We prove existence of a competitive equilibrium in a version of a Ramsey model in which leisure enters the utility function. The analysis is carried out by means of a direct and technically simple approach that allows us to obtain detailed results concerning the behavior of equilibrium allocations and prices.

It is difficult to wander far in contemporary metaphysics without bumping into talk of possible worlds. And reference to possible worlds is not confined to metaphysics. It can be found in contemporary epistemology and ethics, and has even found its way into linguistics and decision theory. But what are those possible worlds, the entities to which theorists in these disciplines all appeal? Call ...

In this paper we study, via variational methods, the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface. The boundary ∂D is assumed to lie within a finite distance of a flat plane and the incident wave is that arising from an inhomogeneous term in the Helmholtz equation whose support lies within some finite distance of the boundary ∂D. Via analysis of an eq...

A probabilistic relational database is a compact form of a set of deterministic relational databases (namely, possible worlds), each of which has a probability. In our framework, the existence of tuples is determined by associated Boolean formulae based on elementary events. An estimation, within such a setting, of the probabilities of possible worlds uses a prior probability distribution speci...

There are many interpretations of quantum mechanics, and new ones continue to appear. The Many-Worlds Interpretation (MWI) introduced by Everett (1957) impresses me as the best candidate for the interpretation of quantum theory. My belief is not based on a philosophical affinity for the idea of plurality of worlds as in Lewis (1986), but on a judgment that the physical difficulties of other int...

The aim of this work is to model a jet diffusion flame, to show the corresponding proof of existence of solutions, and to present numerical results. The model is based on the flamelet equations for the chemistry and on the mixture fraction for the flow. Numerical tests are carried out for Sandia Flame D and the results are found to compare well with available data found in the literature.

We prove a general finite-dimensional reduction theorem for critical equations of scalar curvature type. Solutions of these equations are constructed as a sum of peaks. The use of this theorem reduces the proof of existence of multi-peak solutions to some test-functions estimates and to the analysis of the interactions of peaks.

We show lower bounds on the number of sample points and on the number of coin tosses used by general sampling algorithms for estimating the average value of functions over a large domain. The bounds depend on the desired precision and on the error probability of the estimate. Our lower bounds match upper bounds established by known algorithms, up to a mul-tiplicative constant. Furthermore, we g...

This paper presents an application of voting geometry to individual decision making. We demonstrate that a number of decision anomalies can arise as a natural consequence of the aggregation of preferences of different neural systems. We present a proof of existence of a set of voting procedures that can account for the attraction effect, the similarity effect and the compromise effect, and prov...