Posted by Afther Hussain in Uncategorized

For instance, if you have a ten-item measure of a given construct, randomly split those ten items into two sets of five (unequal halves are allowed if the total number of items is odd), and administer the entire instrument to a sample of respondents. Then, calculate the total score for each half for each respondent, and the correlation between the total scores in each half is a measure of split-half reliability. The longer is the instrument, the more likely it is that the two halves of the measure will be similar (since random errors are minimized as more items are added), and hence, this technique tends to systematically overestimate the reliability of longer instruments. https://wizardsdev.com/en/news/multiscale-analysis/ This study aimed to translate and revise the AEQ-PE questionnaire, resulting in the development of a brief Chinese version of the Achievement Emotions Questionnaire for Physical Education (AEQ-PE-C) suitable for Chinese university students. Furthermore, we conducted reliability and validity tests on the AEQ-PE-C questionnaire and assessed its measurement invariance across gender and grade groups. Almost all filters are based on some scale parameter, be it the size of the filtering kernel in the case of linear filters (Gonzales and Wintz, 1987), structuring element (Serra, 1982), or time in the case of Partial Differential Equation (PDE)-based methods.

• However, this analytical approach has enormous potential value for defence science.
• Consequently, emotions experienced during physical education learning exhibit greater depth and breadth than those experienced in other subjects.
• In the analysis of system reliability, it is often of interest to compute the conditional probability of a system or subsystem event, given that another system or subsystem event is known or presumed to have occurred.
• In recent years, there has been a growing body of international research focused specifically on the study of achievement emotions in physical education [17,18,19].
• The remaining scales are evaluated for reliability using a measure of internal consistency such as Cronbach alpha.
• Parallel forms reliability measures the correlation between two equivalent versions of a test.

The entire concept of multiscale analysis hinges on the notion of scale (Bangham et al., 1996c; Jackway and Deriche, 1996; Koenderink, 1984; Perona and Malik, 1990). In many cases, such as vessel enhancement (Agam et al., 2005; Du and Parker, 1997; Frangi et al., 1998; Sato et al., 1998; Wilkinson and Westenberg, 2001), the objects are characterized by shape rather than size. Usually, this requires multiple applications of a single filter at different scales and recombination of the results (Du and Parker, 1997; Frangi et al., 1998; Sato et al., 1998). Alternatively, a complex method to determine the local scale is used (Agam et al., 2005). The methods can be applied to Fermi systems in field theory as well as in equilibrium statistical mechanics.

Appl Math Modell

The Boltzmann equation is derived from the Liouville equation and is concerned with the temporal evolution of a single-particle distribution function fx→ξ→t, where x→ denotes the particle location, ξ→ the particle velocity, and t time. The fact that the Boltzmann equation is an integral-differential equation means it is extremely complicated to solve either analytically or numerically. The Boltzmann equation can be simplified through the implementation of various model equations that represent its binary collision integral. One of the most popular collision models is that of Bhatnagar-Gross-Krook (BGK) [12], which is a single-time relaxation model sufficient to capture a wide range of hydrodynamic flows. Applying the Chapman-Enskog multiscale analysis [13] to the LBM with the BGK collision operator can recover the Navier-Stokes equations.

It may lead to wrong results or unsafe design if only random or interval uncertainties are considered. Many efforts have been devoted in recent years [40], [41] for such a situation with both probabilistic and non-probabilistic variables. In composite structures, [42] developed a precise and efficient univariate method for the reliability assessment of composite laminates taking use of Legendre orthogonal polynomials and Monte Carlo Simulation to evaluate the safety of composite laminated structures. [43] proposed an uncertainty analysis approach based on polynomial chaos expansion method for composite structures, where mixed uncertainties including normal random and interval variables were considered simultaneously. However, it should be noticed that current studies mainly focus on single scale problem, while composite structures have clear multiple length scales.

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Such a mathematical procedure enables hydrodynamic variables such as viscosity and the Reynolds number of the flow to be determined. Hierarchy theory is an older approach to multiscale analysis that arose within GST. A hierarchy is a partially ordered set that may be nested, where the members of one level include those at the level below, or non-nested. Simon [Simon, 1962] argued that because nested hierarchies are composed of loosely coupled building blocks, or stable intermediate forms, they could can be assembled orders of magnitude faster than a non-hierarchical assembly process. Hierarchy theory does assume that higher and lower levels are dynamically screened off from each other due to order of magnitude differences between levels, and that information exchange must therefore be interpreted at the boundaries between levels [Salthe, 2002].

These uncertainties typically make mechanical performance difficult to predict, posing a potential threat to the safety of the composite structure. Reliability analysis is an effective probabilistic method used in engineering that quantifies uncertainty using random variables to estimate structural reliability. It is particularly important when the estimated reliability is a constraint in the optimisation of structural performance [2]. Reliability analysis is a topic of interest in uncertainty quantification for composite structures. China has a vast number of university students, with the current number of university students exceeding 44.3 million, constituting one-fifth of the total number of university students worldwide [24]. Despite such a huge teaching group for physical education courses in Chinese universities, there is currently no brief and effective questionnaire available to evaluate the achievement emotions of university students in physical education courses.

Influence of micro-scale uncertainties on the reliability of fibre-matrix composites

Research was conducted by considering the constitutive behaviour with material morphology using a representative volume element (RVE) [16], [17], [18]. Using a periodic RVE, Zhou et al. [19], [20] developed a multiscale reliability analysis scheme for laminated structures with modelled randomness of the constituent elastics. BK et al. [21] simultaneously considered the randomness in constituent elastics and strength, and constructed a structural limit state function using the micromechanics of failure theory. Omairey et al. [22] introduced a geometrically random periodic RVE and investigated the effect of material and micro-geometric uncertainties on reliability. In addition to unidirectional composites, woven fibre composites were considered in the multiscale uncertainty modelling.

Firstly, the model constructed separately with data from male and female participants demonstrated equivalent structural relationships between the six dimensions of the AEQ-PE-C and their corresponding items. This is a prerequisite for meaningful subsequent steps in the measurement invariance test. Secondly, the relationship between the measurement items and the dimensions of the AEQ-PE-C is equivalent across gender groups, indicating that males and females have a consistent understanding of the construct. Thirdly, the intercept between observed variables is invariant, which implies that males and females have the same systematic tendency to understand the content of the measure. Fourthly, the residual equivalence of individual terms between the two groups suggests that the actual scores of the test variables are consistent between males and females. Additionally, cross-grade measurement invariance for the AEQ-PE-C was also demonstrated across different grades.

Validity

Therefore, there is an urgent demand to develop reliability analysis and design methods for FRP bridge structures to accurately evaluate their safety to fully utilize the excellent mechanical properties and design freedom of composite materials. Achievement emotions have a significant impact on both the learning process and outcomes. However, there is currently no brief and effective questionnaire available to evaluate Chinese university students’ achievement emotions in physical education courses. This study aimed to examine the reliability and validity of the Achievement Emotions for Physical Education Questionnaire (AEQ-PE) in a sample of Chinese university students, while also investigating its measurement invariance across gender and grade levels. For multi-scale materials, the interplay of material and design uncertainties and reliability-based design optimization is complex and very dependent on the chosen modeling scale. Uncertainty quantification and management are often introduced at lower scales of the material, while a more macroscopic scale is the preferred design space at which optimization is performed.

These characteristics provide a brief and effective measurement tool for assessing academic emotions in physical education instruction. Usually, convergent validity and discriminant validity are assessed jointly for a set of related constructs. Convergent validity can be established by comparing the observed values of one indicator of one construct with that of other indicators of the same construct and demonstrating similarity (or high correlation) between values of these indicators.

We then simply traverse the Max-tree once and add the grey-level contribution of each Chk to the appropriate bin Figure 10. These 2D spectra have been highly successful in classifying diatom images (Du Buf and Bayer, 2002; Urbach et al., 2007; Westenberg and Roerdink, 2002; Wilkinson et al., 2009). There are several methods that can be used to evaluate reliability, such as Monte Carlo Simulations (MCS), the First Order Reliability Method (FORM), and the Second Order Reliability Method (SORM). The paper provides a enough description of the proposed method so that the results can be replicated.

The CNN training set includes graphical samples and corresponding stress components and strength characteristics of the lamina. A method for generating a graphical sample is developed, which integrates the stochasticity of the fibre shape, misalignment, arrangement, volume fraction, matrix voids, and stacking sequences of the laminates. The corresponding stress components are simulated using the Kernal–Hashin model and laminate plate theory.