On the irreducibility of a competitive economy.

In the case of a private ownership economy, we unify McKenzie-Debreu's and Arrow-Hahn's concepts of irreducibility by a generalization of Bergstrom irreducibility to economies with production. This, together with existence of a quasi-equilibrium, will be shown to imply existence of a Walras equilibrium.

Further Representations of the Canonical Commutation Relations

We construct a new class of representations of the canonical commutation relations, which generalizes previously known classes. We perturb the infinitesimal generator of the initial Fock representation (i.e. the free quantum field) by a function of the field which is square-integrable with respect to the associated Gaussian measure. We characterize which such perturbations lead to representations of the canonical commutation relations. We provide conditions entailing the irreducibility of such representations, show explicitly that our class of representations subsumes previously studied classes, and give necessary and sufficient conditions for our representations to be unitarily equivalent, resp. quasi-equivalent, with Fock, coherent or quasifree representations

Indivisible Goods and Fiat Money

In spite of fiat money is useless in a standard Arrow-Debreu model, in this paper we will show that this does not hold true anymore when goods are indivisible. In our setting, although fiat money yields no utility, its price will always be positive and the set of equilibrium allocations changes with the distribution of fiat money. Its role lies in the fact that it could be used to facilitate exchange. Since a Walras equilibrium does not always exist when goods are indivisible, a new equilibrium concept - called rationing equilibrium - is introduced and its existence is proven under weak assumptions on the economy. A Walras equilibrium exists generically on the distribution of fiat moneycompetitive equilibrium, indivisible goods, fiat money.

On the irreducibility of a competitive economy

In the case of a private ownership economy, we unify McKenzie-Debreu's and Arrow-Hahn's concepts of irreducibility by a generalization of Bergstrom irreducibility to economies with production. This, together with existence of a quasi-equilibrium, will be shown to imply existence of a Walras equilibrium

Geometric Modular Action and Spacetime Symmetry Groups

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times -- four-dimensional Minkowski and three-dimensional de Sitter spaces -- for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.Comment: 83 pages, AMS-TEX (format changed to US letter size

Geometric Modular Action, Wedge Duality and Lorentz Covariance are Equivalent for Generalized Free Fields

The Tomita-Takesaki modular groups and conjugations for the observable algebras of space-like wedges and the vacuum state are computed for translationally covariant, but possibly not Lorentz covariant, generalized free quantum fields in arbitrary space-time dimension d. It is shown that for $d\geq 4$ the condition of geometric modular action (CGMA) of Buchholz, Dreyer, Florig and Summers \cite{BDFS}, Lorentz covariance and wedge duality are all equivalent in these models. The same holds for d=3 if there is a mass gap. For massless fields in d=3, and for d=2 and arbitrary mass, CGMA does not imply Lorentz covariance of the field itself, but only of the maximal local net generated by the field

Characterizing the Load Deformation Behaviour of Steel Deck Diaphragms

Lateral loads flow through a building’s horizontal roof and floor diaphragms before being transferred to the vertical lateral force resisting system (e.g. braced frames, moment frames or shear walls). These diaphragms are therefore a critical structural component in the resistance of lateral loads. A review of the literature shows that a large number of experimental programs have been performed to obtain the in-plane load-deformation behavior of steel deck and concrete on steel deck diaphragms. The tested diaphragm behavior was found to be dependent on a set of factors including loading protocol, fastener type, fastener size and spacing, and more. There does not currently exist a single, unifying review of these diaphragm tests and their relevant results. A research program is being conducted to collect and consolidate the available literature about tested steel deck diaphragms and their results. A database has been created that includes over 450 tested specimens with more than 130 cyclic tests. In addition, an effort is made to characterize diaphragms’ load-deformation response as grouped by sidelap and support fastener type. The test programs and results collected into this database as well as the characterization of diaphragm behavior are discussed in this paper

The second law of thermodynamics, TCP, and Einstein causality in anti-de Sitter space-time

If the vacuum is passive for uniformly accelerated observers in anti-de Sitter space-time (i.e. cannot be used by them to operate a "perpetuum mobile"), they will (a) register a universal value of the Hawking-Unruh temperature, (b) discover a TCP symmetry, and (c) find that observables in complementary wedge-shaped regions are commensurable (local) in the vacuum state. These results are model independent and hold in any theory which is compatible with some weak notion of space-time localization.Comment: 8 pages, slightly improved results, minor changes in the expository part, new title; to appear in "Classical and Quantum Gravity