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.

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.

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。

基于二维离散混沌系统和DNA的图像加密方案

为丰富低维离散混沌系统的动力学特性以及克服脱氧核糖核酸(deoxyribonucleic acid,DNA)编码的引入使混沌图像加密系统安全性易于降低的问题,基于Arnold映射构建具有恒定正Lyapunov指数的2维离散混沌系统,并将其与DNA编码结合,设计一个混沌图像加密方案.所设计的混沌系统模型中不含非线性项,系统具有超混沌动力学行为;加密方案中用于加密的混沌序列为明文图像像素与密钥的加取模运算结果,图像按4×4大小予以分块,扩散算法中的DNA加减、异或、同或等运算分别基于DNA编码规则1、规则4和规则7.仿真实验和性能分析结果表明:加密方案的密钥空间达到2^(266),信息熵为7.9993 bit,密钥灵敏度达到10^(−15),平均像素变化率(number of pixel change rate,NPCR)、统一平均变化强度(unified average change intensity,UACI)、块平均变化强度(block average change intensity,BACI)分别为99.6092%、33.4664%、26.7718%.

融入智能网联汽车的混行交通流混沌特性

为了研究混行交通流混沌特性、辨析影响混行车队混沌程度的因素,在传统交通流理论基础上,利用Cao方法和改进的Cao方法确定混行交通流延迟时间和嵌入维数,对混行交通流序列进行相空间重构并通过计算最大Lyapunov指数判定其混沌特性.对混行交通流中智能网联汽车(intelligent connected vehicle,ICV)协同自适应巡航(cooperative adaptive cruise control,CACC)车辆比例及延迟时间关键参数进行影响分析.结果表明:在跟驰过程中车头间距序列的最大Lyapunov指数小于0时,混行交通流存在混沌;CACC车辆比例增加能够减弱混沌的时间区域,比如当CACC车辆比例达到0.6时,跟驰系统趋于稳定;CACC车辆的延迟时间对混沌的影响显著,保持低通信延迟才能发挥CACC车辆的作用,从而有效抑制混沌.

炭黑对CMDB推进剂燃烧性能的影响

采用燃烧–靶线法分析了炭黑的种类、含量及粒径对复合改性双基(CMDB)推进剂燃烧性能的影响。结果表明:在压强为1~8MPa时,添加炭黑可以提高推进剂的燃速,Y1炭黑可以有效减小推进剂配方的压强指数;当Y1炭黑在推进剂配方中含量较低时,推进剂样品在压强为3~8MPa时具有平台燃烧特性,小粒径的Y1炭黑有利于推进剂配方压强指数的降低。

长相关随机模型FBM对光伏发电短期预测

针对光伏发电功率具有较强的波动性、间歇性输出,光伏功率预测精度较低,且难于给出具体预测时间长度等问题,提出了一种长相关随机模型分数阶布朗运动(fractional Brownian motion,FBM),用于光伏功率预测。首先,采用重标极差法计算长相关(long-range dependence,LRD)参数-Hurst指数,Hurst指数用于判断光伏功率数据是否满足长相关性,并通过最大李雅普诺夫指数(Lyapunov)计算出模型最大可预测时间尺度;其次,采用随机微分法建立FBM光伏功率预测模型,同时估计FBM预测模型参数值;最后,选取澳大利亚沙漠知识太阳能中心(Desert Knowledge Australia Solar Center,DKASC)、美国国家可再生能源实验室(National Renewable Energy Laboratory,NREL)以及北京国能日新科技有限公司的光伏功率数据集,从不同的地理环境、不同的气候特征、不同的规模大小电站进行验证。仿真结果表明,该模型较传统的Kalman、LSTM模型具有更高的预测精度,可为光伏并网的稳定和安全运行提供更好的理论支持,对电网调度部门具有较高的参考价值。

伪抛物型p-Kirchhoff方程的爆破解

该文研究了一类具有变指数的伪抛物型p-Kirchhoff方程的齐次Dirichlet初边值问题.首先,采用改进的势阱法和辅助函数法,对初始能量进行最优分类,得到解的爆破和整体存在的判据.其次,分别得到了解的爆破时间估计和整体解的大时间性态.

铁路悬索桥车致纵向运动混合阻尼减振研究

针对铁路悬索桥在列车过桥时梁端纵向运动响应控制问题,提出了一种创新的混合阻尼减振方案,采用多种类型的阻尼器控制梁端位移,以满足不同的减振需求.以某在建大跨铁路悬索桥为工程背景,建立了空间桁架精细模型和等效单梁简化模型,系统研究了混合阻尼减振方案不同阻尼器参数对减振效果的影响.该方案将低指数黏滞阻尼器纵向安装于桥塔与加劲梁之间,同时在桥台与加劲梁之间纵向安装电涡流阻尼器.鉴于桥台结构的特殊性,电涡流阻尼器被设计为仅能承受压力的装置,并通过样机试验进行了验证.为了进一步提升减振性能,电涡流阻尼器还配备了摩擦耗能元件.该混合阻尼减振方案能够有效控制列车过桥时梁端的纵向运动响应,显著提高桥梁结构的安全性和耐久性,在类似工程中具有重要的参考价值和借鉴意义.