Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems

We consider chains of random constraint satisfaction models that are spatially coupled across a finite window along the chain direction. We investigate their phase diagram at zero temperature using the survey propagation formalism and the interpolation method. We prove that the SAT-UNSAT phase transition threshold of an infinite chain is identical to the one of the individual standard model, and is therefore not affected by spatial coupling. We compute the survey propagation complexity using population dynamics as well as large degree approximations, and determine the survey propagation threshold. We find that a clustering phase survives coupling. However, as one increases the range of the coupling window, the survey propagation threshold increases and saturates towards the phase transition threshold. We also briefly discuss other aspects of the problem. Namely, the condensation threshold is not affected by coupling, but the dynamic threshold displays saturation towards the condensation one. All these features may provide a new avenue for obtaining better provable algorithmic lower bounds on phase transition thresholds of the individual standard model.     

General synthesis of tetrasubstituted alkenyl-1,3,4-oxadiazoles

Tetrasubstituted alkenyl-1,3,4-oxadiazoles were synthesized in moderate to excellent yield, under mild conditions and in the presence of sensitive functional groups, via the cyclization of diacylhydrazides using PPh₃ and hexachloroethane in the presence of Hünig’s base. An efficient one-pot acylation/cyclization approach for the conversion of acylhydrazides to 1,3,4-oxadiazoles is also described. The complexity of our substrate as well as the wide range of functional groups incorporated substantially broadens the scope of this methodology.     

Investigation of the stability of Mn<Subscript>12</Subscript> single molecule magnets

The stability of single crystals and monolayers of Mn₁₂ single molecule magnets under the influence of X-ray radiation and other possibly disruptive influences has been investigated by means of synchrotron radiation. Clear evidence for radiation induced sample degradation was found for both single crystals and monolayers. The comparison with spectra obtained after damaging the molecules by Ar⁺ sputtering, metal evaporation or water moistening indicates a possibility to distinguish between radiation damage and other external influences. The results clarify some of the previous conflicting reports on the integrity of Mn₁₂ molecules deposited on surfaces and are linked to the investigations aiming at studies of the electronic and magnetic properties of individual Mn₁₂ clusters.     

To Coordinate or not to Coordinate: The Special Role of Chalcogen Ether Functionalities in the Design of Twofold Functionalized Cyclopentadienyl Ligands [Cp,O,Ch (Ch = S,Se)]

The solvent‐ and catalyst free synthesis of two β‐thio ketones L1a and L1b is reported. L1a , L1b , and a β‐seleno ketone L1c were successfully employed as ligand precursors in the synthesis of a novel series of cationic titanium complexes 4a – 4c via a well‐established reaction sequence: insertion of the carbonyl functional group into the polarized Ti–C_q,exo bond of the monopentafulvene complex Cp*Ti(Cl)(π‐η⁵:σ–η¹‐C₅H₄=CR₂) ( 1 ) (CR₂ = adamantylidene), subsequent methylation, and final activation with B(C₆F₅)₃. The cationic titanium complexes 4a – 4c bear twofold functionalized cyclopentadienyl [Cp,O,Ch (Ch = S, Se)] ligand frameworks built directly in the coordination sphere of the metal, in which the chalcogen ether functionalities do not coordinate to the central metal atoms as demonstrated by NMR experiments. Consequently, Cp,O σ,π chelating ligand systems are formed with free coordination sites at the central titanium atoms and pendant chalcogen ether moieties.     

Cyclobutendion und methylencyclobutenon. Synthese,dienophile reaktivität und exo,endo-selektivität

A new synthesis of cyclobutenedione and methylenecyclobutenone and their reactions with 1,3-dienes are described.     

Percolation in carbon black filled epoxy resin

The conditions to form a conductive network in carbon black filled epoxy resin were examined. It was found that the formation is controlled by particle-particle interaction which can be influenced by shear forces or by the ionic concentration of the resin. Therefore the network morphology and thus the percolation threshold depends strongly upon the processing route. On best conditions the percolation threshold was reduced to 0.06 vol.-%. That a continuous network can form with such a low volume fraction can be explained by the fractal dimension of agglomerates the network is made of.     

Unexpected Selective Methyl Group Abstractions from SiMe3 Moieties of CH2SiMe3 Ligands To Give New Cationic Titanium Complexes

The synthesis of the alkylated pentafulvene titanium complex Cp*Ti(CH₂SiMe₃)(π-η⁵:σ-η¹-C₅H₄=CR₂) (CR₂=adamantylidene) is described. The coordination mode of the pentafulvene ligand in this complex allowed for the subsequent synthesis of a series of nitrile-insertion products. By reacting these neutral compounds with the strong Lewis acid B(C₆F₅)₃, unprecedented selective methyl-group abstractions from the SiMe₃ moieties under formation of novel cationic titanium complexes with the corresponding MeB(C₆F₅)₃⁻ anion are demonstrated. The proposed silylium ion intermediates of these reactions are directly stabilized by either the exocyclic carbon atom of the pentafulvene ligand or by the lone pairs of the nitrogen atoms of the chelating Cp,N-ligands. In addition, a titanium enamine complex and its reaction with B(C₆F₅)₃ is reported, which results in the formation of a betaine.