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.

Strong invariance principle for a counterbalanced random walk

We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).

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.

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.

Novel camera calibration method based on invariance of collinear points and pole-polar constraint

To address the eccentric error of circular marks in camera calibration,a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper.Firstly,the centers of the ellipses are extracted,and the real concentric circle center projection equation is established by exploiting the cross ratio invariance of the collinear points.Subsequently,since the infinite lines passing through the centers of the marks are parallel,the other center projection coordinates are expressed as the solution problem of linear equations.The problem of projection deviation caused by using the center of the ellipse as the real circle center projection is addressed,and the results are utilized as the true image points to achieve the high precision camera calibration.As demonstrated by the simulations and practical experiments,the proposed method performs a better location and calibration performance by achieving the actual center projection of circular marks.The relevant results confirm the precision and robustness of the proposed approach.

Factor Structure and Measurement Invariance of the Japanese Version of the Mother-to-Infant Bonding Scale

Background: Bonding disorders affect the growth and development of infants. In Japan, the Japanese version of the Mother-to-Infant Bonding Scale (MIBS-J) is widely used for early detection of bonding disorders. Repeated use of a questionnaire has problems of reduced validity. In order to correctly detect bonding disorders at multiple time points, it is necessary to confirm the measurement invariance of the scale. Baba et al. reported that invariance of the MIBS-J factor structure could only be obtained by abridging the scale into three items. Purpose: The aim of this study was to 1) confirm the factor structure and measurement invariance of the MIBS-J between two measurement times and 2) to examine factors that can be used without being affected by measurement time in order to identify item that contribute to measure met invariance. Methods: We analysed the data of 1049 and 878 mothers with a neonate collected in two waves: 5 days (Wave 1) and 1 month postpartum (Wave 2). Exploratory and confirmatory factor analyses were conducted on the data randomly divided into two groups in each wave. Results: The three-item model (MIBS-J items 1, 6, and 8) was most accepted. Measurement invariance and structural invariance were confirmed in the model. This was consistent with Baba et al.’s model. Conclusion: The three MIBS-J items showed measurement invariance and structural invariance in Japanese mothers during 1 month postpartum.

Constraining Lorentz Invariance Violation Using Short Gamma-Ray Bursts

Lorentz Invariance is a foundational principle in modern physics, but some recent quantum gravity theories have hinted that it may be violated at extremely high energies. Gamma-ray bursts (GRBs) provide a promising tool for checking and constraining any deviations from Lorentz Invariance due to their huge energies and cosmological distances. Gamma-ray bursts, which are the most intense and powerful explosions in the universe, are traditionally divided into long bursts whose observed duration exceeds 2 s, and short bursts whose observed duration is less than 2 s. In this study, we employ a recent sample of 46 short GRBs to check for any deviation from Lorentz Invariance. We analyze the spectral lag of the bursts in our data sample and check for any redshift dependence in the GRB rest frame, which would indicate a violation of Lorentz Invariance. Our results are consistent, to within 1σ, with no deviation from Lorentz Invariance.

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.

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。

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。

三维度生命意义感量表的中文版翻译及其信效度检验

引入三维度生命意义感量表(Three Dimensional Meaning in Life Scale,3DM),包含目标、重要性和一致性3个维度,检验其中文翻译版的信效度和测量等值性。样本1(544名大学生)用于探索性因素分析,样本2(559名成年人)用于验证性因素分析和测量等值性检验。选取生命意义感问卷作为效标效度,正性负性情绪量表和生活满意度量表作为聚合–区分效度。间隔1个月,对345人进行重测,考察重测信度。结果表明,探索性和验证性因素分析支持三维度结构,总量表及分量表的内部一致性系数在0.82~0.95之间,重测信度在0.71~0.83之间。3DM量表总分及分维度与拥有意义感、寻求意义感、正性情绪和生活满意度显著正相关,与负性情绪显著负相关。3DM量表具有跨性别与跨时间的测量等值性。研究结果证明,3DM量表具有良好的信效度,可以在中国用于测量生命意义感的不同成分。

高等代数中的不变性哲学思想及其应用

本文探讨高等代数课程中变与不变的对立统一性,以便从更高的视角理解其本质.

两个酉不变范数不等式的推广

本文研究了矩阵酉不变范数不等式的问题.在v∈[0,1]时,利用函数ϕ(v)=||A^(v)XB^(1−v)+A^(1−v)XB^(v)||的凸性,推广了两个酉不变范数不等式.

基于区域渐进校准网络的人脸检测与定位

为解决角度变化下的人脸检测中存在参数量大及角度幅度变量小的问题,提出区域渐进校准网络用于任意平面角度的人脸检测,通过级联网络结构降低角度变化、提升网络运行速度。采用区域生成网络产生高质量的候选区域,构造渐进校准网络,逐步缩小面部平面角度变化范围,同时由粗到细地对候选区域执行面部检测。其中,特征提取的中间层融合参数量较少时,更好地表示了面部特征,调整锚的设置解决小尺度面部问题。在角度增强的FDDB(face detection data set and benchmark)数据集与WIDER FACE数据集上的实验结果表明,提出的方法分别取得了89.1%与90.4%的平均召回率,准确度高于快速区域卷积神经网络(Faster RCNN),且运行速度更快。在实际项目中使用该算法,验证了该方法的有效性及可行性。

基于总体最小二乘-旋转不变算法的地表核磁共振信号参数估计

在地表核磁共振(SNMR)找水系统中,根据SNMR信号的参数能够预估地下含水层的储水量、导电性以及孔隙结构等信息。然而在实际应用中探测现场采集的SNMR信号十分微弱,易受到环境噪声干扰,导致无法直接获取SNMR信号的参数。针对这一问题,该文提出基于总体最小二乘-旋转不变法(TLS-ESPRIT)的地表核磁共振信号参数估计方法。基于谐波噪声与SNMR信号的相似信号特征构成一个由多个正弦衰减信号叠加的混合信号模型,使用TLS-ESPRIT将混合信号参数提取问题转换为旋转不变矩阵的广义特征值求解,从而获得SNMR信号的拉莫尔频率和弛豫时间,并结合最小二乘法求得其初始振幅和相位。仿真信号和实测信号实验结果表明此方法能够估计出混有随机噪声和工频谐波噪声的SNMR信号的参数,相比传统的谐波建模方法,在参数提取精度上效果更好。