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Illegal food production in China has proliferated in recent years, triggering serious public concerns on food safety. In this work, we model a regulatory event in a food supply chain comprising a local government, a dealer, and a producer involved in illegal food production, and get equilibrium regulatory decisions of the government and the dealer, and equilibrium production decisions of the producer. The results show that: 1) in a situation where the producer is likely to produce illegally, the government does not regulate, and implements insufficient or sufficient regulation according to the utility-cost ratio of regulating. 2) The regulatory decisions of the dealer depend not only on the regulatory decisions of the government but also on the utility-cost ratio of regulating. 3) Only when the joint regulatory intensity of the government and the dealer is not less than a certain threshold value, the producer will not produce illegally, and the threshold value is the optimal regulatory intensity jointly implemented by the government and the dealer. Otherwise it is ineffective, inadequate, or excessive regulation. Therefore, we suggest that the government and the dealer jointly make regulatory decisions to achieve optimal regulation at the lowest regulatory cost and evade illegal food production by the producer.

This paper considers a rumor transmission model with incubation that incorporates constant recruitment and has infectious force in the latent period and infected period. By carrying out a global analysis of the model and studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium, we use the geometric approach for ordinary differential equations which is based on the use of higher-order generalization of Bendixson’s criterion. It shows that either the number of rumor infective individuals tends to zero as time evolves or the rumor persists. We prove that the transcritical bifurcation occurs at R0 crosses the bifurcation threshold R0=1 by projecting the flow onto the extended center manifold. Since the rumor endemic level at the equilibrium is a continuous function of R0, as a consequence for successful eradication of the rumor, one should simply reduce R0 continuously below the threshold value 1. Finally, the obtained results are numerically validated and then discussed from both the mathematical and the sociological perspectives.

A group decision-making approach fusing preference conicts and compatibility measure is proposed, focused on dynamic group decision making with preference information of policymakers at each time describing with dynamic preference Hasse diagram with the identification framework of relation between alternative pairs is H={≻, ‖,⩾,⩽,≈,≺, ø,} and the preference graph may contain incomplete decision making alternatives. First, the relationship between preference sequences is be defined on the basis of concepts about preference, preference sequence and preference graph; and defining the decision function that can reect dynamic preference, such as conict, comply support and preference distance measure. Finally, through the perspective of conict and compatible aggregating the comprehensive preference of each decision makers in each period, and by establishing the optimization model based on lattice preference distance measure to assemble group preference, gives the specific steps of the decision making. The feasibility and e ectiveness of the approach proposed in this paper are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

Silver tungstate was successfully developed as a bifunctional catalyst for the ligand-free carboxylation of various terminal alkynes with electron-withdrawing or electron-donating groups under atmospheric pressure of carbon dioxide (CO2) at room temperature. In this protocol, dual activation - i.e., the terminal alkyne activated by silver, and CO2 activation by the tungstate anion - was verified using nuclear magnetic resonance spectroscopy, and means that this reaction can be run under ambient conditions. Notably, this protocol can be applied to the preparation of a phenylacrylate derivative by a cascade reaction using phenylacetylene, CO2 and benzylamine as starting materials. [ABSTRACT FROM AUTHOR]