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In this paper, we introduce the concept of a supporting set for a general system. We study basic properties of supporting sets for a general system, supporting sets for subsytems of a system, homomorphic images of supporting sets for a system, and supporting sets for free sums and direct sums of systems.

Several coefficients, called divergences, have been suggested in the statistical literature to reflect the fact that some probability distributions are “closer together” than others and consequently that it may be easier to distinguish between the distributions of one pair than between those of another. When comparing three biological populations, it is often interesting to measure how two of them “move apart” from the third. Deals with the statistical analysis of this problem by means of bivariate divergence statistics. Provides a unified study, depicting the behaviour and relative merits of traditional divergences, by using the (h,ø), divergence family of statistics introduced by Menéndez et al.

The concept of L‐fuzzy systems is introduced as a generalisation of that of general systems. A universal structure of a special kind of L‐fuzzy system is given, some mapping properties of L‐fuzzy systems are studied and a number of open questions posed.

Following Ma, Yonghao and Yi Lin's definition of a mathematical model of general systems in 1987, shows the class of all general systems with relation‐reversion mappings and that of all general systems with relation‐preserving mappings to be productive, co‐productive categories Answers two questions posed in earlier published papers and poses some more questions for solution.

The reducing transformation and global optimization technique called Alienor has been developed in the 1980s by Cherruault and Guillez. These methods are based on the approximating properties of α ‐dense curves. The aim of this work is to give a very large class of functions generating α ‐dense curves in a hyper‐rectangle of Rⁿ.

In the course of development of human communities towards industrially advanced societies of today, there have been changes not only in economic conditions in the majority of fields of human activity but also in the ways of providing for food, which went hand in hand with changes in living conditions. Large‐scale industrial production has brought about major changes in the way of life of the population. The development of industrial agglomerations results in a growing number of city dwellers, most of whom have no chance of producing foodstuffs of their own in kind. The distance between residential and industrial areas has been growing, the number of employed women has risen considerably. These are but a few factors affecting the way of boarding, particularly in households.

Describes Childreach – a US child‐focuses development organization which sponsors children and their families in developing countries – and a recent project in development education, “Buffalo banks and borewells: Childreach makes sense of development”, which involved creating and distributing educational newsletters on Third World and development issues. Lists the goals of the project and how they were addressed. Outlines what was gained from the exercise. Links this to the paradoxical situation in the USA whereby the public think money should go towards foreign aid but are reluctant to actually fork out any money themselves. Considers the role of trust and the concept of social capital, emphasizing that sponsors need to trust that their investment is making an important contribution to improving the life of the sponsored child and its family or community.

The purpose of the present article is to obtain the similarity solution for the shock wave generated by a piston propagating in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows.

The Lie group theoretic method given by Sophus Lie is used to obtain the similarity solution in the present article.

Similarity solution with exponential law shock path is obtained for both ideal and nonideal gas cases. The effects on the flow variables, density ratio at the shock front and shock strength by the variation of the shock Cowling number, adiabatic index of the gas, gravitational parameter and nonidealness parameter are investigated. The shock strength decreases with an increase in the shock Cowling number, nonidealness parameter and adiabatic index, whereas the strength of the shock wave increases with an increase in gravitational parameter.

Propagation of shock wave with spherical geometry in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows has not been studied by any author using the Lie group theoretic method.

Natural gas hydrate (NGH) has been regarded as one of the most important resources due to NGH's large amounts of reserve. However, NGH development still faces many technical challenges, such as low production rate and reservoir instability resulting from NGH decomposition. Therefore, developing a fully coupled THMC model for simulating the hydrate decomposition and studying its mechanical behavior is very important and necessary. The purpose of this article is to develop and solve a multi-phase, strong nonlinearity and large-scale fully coupled thermal-hydro-mechanical–chemical (THMC) model for simulating the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and rock deformation during NGH decomposition.

In this paper, a multi-phase, strong nonlinearity and large-scale fully coupled THMC model is developed for simulating the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and rock deformation during NGH dissociation. The fully coupled THMC model is solved by using a fully implicit finite element method, in which the gas pressure, water pressure, temperature and displacement are taken as basic unknown variables. The proposed model is validated against with the experimental data, showing high accuracy and reliability.

A multi-phase, strong nonlinearity and large-scale fully coupled THMC model is developed for simulating the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and rock deformation during NGH decomposition. The proposed model is validated against with the experimental data, showing high accuracy and reliability.

Some assumptions are made to make the model tractable, including (1) the composition gas of hydrate is pure methane; (2) the gas-liquid multi-phase flow in the pore obeys Darcy's law; (3) hydrate occurs on the surface of soil particles, both of them form the composite consolidation material; (4) the small-strain assumption is applied to composite solid materials, which are treated as skeletons and cannot be moved; (5) momentum change caused by phase change is not considered.

NGH has been regarded as one of the most important resources due to its large amounts of reserve. However, NGH development still faces many technical challenges, such as low production rate and reservoir instability resulting from NGH decomposition. Most of the existing studies decouple the process with solid deformation and seepage behavior, but the accuracy of the numerical results will be sacrificed to certain extent. Therefore, it is very important and necessary to develop a fully coupled THMC model for simulating the hydrate decomposition and studying its mechanical behavior.

NGH, widely distributed in shallow seabed or permanent frozen region, has the characteristics of high energy density and high combustion efficiency (Yan et al., 2020). A total of around 7.5 × 1,018 m³ has been proved to exist around the world and 1 m³ of NGH can release about 160–180 m³ of natural gas (Kvenvolden and Lorenson) under normal conditions. Safely and sustainably extracting NGH commercially can effectively relieve global energy pressure and contribute to achieving carbon reduction goals.

The novelty of the present work lies in mainly two aspects. First, a fully coupled THMC model is developed for studying the multi-physics processes involving solid-liquid-gas flow, heat transfer, NGH phase change and solid deformation during NGH dissociation. Second, the numerical solution is obtained by using a fully implicit finite element method (FEM) and is validated against experimental data.

This study aims to propose a consensus model that considers dynamic trust and the hesitation degree of the expert's evaluation, and the model can provide personalized adjustment advice to inconsistent experts.

The trust degree between experts will be affected by the decision-making environment or the behavior of other experts. Therefore, based on the psychological “similarity-attraction paradigm”, an adjustment method for the trust degree between experts is proposed. In addition, we proposed a method to measure the hesitation degree of the expert's evaluation under the multi-granular probabilistic linguistic environment. Based on the hesitation degree of evaluation and trust degree, a method for determining the importance degree of experts is proposed. In the feedback mechanism, we presented a personalized adjustment mechanism that can provide the personalized adjustment advice for inconsistent experts. The personalized adjustment advice is accepted readily by inconsistent experts and ensures that the collective consensus degree will increase after the adjustment.

The results show that the consensus model in this paper can solve the social network group decision-making problem, in which the trust degree among experts is dynamic changing. An illustrative example demonstrates the feasibility of the proposed model in this paper. Simulation experiments have confirmed the effectiveness of the model in promoting consensus.

The authors presented a novel dynamic trust consensus model based on the expert's hesitation degree and a personalized adjustment mechanism under the multi-granular probabilistic linguistic environment. The model can solve a variety of social network group decision-making problems.