULTIPLE CRITICAL EXPONENTS AND SINGULAR CYLINDRICAL POTENTIAL

In this paper, we deal with the following problem：By variational method, we prove the existenceof a nontrivial weak solution whenand the existence of a cylindricalweak solution when

Construction of Different Kinds of Atomic and Molecular Orbitals Using Complete Orthonormal Sets of ψ^α-ETO in Single Exponent Approximation

Using complete orthonormal sets of ψ^α-exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theory of linear combination of atomic orbitals. These functions can be chosen properly according to the nature of the problems under consideration. This is rather important because the choice of the basis set may be play a crucial role in applications to atomic and molecular problems. As an example of application, different atomic orbitals for the ground states of the neutral and the first ten cationic members of the isoelectronic series of He atom are constructed by the solution of Hartree-Fock-Roothaan equations using ψ^1, ψ^0 and ψ^-1 basis sets. The cMculated results are close to the numerical Hartree-Fock values. The total energy, expansion coefficients, orbital exponents and virial ratio for each atom are presented.

Multiple Solutions to the Problem of Kirchhoff Type Involving the Critical Caffareli-Kohn-Niremberg Exponent, Concave Term and Sign-Changing Weights

In this paper, we establish the existence of at least four distinct solutions to an Kirchhoff type problems involving the critical Caffareli-Kohn-Niremberg exponent, concave term and sign-changing weights, by using the Nehari manifold and mountain pass theorem.

Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension

The persistence exponent for the simple diffusion equation , with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field at a specified spatial coordinate remains positive throughout for a certain time t behaves as for asymptotically large time t. The value of , calculated here for any integer dimension d, is for and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values for respectively.

TWO DISJOINT AND INFINITE SETS OF SOLUTIONS FOR AN ELLIPTIC EQUATION INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS

In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with 0∈?Ωand all the principle curvatures of?Ωat 0 are negative,a∈C1(Ω,R*+),μ>0,0<s<2,1<q<2 and N>2(q+1)/(q-1).By2*:=2N/(N-2)and 2*(s):(2(N-s))/(N-2)we denote the critical Sobolev exponent and Hardy-Sobolev exponent,respectively.

Solutions for Schrodinger-Poisson system involving nonlocal term and critical exponent

In this paper,we consider the following Kirchhoff-Schrodinger-Poisson system:{−(a+b∫_(R^(3))|∇u|^(2))△u+u+ϕu=μQ(x)|u|^(q-2)u+K(x)|u|^(4)u,in R^(3),−△ϕ=u^(2) the nonlinear growth of|u|^(4)u reaches the Sobolev critical exponent.By combining the variational method with the concentration-compactness principle of Lions,we establish the existence of a positive solution and a positive radial solution to this problem under some suitable conditions.The nonlinear term includes the nonlinearity f(u)~|u|^(q-2)u for the well-studied case q∈[4,6),and the less-studied case q∈(2,3),we adopt two different strategies to handle these cases.Our result improves and extends some related works in the literature.

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts:Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved.To demonstrate the validity of this mapping,we apply it to two non-Hermitian localization models:an Aubry-Andre-like model with nonreciprocal hopping and complex quasiperiodic potentials,and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping.We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models.This general mapping may catalyze further studies on mobility edges,Lyapunov exponents,and other significant quantities pertaining to localization in non-Hermitian mosaic models.

塔里木盆地中下寒武统膏质白云岩盖层突破压力预测方法

针对塔里木盆地中下寒武统白云岩盖层层段不易精确厘定和物性变化复杂的问题,在运用岩性统计分析和实验测试手段的基础上,以优势盖层岩性膏质白云岩为主要研究对象,确定其具有不同物性特征的分散状、斑块状、裂缝分散状、裂缝斑块状4种微观结构,进而得到颗粒结构、石膏-黏土含量和裂缝发育程度是影响白云岩突破压力的3个主要因素。据此选取能够响应膏质白云岩岩性和物性特征的测井曲线,运用逐步线性回归分析,明确膏质白云岩突破压力与自然伽马和补偿中子测井数据相关性最强,进而构建其突破压力的预测公式。应用该方法可以准确地预测塔里木盆地中下寒武统膏质白云岩的突破压力,并通过单井分析和连井剖面初步确定巴楚-塔中隆起地区中下寒武统盖层发育特征为“横向上彼此相连,纵向上互相叠置”,对其下部储层内的油气封闭起着积极作用。研究结果与目前油气发现部位具有良好的一致性,可以为塔里木盆地中下寒武统天然气保存条件分析及明确下一步勘探层位提供指导。

不同建筑环境下平均风速剖面的数值模拟

基于计算流体力学(CFD)方法对具有不同建筑环境参数的城市上空的风场进行系统性的数值模拟,并对平均风速剖面指数的变化规律进行讨论。研究结果表明,建筑平均高度对平均风速剖面指数的影响较大,建筑密度对平均风速剖面指数的影响较小。文中还给出了以建筑平均高度和建筑密度为自变量的平均风速剖面指数经验公式。

基于观测与预报数据融合的森林火险预报

针对气象因子日变化波动大容易引起森林火险气象等级预报变动大这一问题,参考布龙-戴维斯方案森林火险气象预报模型的构建思路,利用2016—2020年广西1785个森林火灾样本和气象观测数据,建立森林火险气象指数模型(简称“模型”)。将气象观测数据输入模型,计算出每日森林火险气象监测指数,同时,将智能网格预报数据输入模型,计算出每日森林火险气象预报指数,然后利用加权算法将每日森林火险气象监测指数和每日森林火险气象预报指数进行融合计算,得到森林火险气象融合预报指数。利用2021年6月—2023年6月789个火灾样本,对林火险气象融合预报指数进行验证,结果表明:融合后未来1~7 d森林火险等级预报准确率从82%~56%,较融合前预报准确率提升1%~3%,基本满足目前广西森林火险气象等级预报业务应用。

一种基于SAM-MSFF网络的低照度目标检测方法

由于低照度图像具有对比度低、细节丢失严重、噪声大等缺点,现有的目标检测算法对低照度图像的检测效果不理想.为此,本文提出一种结合空间感知注意力机制和多尺度特征融合(Spatial-aware Attention Mechanism and Multi-Scale Feature Fusion,SAM-MSFF)的低照度目标检测方法 .该方法首先通过多尺度交互内存金字塔融合多尺度特征,增强低照度图像特征中的有效信息,并设置内存向量存储样本的特征,捕获样本之间的潜在关联性;然后,引入空间感知注意力机制获取特征在空间域的长距离上下文信息和局部信息,从而增强低照度图像中的目标特征,抑制背景信息和噪声的干扰;最后,利用多感受野增强模块扩张特征的感受野,对具有不同感受野的特征进行分组重加权计算,使检测网络根据输入的多尺度信息自适应地调整感受野的大小.在ExDark数据集上进行实验,本文方法的平均精度(mean Average Precision,mAP)达到77.04%,比现有的主流目标检测方法提高2.6%~14.34%.

一类本原双色有向图的指数界

对一类相对特殊的双色本原有向图给出了本原条件,结合圈矩阵给出了本原指数的上下界,并刻画了取得指数上下界时所对应的极图。

分数阶立方映射的混沌行为

本文研究了分数阶立方映射的混沌特征.首先,在立方映射基础上,本文定义了分段常数分数阶微分方程,进而对其进行离散化处理得到分数阶立方映射.然后,通过研究映射的分岔和Lyapunov指数,本文揭示了分数阶立方映射通过倍周期分岔进入混沌,且相较传统立方映射具有更加丰富的混沌行为.此外本文还研究了更具普适性的时滞分数阶立方映射,发现该映射的混沌分岔点会随着参数的变化而变化.