Crystal structure of a silver(I) complex with the 1,2,4,5-benzenetetracarboxylic acid (pyromellitic acid)

The reaction between freshly precipitated silver oxide Ag₂O and an aqueous solution of tetrabenzenecarboxylic acid H₄L leads to the anhydrous Ag₂H₂L complex. It crystallizes in the space groupP2₁/c, witha=6.457(1),b=8.180(1),c=9.982(1) Å, β=97.83(1)°,V=522.3(1) ų,Z=2,d=2.976 g cm^?3. This structure is a three dimensional polymeric network polymer without any silver...silver interaction. The silver environment is a bipyramid trigonal polyhedron with three short bond distances in the equatorial plane (Ag?O=2.255(2), 2.295(2), and 2.499(2) Å) and two longer bond distances in axial positions (Ag?O=2.558(2) and 2.617(2) Å). Thus, the silver polyhedron involves five different ligands. It is noteworthy that the (H₂L₂)^2? ligand is located around an inversion centre.     

On SCH and the approachability property

We construct a model of (Very Good Scale). This answers questions of Cummings, Foreman, Magidor and Woodin.

     

The Burnside ring of fusion systems

Given a saturated fusion system on a finite p-group S we define a ring modeled on the Burnside ring of finite groups. We show that these rings have several properties in common. When is the fusion system of G we describe the relationship between these rings.     

Entropic order quantity (EnOQ) model for deteriorating items

Jaber et al. [M.Y. Jaber, R.Y. Nuwayhid, M.A. Rosen, Price-driven economic order systems from a thermodynamic point of view, Int. J. Prod. Res. 42 (24) (2004) 5167–5184] suggested that it might be possible to improve production systems performance by applying the first and second laws of thermodynamics to reduce system entropy (or disorder). They then used these laws to modify the economic order quantity (EOQ) model to derive an equivalent entropic order quantity (EnOQ). The results suggested that larger quantities should be ordered than is suggested by the classical EOQ model.     

Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem

We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is D-equivalent to an ultrametric, where D ∈ (2,∞) is a prescribed target distortion. Since this procedure works for D arbitrarily close to the nonlinear Dvoretzky phase transition at distortion 2, we thus obtain a much simpler probabilistic proof of the main result of [3], answering a question from [12], and yielding the best known bounds in the nonlinear Dvoretzky theorem. Our method utilizes a sequence of random scales at which a given metric space is fragmented. As in many previous randomized arguments in embedding theory, these scales are chosen irrespective of the geometry of the metric space in question. We show that our bounds are sharp if one utilizes such a “scale-oblivious” fragmentation procedure.     

Absolutely minimal Lipschitz extension of tree-valued mappings

We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called Politics??a generalization of a game called Tug of War that has been used in Peres et?al. (J Am Math Soc 22(1):167?C210, 2009) to study real-valued AMLEs.     

Isomorphic embedding of ℓ p n , 1<p<2, into ℓ 1 (1+ε)n

In this paper we partially answer a question posed by V. Milman and G. Schechtman by proving that ℓ _p ⁿ , (C logn)^1/q(1+1/ε)-embeds into ℓ ₁ ^(1+ε)n , where 1<p<2 and 1/p+1/q=1. Supported by ISF.     

Dynamic Sampling Applied to Problems in Optimal Control

Dynamic sampling utilizes the option of varying the sampling rates according to the situation of the systems, thus obtaining procedures with improved efficiencies. In this paper, the technique is applied to a typical problem in optimal control theory, that of tracking and controlling the position of an object. It is shown that the dynamic sampling results in a significantly improved procedure for this case, even when applying a suboptimal policy which can be analyzed in closed form.     

Universal spaces for homotopy limits of modules over coaugmented functors (I)

For a coaugmented functor J on spaces, we consider J-modules and finite J-limits. The former are spaces X which are retracts of JX via the natural map. The latter are homotopy limits of J-modules arranged in diagrams whose shape is finite dimensional. Familiar examples are generalised Eilenberg MacLane spaces, which are the SP^∞-modules. Finite SP^∞-limits are nilpotent spaces with a very strong finiteness property. We show that the cofacial Bousfield-Kan construction of the functors J_n is universal for finite J-limits in the sense that every map X→Y where Y is a finite J-limit, factors through such natural map X→J_nX, for some n<∞.