Initial conditions of the universe: how much isocurvature is allowed?

We investigate the constraints imposed by current data on correlated mixtures of adiabatic and nonadiabatic primordial perturbations. We discover subtle flat directions in parameter space that tolerate large (approximately 60%) fractions of nonadiabatic fluctuations. In particular, larger values of the baryon density and a spectral tilt are allowed. The cancellations in the degenerate directions are explored and the role of priors is elucidated.     

Free products with amalgamation and HNN-extensions of uniformly exponential growth

We prove that, with rare exceptions, groups that are free products with amalgamation or HNN-extensions are of uniformly exponential growth. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 811–815, June, 2000.     

CO Extrusion in Homogeneous Gold Catalysis: Reactivity of Gold Acyl Species Generated through Water Addition to Gold Vinylidenes

Herein, we describe a new gold‐catalyzed decarbonylative indene synthesis. Synergistic σ,π‐activation of diyne substrates leads to gold vinylidene intermediates, which upon addition of water are transformed into gold acyl species, a type of organogold compound hitherto only scarcely reported. The latter are shown to undergo extrusion of CO, an elementary step completely unknown for homogeneous gold catalysis. By tuning the electronic and steric properties of the starting diyne systems, this new reactivity could be exploited for the synthesis of indene derivatives in high yields.     

Total Synthesis and Biological Assessment of Mandelalide A

A new convergent total synthesis of the marine macrolide mandelalide A ( 1 ) has been developed that is based on macrocyclic ring closure by a Shiina‐type macrolactonization and the construction of the requisite precursor seco acid by a highly efficient Sonogashira cross‐coupling reaction between two fragments of comparable complexity. Key steps in the elaboration of the acid building block were the enantioselective, catalytic addition of a protected acetylene to crotonaldehyde and the construction of the tetrahydropyran unit that is embedded in the macrocycle by means of an acid‐catalyzed Prins reaction. The synthesis of the alcohol fragment features the formation of the trisubstituted tetrahydrofuran ring through an acetal cleavage/epoxide opening cascade reaction and a rarely used radical alkynylation of a primary alkyl iodide. Intriguingly, the dihydroxylation of a terminal double bond as part of the synthesis of this building block gave the same major product for both the α‐ and β‐AD‐mix reagents, albeit with moderate or low selectivity. Synthetic mandelalide A ( 1 ) was a potent proliferation inhibitor of A549, HT460, and H1299 human lung cancer cells in vitro, but not of SK‐N‐SH neuroblastoma cells. However, in no case did we observe complete cell kill even at the highest compound concentration tested (5 μm ).     

Surface bundles over surfaces: new inequalities between signature,simplicial volume and Euler characteristic

Geometriae Dedicata - Given a pants decomposition $$\mathcal {PC} = \{\sigma _1, \ldots , \sigma _{\xi }\}$$ on a hyperbolizable surface $$\Sigma $$ and a vector $${{\underline{c}}}= (c_1, \ldots ,...