Our aim is to model the dynamics of social networks, which comprises the problem of how people get to know each other, like each other, detest each other, etc. Most existing models are stochastic in nature and, obviously, based on random events. Our approach is deterministic and based on ordinary differential equations. This should not be seen as a challenge to stochastic models, but rather as a complement.
The paper considers a methodology of mathematical modeling of ecological-economic processes at the regional level. The basis of the model is formed by equations, which describe two interacting blocks: economic and ecological ones. Equations of the economic block are represented by relations of generalized inter-branch balance, while the ecological part is described in terms of differential equations with deviations with respect to some given state of natural resources. Issues of i) information...
In the wine AOC system, the regulation of quantities performed by the professional organizations is aimed to smooth the variations of the quality of the wine due to the variations in the climate that affect the quality of the grapes. Nevertheless, this regulation could be damaging to the consumers due to the price increase resulting from the reduction of the quantities sold on the market. We propose a stochastic control model and a simulation tool able to measure the effects of this mechanism...
The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow-Debreu-McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow-Debreu-McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to...
Les hypothèses de différentiabilité jouent un rôle essentiel dans plusieurs travaux récents consacrés à l'étude des propriétés de l'équilibre économique. Cet article présente une synthèse aussi élémentaire que possible d'une partie de ces travaux et fait aussi le lien avec la théorie des catastrophes de Thom.
For a simple graph, we consider the minimum number of edges which block all the odd cycles and the maximum number of odd cycles which are pairwise edge-disjoint. When these two coefficients are equal, interesting consequences appear. Similar problems (but interchanging “vertex-disjoint odd cycles” and “edge-disjoint odd cycles”) have been considered in a paper by Berge and Fouquet.
The known hierarchical clustering scheme is equivalent to the concept of ultrametric distance. Every distance can be represented in a spatial model using multidimensional scaling. We relate both classes of representations of proximity data in an algebraic way, obtaining some results and relations on clusters and the eigenvalues of the inner product matrix for an ultrametric distance. Principal coordinate analysis on an ultrametric distance gives two classes of independent coordinates, describing...