Critical Indices and Self-Similar Power Transform

“Odd” factor approximants of the special form suggested by Gluzman and Yukalov (J. Math. Chem. 2006, 39, 47) are amenable to optimization by power transformation and can be successfully applied to critical phenomena. The approach is based on the idea that the critical index by itself should be optimized through the parameters of power transform to be calculated from the minimal sensitivity (derivative) optimization condition. The critical index is a product of the algebraic self-similar renormalization which contributes to the expressions the set of control parameters typical to the algebraic self-similar renormalization, and of the power transform which corrects them even further. The parameter of power transformation is, in a nutshell, the multiplier connecting the critical exponent and the correction-to-scaling exponent. We mostly study the minimal model of critical phenomena based on expansions with only two coefficients and critical points. The optimization appears to bring quite accurate, uniquely defined results given by simple formulas. Many important cases of critical phenomena are covered by the simple formula. For the longer series, the optimization condition possesses multiple solutions, and additional constraints should be applied. In particular, we constrain the sought solution by requiring it to be the best in prediction of the coefficients not employed in its construction. In principle, the error/measure of such prediction can be optimized by itself, with respect to the parameter of power transform. Methods of calculation based on optimized power-transformed factors are applied and results presented for critical indices of several key models of conductivity and viscosity of random media, swelling of polymers, permeability in two-dimensional channels. Several quantum mechanical problems are discussed as well.

The Influence of Phases Division Surface in Nanocomposites Polymer/2D-Nanofiller on their Reinforcement Degree - The Percolation Model

The simple percolation model, in which critical indices are defined by the form of a reinforcing component of nanostructured composite structure, was proposed for the description of reinforcement degree for nanostructured composites polymer/2D-nanofiller. The indicated critical indices are close by absolute values to standard percolation indices. The form of reinforcing component controls the type of nanostructured composite. It has been shown that reinforcement degree of these nanomaterials is independent on modulus of elasticity of nanofiller, but is defined by its structure (aggregation level), created in polymer matrix. The percolation indices of a percolation model, which are due to the form of reinforcing component and nanocomposite type, are defined by its main characteristic – the fraction of phases division surface in overall sample volume and are the basic factor, controlling reinforcement degree of nanostructured composites.

Food Safety Practices of Household Food Preparers in Akwa Ibom State, Nigeria.

Generally, study analysed the food safety practices of household food preparers in Akwa Ibom state. A multi-stage sampling procedure was used to collect cross-sectional data from 457 respondents. Specifically, study determined the prevalence, margin and intensity of and factors influencing food safety practices of household food preparers. Given two critical indices 0.62 and 0.42, the study showed that the prevalence of best food safety practices is 49.45% and 97.8% respectively. Results of the disaggregated mean prevalence show that households that carry out less than best food safety practices do so sometimes and not often respectively while those who carry out best practices, do so most times. The mean margins, based on the two respective critical indices 0.62 and 0.42, suggest that, minimally, policy could seek to raise the value of the food safety and dietary practices index of households with less than best practices by 0.08 and 0.04 respectively. The values of the intensity (of the mean margin)0.009, 0.002 and 0.004, 0.0003 , in pairs each representative of the two critical indices-0.62 and 0.42, show that the deviation is more severe when the mean is adopted as critical index both when only deviating and all households are considered. Results of the fractional probit regression indicated that education, household income and confidence in safety labels are statistically significant in explaining the probability of households carrying out food safety practices. The gap between households who carry out less than best and best food safety practices should be bridged.

Critical indices and model of uncertainty perception for regional supply chains: insights from a Delphi-based study

Purpose The dynamic nature of uncertainty sources in regional operations represents supply chain management (SCM) imperatives to review uncertainty management frameworks on an ongoing basis with a view to identifying and prioritising critical indices of uncertainty for effective SCM. The purpose of this study is to identify the critical indices of uncertainty for regional supply chains and analyse how SCM practitioners perceive uncertainty. Design/methodology/approach This paper presents a Delphi-based study with a panel of 70 SCM experts from the Sultanate of Oman in the Gulf Cooperation Council (GCC) region. It applies three rounds of a Delphi exercise to identify, select and prioritise the critical indices of supply chain uncertainty perceived by panel experts. The thematic analysis also provides theorisations on the process for uncertainty perception and factors shaping perception. Findings A total of 39 uncertainty indices were identified from demand, supply, manufacturing, control, technology, competitive, project, transport and geological sources. The Delphi selection round captured the top 12 indices of experts. The research found an accumulative–aggregative duality that explains uncertainty perception and a cost–conformance–connection triadic set of factors underlying the perceived critical indices. Project uncertainty produced the top-ranked index in the final Delphi round. Originality/value This paper makes three main contributions. First, it offers a bottom-up based insight into supply chain uncertainty using the Delphi-based study and from a GCC perspective. Second, the research is unique in its focus on Oman and, third, it is of value for the international operations of GCC companies and for international firms with intentions of expanding, moving or outsourcing their operations to a GCC country such as Oman.