Factor Structure and Longitudinal Invariance of the CES-D across Diverse Residential Backgrounds in Chinese Adolescents

Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of these measures over time remains understudied.This research explores the structural components of the Center for Epidemiological Studies Depression Scale(CES-D)and examines its consistency across various living environments and temporal stability in a cohort of Chinese teenagers.Method:In the initial phase,1,042 adolescents furnished demographic details and undertook the CES-D assessment.After a three-month interval,967 of these participants repeated the CES-D evaluation.The study employed Confirmatory factor analysis(CFA)to scrutinize the scale’s structural integrity.We investigated factorial invariance by conducting a twopronged CFA:one comparing urban vs.rural backgrounds,and another contrasting the results from the initial assessment with those from the follow-up.Results:The CES-D demonstrated adequate reliability in both rural and urban high school student samples.The preliminary four-factor model applied to the CES-D demonstrated a good fit with the collected data.Invariance tests,including multigroup analyses comparing rural and urban samples and longitudinal assessments,confirmed the scale’s invariance.Conclusions:The results suggest that the CES-D serves as a reliable instrument for evaluating depressive symptoms among Chinese adolescents.Its applicability is consistent across different living environments and remains stable over time.

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.

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.

A FORM INVARIANCE OF CONSTRAINED BIRKHOFFIAN SYSTEM

The form invariance of constrained Birkhoffian system is a kind of invariance of the constrained Birkhoffian equations under infinitesimal transformations. The definition and criteria of the form invariance of constrained Birkhoffian system are given, and the relation of the form invariance and the Noether symmetry is studied.

Adaptive Attitude Control for a Coaxial Tilt-Rotor UAV via Immersion and Invariance Methodology

Dear Editor,This letter is concerned with the attitude control for a novel tiltrotor unmanned aerial vehicle with two pairs of tiltable coaxial rotors and one rear rotor.An immersion and invariance-based adaptive attitude controller for the tilt-rotor unmanned aerial vehicle is proposed.In the proposed control strategy,an adaptive update law is specially designed to compensate for the uncertainties of damping coefficients.The stability of the resulting closed-loop coaxial tiltrotor unmanned aerial vehicle(CTRUAV)system is proved by the Lyapunov methodology and LaSalle’s invariance theory.Finally。

A New Discriminating Experiment on the Invariance Hypothesis of Light Speed

This thesis puts forward a conjecture that, owing to some unknown special character of light, it is impossible to determine whether the speed of light is variable by the interference method. To verify the hypothesis of the invariance of light speed, a new method must be found to take accurate measurement of the infinitesimal change in the travelling time of light. The thesis suggests the adoption of high frequency laser pulse technology to carry out the measurement. On the basis of this idea a new discriminating experiment is proposed to test the hypothesis of the invariance of light speed. The thesis also makes some forecast of the future prospects of this experiment and of the future development of the theory of special relativity.

Loop Peeling Based on Quasi-Invariance/Induction Variables

Loop optimization plays an important role in compiler optimization and program transformation. Many sophisticated techniques such as loop invariance code motion have been developed. Loop peeling is a technique to assist parallelization of loops by unfolding loops a few times. This paper introduces a novel technique called loop peeling based on quasi invariance/induction variables. It aims at finding a general and automatic method to derive how many times a given loop should be peeled. Our technique allows for a number of iterations before some variables assigned inside a given loop become invariance or induction variables. In this paper we define the notion of quasi invariance/induction variables, present an algorithm for statically computing the optimal peeling length of a given loop. Our technique can increase the accuracy of program analyses, improve the effectiveness of loop peeling and is well suited as supporting other optimization techniques in the context of supercomputers.

MULTI-INVARIANCE ESPRIT-LIKE ALGORITHMS FOR COHERENT DOA ESTIMATION

Estimation of Signal Parameters via Rotational Invariance Technique(ESPRIT) algorithm can estimate Direction-Of-Arrival(DOA) of coherent signal,but its performance can not reach full satisfaction.We reconstruct the received signal to form data model with multi-invariance property,and multi-invariance ESPRIT algorithm for coherent DOA estimation is proposed in this paper.The proposed algorithm can resolve the DOAs of coherent signals and performs better in DOA estimation than that of ESPRIT-like algorithm.Meanwhile,it identifies more DOAs than ESPRIT-like algorithm.The simulation results demonstrate its validity.

Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems

Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D'Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.

Measurement invariance and latent mean differences of the Chinese version physical activity self-efficacy scale across gender and education levels

Background: Self-efficacy has been identified as an important determinant of youth's behavior change including physical activity(PA) participation. However, the dimensionality check of a PA self-efficacy scale has rarely been conducted in China. The current study aims to examine(1) the unidimensionality of a shortened Chinese version of PA self-efficacy scale(S-PASESC);(2) the measurement invariance of S-PASESC across gender and levels of education;(3) the latent factor mean difference between gender and levels of education;(4) the direct effects of self-efficacy on PA by different gender and education levels; and(5) the comparisons of the direct effects of self-efficacy on PA across gender and education levels.Methods: The participants were 5 th through 11 th grade public school students recruited from 7 cities located in different geographic regions of China. The final data include a total of 3003 participants(49.7% boys) who have completed the scales.Results: Confirmatory factor analysis(CFA) test supported the unidimensionality of S-PASESC. The S-PASESC is invariant across gender and 3 levels of education at both configural, full metric, and full scalar levels. Findings from latent mean comparisons showed that boys reported higher PA self-efficacy than girls. Students' perceived PA self-efficacy tend to decrease from elementary to high school. Finally, self-efficacy positively related to PA by groups of different gender and education levels and the relationship between self-efficacy and PA is stronger among middle school boys than girls.Conclusion: Findings suggest S-PASESC is a valid scale for measuring Chinese students' PA self-efficacy.

Identity for the Exponential-Type Molecule Potentials and the Supersymmetry Shape Invariance

The identity and the supersymmetry shape invariance for a class of exponential-type molecule potentials are studied by introducing a deformed five-parameter exponential-type potential (DFPEP) and via the multi-parameter deformations. It has been shown that the DFPEP is a shape-invariant potential with a translation of parameters. By making use of the shape invariance approach, the exact energy levels are determined for the bound states with zero angular momentum. A class of molecule potentials and their exact energy spectra for the zero angular momentum states are reduced from the DFPEP and a general energy spectrum formula, respectively. The interrelations for some molecule potentials are also discussed.

A note on the Galilean invariance of aerodynamic force theories in unsteady incompressible flows

As a basic principle in classical mechanics,the Galilean invariance states that the force is the same in all inertial frames of reference.But this principle has not been properly addressed by most unsteady aerodynamic force theories,if the partial force contributed by a local flow structure is to be evaluated.In this note,we discuss the Galilean-invariance conditions of the partial force for several typical theories and numerically test what would happen if these conditions do not hold.

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space.The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given.By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry,expressions of conformal factors of the system under these circumstances are obtained,and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given.Two examples are given to illustrate the application of the results.

Conformal invariance and integration of first-order differential equations

This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.

Conformal invariance and conserved quantity of Hamilton systems

This paper studies conformal invariance and conserved quantities of Hamilton system.The definition and the determining equation of conformal invariance for Hamilton system are provided.The relationship between the conformal invariance and the Lie symmetry are discussed,and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced.It gives the conserved quantities of the system and an example for illustration.

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion.The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations.Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations.Finally an example is given to illustrate the application of the results.

A conformal invariance for generalized Birkhoff equations

在这篇文章，概括了 Birkhoff 方程被把增补术语加到 Birkhoff 方程提出。Birkhoff 方程的保角的不变性能被用来学习概括 Birkhoff 方程，并且二个例子被举说明结果的申请。

Form invariance and new conserved quantity of generalised Birkhoffian system

A form invariance and a conserved quantity of the generalised Birkhoffian system are studied.First,a definition and a criterion of the form invariance are given.Secondly,through the form invariance,a new conserved quantity can be deduced.Finally,an example is given to illustrate the application of the result.