Using Multi-Group Invariance Analysis in Exploring Cross-Cultural Differences in Mathematics Anxiety: A Comparison of Australia and Russia

Mathematics anxiety is well known and studied concept. Most of the studies have been focused on the effects of mathematical anxiety on students’ academic achievement, especially from the viewpoint of analysing large national and international data sets. We aim to bring a different perspective to the existing research on mathematics anxiety and resilience by considering the measurement equivalence across cultures, so they can be compared fairly. We used Multi Group Invariance analysis with this purpose. Our findings suggested that full metric and partial scalar model invariance were confirmed which advise that the mathematics anxiety scale can be compared across two countries. We also ran multiple regression using Fisher’s Z to understand the reciprocal relationship among the variables across two samples. Preliminary results revealed that the perceived mathematics anxiety and perceived mathematics ability predict the measured mathematics anxiety equally well for both Australia and Russia.

Confirmatory Factor Analysis of the Athlete Sleep Behavior Questionnaire

Context: Sleep has long been understood as an essential component for overall well-being, significantly impacting physical health, cognitive functioning, mental health, and quality of life. Currently, the Athlete Sleep Behavior Questionnaire (ASBQ) is the only known instrument designed to measure sleep behaviors in the athletic population. However, the psychometric properties of the scale in a collegiate student-athlete and dance population have not been established. Objective: To assess model fit of the ASBQ using a sample of collegiate student-athletes and competitive dancers. Design: Observational study. Setting: Twelve colleges and universities. Patients or Other Participants: Student-athletes and dancers competing at the collegiate level. Main Outcome Measure(s): A confirmatory factor analysis (CFA) was conducted to assess the factor structure of the ASBQ. Principal component analysis (PCA) extraction and covariance modeling analyses were performed to identify an alternate model. Multi-group invariance testing was performed on the alternate model to identify if group differences existed between sex, athletic activity, injury status, and division of competition. Results: The CFA on the ASBQ indicated the model did not meet recommended model fit indices. An alternate three-factor, nine-item model with improved fit was identified; however, the scale structure was not consistently supported during multi-group invariance testing procedures. Conclusions: The original three factor, 18-item ASBQ was not supported for use with collegiate athletes in our study. The alternate ASBQ was substantially improved; however, more research should be completed to ensure the nine-item instrument accurately captures all dimensions of sleep behavior relevant for collegiate athletes.

Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field

The propagation of a cylindrical shock wave in rotating medium with azimuthal magnetic field under the action of monochromatic radiation using a method of group invariance is investigated. To derive similarity solutions as well as exact solutions, the group invariance technique is used. All classes of the solutions depending on the absorption coefficient are discussed by considering absorption coefficient to be variable or constant. A similarity solution is obtained, when the absorption coefficient is assumed to be variable. Two cases of solutions with a power law shock path are obtained by the different choices of arbitrary constants involving in the infinitesimal generators of the Lie group of transformations. To obtain the similarity solution in the case of the power law shock path, the density, magnetic field, axial and azimuthal velocity components are assumed to be varying and obeying power laws in the undisturbed medium. It is observed that with increase in the values of Alfven Mach number, adiabatic exponent and rotational parameter, shock strength decreases. The effects of variation of magnetic field strength, adiabatic exponent, rotational parameter and initial magnetic field variation index on the flow variables and on shock waves are analyzed graphically. Also, all classes of exact solutions are obtained by considering a constant absorption coefficient.

Polymer Dynamics Through Group Invariance of SL(2R) - Type in a Fractal Paradigm

We analyze polymer dynamics in a fractal paradigm. Then, it is shown that polymer dynamics in the form of Schrödinger - type regimes imply synchronization processes of the polymers� structural units, through joint invariant function of two simultaneous isomorphic groups of SL(2R) - type, as solutions of Stoka equations. In this context, period doubling, damped oscillations, self - modulation and chaotic regimes emerge as natural behaviors in the polymer dynamics. The present model can also be applied to a large class of materials, such as biomaterials, biocomposites and other advanced materials.

RANDOMIZATION TESTS OF COPULA SYMMETRY

New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may be viewed as feasible versions of randomization tests of symmetry, the latter being inapplicable due to the unobservability of marginals. Our tests are simple to compute, control size asymptotically, consistently detect arbitrary forms of asymmetry, and do not require the specification of a tuning parameter. Simulations indicate excellent small sample properties compared with existing procedures involving the multiplier bootstrap.

Investigations of Laser Produced Plasmas Generated by Laser Ablation on Geomaterials. Experimental and Theoretical Aspects

Several surface investigation techniques, such as X-ray diffraction (XRD), EDX, and optical microscopy, were employed in order to describe the mineral contents in several geomaterials. Space and time resolved optical emission spectroscopy was implemented to analyze the plasma generated by the laser–geomaterial interaction. The values of the plasma parameters (velocity and temperature) were discussed with respect to the nature of the minerals composing the geomaterials and the morphological structure of the samples. Correlations were found between the excitation temperatures of the atomic and ionic species of the plasmas and the presence of calcite in the samples. A mathematical model was built to describe the dynamics in ablation plasma using various mathematical operational procedures: multi structuring of the ablation plasma by means of the fractal analysis and synchronizations of the ablation plasma entities through SL (2R) type group invariance and in a particular case, through self-modulation in the form of Stoler type transformations. Since Stoler type transformations are implied in general, in the charge creation and annihilation processes, then the SL (2R) type group invariance become fundamental in the description of ablation plasma dynamics.