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In this paper, we study a rumor spreading model in which several types of ignorants exist with trust rate distributions λ i , 1 ≤ i ≤ N. We rigorously show the existence of a threshold on a momentum type initial quantity related to rumor outbreak occurrence regardless of the total initial population. We employ a steady state analysis to obtain the final size of the rumor. Using numerical simulations, we demonstrate the analytical result in which the threshold phenomenon exists for rumor size and discuss interaction between the ignorants of several types of trust rates.

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Pro‐environmental consumption is necessary for sustainable development, but the sales of eco‐friendly products have been limited. In this regard, the present study analyses the failure factors of eco‐friendly product consumption activation from the consumer's perspective, specifically focusing on detergent‐free washing machines, which are representative innovative products of eco‐friendly home appliances. This study analyses: (1) the attitude‐behaviour gap that occurs in the consumer decision‐making process, and (2) the consumer preference with respect to the core attributes. A recursive model considering the decision‐making stage was constructed and a mixed logit model was utilized to analyse the preference for the core attributes. As a result, the product compatibility and transfer of expert information must be secured to reduce the attitude‐behaviour gap. Additionally, washing power is an important attribute for improving product saleability. The analysis framework of this study can be used to establish sustainable policies for activating eco‐friendly products.

Abstract. In this paper, we investigate a localized approximation of a continuously differentiable function by neural networks. To do this, we first approximate a continuously differentiable function by B-spline functions and then approximate B-spline functions by neural networks. Our proofs are constructive and we give numerical results to support our theory.