In this paper, we establish an equivalent version of the hairy ball theorem in the form of a fixed point theorem. By using a version of Mas-Colell theorem [6] and by applying homotopy and approximation methods, we obtain our main result.

In the case of a large nuclear set (like the French set), nuclear production needs to be flexible to adjust to the predicted evolutions of the energy demmand. Consequently, the dominant position of nuclear in the national energy mix makes it responsible for the overall equilibrium of the...

We look at the optimal inter-temporal management of the fuel reservoir of nuclear units in a liberalized electricity market. We use the assumption that nuclear fuel works as a "reservoir" of energy due to the periodical shutdown of nuclear units to reload their fuel. In the medium-term, how a...

In many countries, the electricity systems are quitting the vertically integrated monopoly organization for an operation framed by competitive markets. It therefore questions how flexible nuclear plants capable of load-following should be operated in an open market framework. A number of...

In many countries, the electricity systems are quitting the vertically integrated monopoly organization for an operation framed by competitive markets. In such a competitive regime one can ask what the optimal operation/management of the nuclear generation set is. We place ourselves in a...

We consider an extension of a general equilibrium model with incomplete markets that considers cash-in-advance constraints. The total amount of money is supplied by an authority, which produces at no cost and lends money to agents at short term nominal rates of interest, meeting the demand....

We present a theorem on the existence of a maximal element for a correspondence which is upper hemi-continuous in some variables and which satisfies with respect to the other ones one the following conditions : (i) lower semi-continuous if the space has a finite dimension, (ii) lower...

In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex...

This paper studies the existence of solutions in continuous time optimization problems. It provides a theorem whose conditions can be easily checked in most models of the optimal growth theory, including those with increasing returns and multi-sector economies.

In electricity markets where competition has been established for a long time, a nuclear operator familiar with the operation of such markets could be interested in the optimal long-term management of a flexible nuclear set (like the French) in a competitive market. To obtain a long vision of...