Contents 1. Introduction 2. The classical model 3. Existence of equilibrium 3.1 Equilibrium and quasi-equilibrium of abstract economies 3.2 Application to quasi-equilibrium existence for private ownership economies 3.3 From quasi-equilibrium to equilibrium 4. Optimality properties of equilibrium 4.1 Optimality, core and limit-core concepts 4.2 Non-emptiness results 4.3 Price-decentralization re...

We evaluate quasi-classically the Ramond partition function of Euclidean D = 10 U(N) super-Yang{Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasi-class...

It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (s d)O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. We associate to each of these problems an intrinsic system degree which becomes in wor...

We construct a time-optimal quasi-solution of the firing mob synchronisation problem over finite, connected, and undirected multigraphs whose maximum degrees are uniformly bounded by a constant. It is only a quasi-solution because its number of states depends on the graph or, from another perspective, does not depend on the graph but is countably infinite. To construct this quasi-solution we in...

In this paper we investigate the structure of quasi-BCH codes. In the first part of this paper we show that quasi-BCH codes can be derived from Reed-Solomon codes over square matrices extending the known relation about classical BCH and Reed-Solomon codes. This allows us to adapt the Welch-Berlekamp algorithm to quasi-BCH codes. In the second part of this paper we show that quasi-BCH codes can ...

We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-...

Quasi-orders, that is, reflexive and transitive binary relations, have numerous applications. In educational theories, the dependencies of mastery among the problems of a test can be modeled by quasi-orders. Methods such as item tree or Boolean analysis that mine for quasi-orders in empirical data are sensitive to the underlying quasi-order structure. These data mining techniques have to be com...