Integration of a larger stiff system initial value problems emerging from chemical kinetics models requires method that is both efficient and accurate, with large absolute stability region. To determine the solutions ordinary differential equations help in explaining chemically reactive flows, numerical integration methodology known as 3-point variable step block hybrid has been devised. An app...

Aiming at solving the uncertainty of knowledge in variable precision fuzzy soft rough set model. Firstly, from perspectives approximated and equivalent approximation space, measurement methods model are defined, such as information granularity, entropy, etc; Secondly, many related theorems given proved, monotonicity obtained when relation satisfies inclusion condition; Finally, feasibility vali...

In this paper we outline some mathematical questions that emerge from trying to “turn the scientific method into math”. Specifically, we consider the problem of experiment planning (choosing the best experiment to do next) in explicit probabilistic and information theoretic terms. We formulate this as an information measurement problem; that is, we seek a rigorous definition of an information m...

A semi-analytical dynamical mean-field approximation (DMA) has been developed for large but finite N -unit active rotator (AR) networks subject to individual white noises. Assuming weak noises and the Gaussian distribution of state variables, we have derived equations of motions for moments of local and global variables up to the infinite order. In DMA, the original N -dimensional stochastic di...

This paper concerns measurement invariance analysis for situations with many groups or time points. A BSEM (Bayesian Structural Equation Modeling) approach is proposed for detecting non-invariance that is similar to modification indices with maximum-likelihood estimation, but unlike maximum-likelihood is applicable also for high-dimensional latent variable models for categorical variables. Unde...

Many scales in psychology, education and social measurement in general, constructed to measure a single variable, are nevertheless designed to measure different aspects of the variable. The scales are often composed of subscales which measure these various aspects. These different aspects are conceptually related to the variable and are employed because they make the scale more valid than if on...