Version Of Property Research Articles

The Penrose property with a cosmological constant

A spacetime satisfies the non-timelike boundary version of the Penrose property if the timelike future of any point on contains the whole of . This property was first discussed for asymptotically flat spacetimes by Penrose, along with an equivalent definition (the finite version). In this paper we consider the Penrose property in greater generality. In particular we consider spacetimes with a non-zero cosmological constant and we note that the two versions of the property are no longer equivalent. In asymptotically AdS spacetimes it is necessary to re-state the property in a way which is more suited to spacetimes with a timelike boundary. We arrive at a property previously considered by Gao and Wald. Curiously, this property was shown to fail in spacetimes which focus null geodesics. This is in contrast to our findings in asymptotically flat and asymptotically de Sitter spacetimes. We then move on to consider some further example spacetimes (with zero cosmological constant) which highlight features of the Penrose property not previously considered. We discuss spacetimes which are the product of a Lorentzian and a compact Riemannian manifold. Perhaps surprisingly, we find that both versions of the Penrose property are satisfied in this product spacetime if and only if they are satisfied in the Lorentzian spacetime only. We also discuss the Ellis–Bronnikov wormhole (an example of a spacetime with more than one asymptotically flat end) and the Hayward metric (an example of a non-singular black hole spacetime).

Analytic properties of approximate lattices

Nous introduisons une notion d’induction de cocycle pour les réseaux approximatifs uniformes forts dans les groupes localement compacts à base dénombrable, et nous l’utilisons pour mettre en relation les réseaux approximatifs de type Kazhdan et Haagerup (relatifs) avec les propriétés correspondantes des groupes ambiants localement compacts. Notre approche s’applique à de larges classes de réseaux approximatifs uniformes (bien que pas toutes) et est suffisamment souple pour couvrir les versions L p de propriété (FH) et a-(FH)-moyennabilité, ainsi que leurs versions quasi à la Burger–Monod et Ozawa.

On constructions with 2-cardinals

We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets originating with Velleman’s neat simplified morasses called 2-cardinals. The theory of related trees, gaps, colorings of pairs and forcing notions is reformulated and sketched from a unifying point of view with the focus on the applicability to constructions of mathematical structures like Boolean algebras, Banach spaces or compact spaces. The paper is dedicated to the memory of Jim Baumgartner whose seminal joint paper (Baumgartner and Shelah in Ann Pure Appl Logic 33(2):109–129, 1987) with Saharon Shelah provided a critical mass in the theory in question. A new result which we obtain as a side product is the consistency of the existence of a function \(f:[\lambda ^{++}]^2\rightarrow [\lambda ^{++}]^{\le \lambda }\) with the appropriate \(\lambda ^+\)-version of property \(\Delta \) for regular \(\lambda \ge \omega \) satisfying \(\lambda ^{<\lambda }=\lambda \).

Versions of properties ( a) and [formula omitted

In this paper we define and study several versions of properties ( a) and ( p p ) and their relationships with other covering properties. Especially, we investigate when the Alexandroff duplicate AD ( X ) of a space X has considered properties.

An inverse problem with data on the part of the boundary

Let u t = ∇ 2 u − q( x) u ≔ Lu in D × [0, ∞), where D ⊂ R 3 is a bounded domain with a smooth connected boundary S, and q( x) ∈ L 2( S) is a real-valued function with compact support in D. Assume that u( x, 0) = 0, u = 0 on S 1 ⊂ S, u = a( s, t) on S 2 = S⧹ S 1, where a( s, t) = 0 for t > T, a( s, t) ≢ 0, a ∈ C 1([0, T]; H 3/2( S 2)) is arbitrary. Given the extra data u N ∣ S 2 = b ( s , t ) , for each a ∈ C 1([0, T]; H 3/2( S 2)), where N is the outer normal to S, one can find q( x) uniquely. A similar result is obtained for the heat equation u t = L u ≔ ∇ · ( a ∇ u ) . These results are based on new versions of Property C.

Lazard's Theorem forS‐posets

AbstractIn 1971, inspired by the work of Lazard and Govorov for modules over a ring, Stenström proved that the strongly flat right actsASover a monoidS(that is, the acts that are directed colimits of finitely generated free acts) are those for which the functorAS⊗ (from the category of leftS‐acts into the category of sets) preserves pullbacks and equalizers. He also provided interpolation‐type conditions (now referred to in the literature as Property (P) and Property (E)) characterizing strong flatness. Unlike the situation for modules over a ring, strong flatness is strictly stronger than (mono‐) flatness (wherein the functorAS⊗ is required only to preserve monomorphisms). The study of flatness properties of partially ordered monoids acting on partially ordered sets was initiated by S. M. Fakhruddin in the 1980s, and has been continued recently in the paper “Indecomposable, projective, and flatS‐posets” by Shi, Liu, Wang, and Bulman–Fleming, Comm. Algebra33, 235–251 (2005). In that paper, a criterion for the equality of elements in a tensor product ofS‐posets is given and a version of Property (P) is presented that, as in the unordered case, implies flatness and is implied by projectivity. The present paper introduces a corresponding Property (E) and establishes an analogue of the Lazard–Govorov–Stenström theorem in the context ofS‐posets. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

General allocation problems with single-peaked preferences: path-independence and related topics

We face the problem of allocationg a fixed amount of a perfectly divisible good among a group of agents with single-peaked preferences. We survey the three different cases studied in the literature: the pure distribution case, the redistribution case, and the gerneral case. The so called general case provide with a natural framework to analyze the idea of path-independence. In this framework, we explore the existence of rules fulfilling this property. Our first result is negative: a strong version of this property cannot be fulfilled together with efficiency. Nonetheless, some restricted versions of the path-independence property are compatible with interesting properties, in particular no manipulability, and no envy. We then identify two solutions satisfying this sort of property: the equal distance rule, and a new extension of the uniform rule.