Constructing Hopf Insulator from Geometric Perspective of Hopf Invariant

We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.

CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS

This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.

Estimating the ultimate bound and positively invariant set for a generalized Lorenz system

A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].

Invariants of Multi-Component Ermakov Systems

It is shown that certain multi-component Ermakov systems admit Lewis-Ray-Reid invariants.This extendsthe result to the two-component Ermakov system.

Optimized Evaluation of Mobile Base Station by Modern Topological Invariants

Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifthgeneration(5G)cellular networks.For the formal reason,the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory.Any number that can be uniquely calculated by a graph is known as a graph invariant.During the last two decades,innumerable numerical graph invariants have been portrayed and used for correlation analysis.In any case,no efficient assessment has been embraced to choose,how much these invariants are connected with a network graph.This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks.Since K-banhatti sombor invariants(KBSO)and Contrharmonic-quadratic invariants(CQIs)are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks.As the hexagonal networks are used in mobile base stations in layered,forms called honeycomb.The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms.The deduced outcomes can be utilized for the modeling of mobile cellular networks,multiprocessors interconnections,microchips,chemical compound synthesis and memory interconnection networks.The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network(MBSN)for the high load of traffic and minimal traffic also.

On the Construction and Classification of the Common Invariant Solutions for Some P(1,4) -Invariant Partial Differential Equations

We consider the following (1 + 3)-dimensional P(1,4)-invariant partial differential equations (PDEs): the Eikonal equation, the Euler-Lagrange-Born-Infeld equation, the homogeneous Monge-Ampère equation, the inhomogeneous Monge-Ampère equation. The purpose of this paper is to construct and classify the common invariant solutions for those equations. For this aim, we have used the results concerning construction and classification of invariant solutions for the (1 + 3)-dimensional P(1,4)-invariant Eikonal equation, since this equation is the simplest among the equations under investigation. The direct checked allowed us to conclude that the majority of invariant solutions of the (1 + 3)-dimensional Eikonal equation, obtained on the base of low-dimensional (dimL ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4), satisfy all the equations under investigation. In this paper, we present obtained common invariant solutions of the equations under study as well as the classification of those invariant solutions.

Invariant manifold growth formula in cylindrical coordinates and its application for magnetically confined fusion

For three-dimensional vector fields,the governing formula of invariant manifolds grown from a hyperbolic cycle is given in cylindrical coordinates.The initial growth directions depend on the Jacobians of Poincarémap on that cycle,for which an evolution formula is deduced to reveal the relationship among Jacobians of different Poincarésections.The evolution formula also applies to cycles in arbitrary finite n-dimensional autonomous continuous-time dynamical systems.Non-Möbiusian/Möbiusian saddle cycles and a dummy X-cycle are constructed analytically as demonstration.A real-world numeric example of analyzing a magnetic field timeslice on EAST is presented.

A road map to higher genus Gromov-Witten invariants of Calabi-Yau quintics

This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for higher genus Gromov-Witten invariants of Calabi-Yau quintics.

Multiple surface states,nontrivial band topology,and antiferromagnetism in GdAuAl_(4)Ge_(2)

Magnetic topological states of matter provide a fertile playground for emerging topological physics and phenomena.The current main focus is on materials whose magnetism stems from 3d magnetic transition elements,e.g.,MnBi_(2)Te_(4),Fe_(3)Sn_(2),and Co_(3)Sn_(2)S_(2).In contrast,topological materials with the magnetism from rare earth elements remain largely unexplored.Here we report rare earth antiferromagnet GdAuAl_(4)Ge_(2)as a candidate magnetic topological metal.Angle resolved photoemission spectroscopy(ARPES)and first-principles calculations have revealed multiple bulk bands crossing the Fermi level and pairs of low energy surface states.According to the parity and Wannier charge center analyses,these bulk bands possess nontrivial Z2 topology,establishing a strong topological insulator state in the nonmagnetic phase.Furthermore,the surface band pairs exhibit strong termination dependence which provides insight into their origin.Our results suggest GdAuAl_(4)Ge_(2)as a rare earth platform to explore the interplay between band topology,magnetism and f electron correlation,calling for further study targeting on its magnetic structure,magnetic topology state,transport behavior,and microscopic properties.

Invariant measures for the strong-facilitated exclusion process

Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.

Lie symmetry analysis and invariant solutions for the(3+1)-dimensional Virasoro integrable model

Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.

Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.

Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics

In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located.

模型未知LTI系统的数据驱动预测控制

针对含有随机噪声的模型未知线性时不变(LTI,linear time invariant)系统模型建立过程复杂且控制律难以得到的问题,提出一种基于数据驱动的预测控制方法;基于系统行为学理论和平衡子系统辨识方法,仅利用测量得到的系统数据构建被控系统的非参数模型,将其和预测控制理论相结合设计出基于数据驱动的预测控制器,对于系统测量数据中存在的有界加性高斯噪声,通过引入数据的松弛变量和L2正则项来降低噪声扰动的影响,采用滚动时域优化策略计算最优控制序列并将其作用于被控系统,实现了系统对设定值的轨迹跟踪;将所提控制策略应用于四容水箱系统,仿真结果表明所提方法能实现四容水箱系统的液位跟踪控制,且与同样基于数据驱动的子空间预测控制方案相比,所提方法具有更好的动态性能,且该策略在抗噪声扰动方面有明显优势,具有更强的鲁棒性。

中国青少年社会与情感能力第二轮测评技术报告

本技术报告基于中国济南参加2023年社会与情感能力(Survey on Social and Emotional Skills,SSES)的测评数据,对第二轮测评工具在中国文化下的心理测量学特征进行分析。本报告简要介绍了学生问卷的开发和实施过程、社会与情感能力指标体系、问卷主要组成部分、数据集的主要内容,并对数据质量进行了分析。分析结果表明,济南参试学生参试态度认真积极,参试率和有效应答率高,但是10岁组产生了高分翘尾现象;采用ω系数和α系数来衡量分量表的信度,结果表明绝大多数分量表信度良好;运用验证性因子分析逐一检验社会与情感能力各个分量表的效度,发现拟合度较为满意;多组验证性因子分析表明,这些分量表跨性别测量等值性好于跨年龄组等值性,故在考察青少年社会与情感子能力的年龄差异时,对于等值性较差的分量表数据应慎重使用。

基于专业课程视角下的复变函数与积分变换课程教学实践

针对傅里叶变换和拉普拉斯变换在后续雷达类和电类等课程中的重要性,立足课程教学课时少的实际,基于联系和发展的理念,以信号与系统课程中的工程背景为依托,理清现行课程知识与后续相关课程知识之间的关系,构建教学中积分变换知识和专业知识的桥梁,探索积分变换理论价值和应用方向,初步解决“学不知用、学不会用”的问题,对本课程的教与学具有一定的启发和借鉴意义.

流行性感冒患儿外周血MAIT细胞的免疫生物学特性

目的探讨流行性感冒患儿外周血黏膜相关恒定T(MAIT)细胞的变化及其临床意义。方法选取2023年1—5月就诊于某儿童医院感染科门诊和住院治疗的流行性感冒患儿,分为普通型组和重症型组,同时选择该院体检的健康儿童作为健康对照组。患儿入院24 h内抽血送检,采用流式细胞技术检测MAIT细胞(CD3^(+)CD161^(+)TCRVα7.2^(+)细胞)比例,表达PD-1、CD69、穿孔素、CD107α的MAIT细胞比例,比较各组差异。结果与对照组相比,普通型、重症型患儿外周血MAIT细胞比例逐步下降,表达CD69和穿孔素阳性的MAIT细胞比例逐步升高,三者间比较,差异均有统计学意义(均P<0.05);表达CD107α的MAIT细胞比例比较,差异无统计学意义(P>0.05);PD-1阳性的MAIT细胞比例升高(P<0.05),但普通型、重症型组间比较,差异无统计学意义(P>0.05)。结论外周血MAIT细胞减少伴免疫活化在流行性感冒发病中起一定作用。