Stereochemistry of decarbalkoxylation of arylmethylene-propanedioic acids dimethyl esters

Halide ions increase the rate of decarbalkoxylation of arylmethylene-propanedioic acids dimethyl esters.     

The pianigiani-yorke measure for topological markov chains

We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.     

FBI transforms in Gevrey classes

In this work we develop the FBI Transform tools in Gevrey classes. Our goal is to extend to a Gevrey-s obstacle withs < 3 the localization of poles result obtained by Sjöstrand [10] in the analytic class. In that work, the author proved that the pole-free zone is controlled by a constantC _0,a (which was only implicit in Bardos-Lebeau-Rauch [1]), improving the constantC _0,∞ of the results of Hargé-Lebeau [13] and Sjöstrand-Zworski [13] valid in C^∞ The works [3], [13] and [10] feature an adapted complex scaling for convex obstacles, but in [10] there is the addition of a small complex “G³ deformation”. The study of such Gevrey deformations for operators with symbols in Gevrey classes is the central point of this work.     

Gauged N = 8 supergravity in five dimensions

We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6,R), specially SO(p, 6?p) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E₆₍₆₎ symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.     

Points and triangles in the plane and halving planes in space

We prove that for any setS ofn points in the plane andn ^3−α triangles spanned by the points inS there exists a point (not necessarily inS) contained in at leastn ^3−3α/(c log⁵ n) of the triangles. This implies that any set ofn points in three-dimensional space defines at most halving planes. Work on this paper by Boris Aronov and Rephael Wenger has been supported by DIMACS under NSF Grant STC-88-09648. Work on this paper by Bernard Chazelle has been supported by NSF Grant CCR-87-00917. Work by Herbert Edelsbrunner has been supported by NSF Grant CCR-87-14565. Micha Sharir has been supported by ONR Grant N00014-87-K-0129, by NSF Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the Israeli National Council for Research and Development, and the Fund for Basic Research administered by the Israeli Academy of Sciences.