[{[(η7-C2B10H12)(η6-C2B10H12)U][K2(thf)5]}2]: A Metallacarborane Containing the Novel η7-C2B10H124− Ligand

The tetranion ligand η⁷-C₂B₁₀H₁₂⁴⁻ has been observed for the first time in 1 , which was obtained from the reaction of o-C₂B₁₀H₁₂ with excess K metal followed by treatment with UCl₄. As shown in the picture (without K cations and coordinated THF molecules), 1 is a centrosymmetric dimer with a bent sandwich structure.     

Palladium‐Catalyzed Direct Dialkenylation of Cage B?H Bonds in o‐Carboranes through Cross‐Coupling Reactions

Palladium‐catalyzed direct dialkenylation of cage B(4,5) H bonds in o‐carboranes has been achieved with the help of a carboxylic acid directing group, leading to the preparation of a series of 4,5‐[trans‐(ArCHCH)]₂‐ocarboranes in high yields with excellent regioselectivity. The traceless directing group, eliminated during the course of the reaction, is responsible for controlling regioselectivity and dialkenylation. A possible catalytic cycle is proposed, involving a tandem sequence of Pd^II‐initiated cage B H activation, alkene insertion, β‐H elimination, reductive elimination, and decarboxylation.     

Ring-opening and ring-expansion reactions of carborane-fused borirane

Though the reaction chemistry of three-membered ring molecules such as cyclopropanes and their heteroatom-containing analogues has been extensively studied, the chemical properties of their boron analogues, boriranes, are little known thus far. This work describes the diverse reactivity patterns of carborane-fused borirane 2. This borirane engages in ring-opening reactions with different types of Lewis acids, such as BBr₃, GeCl₂, GaCl₃, BH₃(SMe₂) and HBpin, affording a series of ring-opening products, in which M–X or B–H bonds add across the B–C(cage) bond of the three-membered ring in 2. On the other hand, borirane 2 can undergo ring-expansion reactions with unsaturated molecules such as PhCHO, CO₂ and PhCN to give ring-expansion products, five-membered boracycles, via a concerted reaction mechanism as supported by DFT calculations. The results of this work not only enrich the reaction chemistry of boriranes, but also offer new routes to boron-containing compounds and heterocycles.

Carborane-fused borirane can not only engage in ring-opening reactions with different types of Lewis acids, but also undergo ring-expansion reactions with unsaturated molecules such as PhCHO, CO₂ and PhCN to give five-membered boracycles.     

Convergence analysis of tight framelet approach for missing data recovery

How to recover missing data from an incomplete samples is a fundamental problem in mathematics and it has wide range of applications in image analysis and processing. Although many existing methods, e.g. various data smoothing methods and PDE approaches, are available in the literature, there is always a need to find new methods leading to the best solution according to various cost functionals. In this paper, we propose an iterative algorithm based on tight framelets for image recovery from incomplete observed data. The algorithm is motivated from our framelet algorithm used in high-resolution image reconstruction and it exploits the redundance in tight framelet systems. We prove the convergence of the algorithm and also give its convergence factor. Furthermore, we derive the minimization properties of the algorithm and explore the roles of the redundancy of tight framelet systems. As an illustration of the effectiveness of the algorithm, we give an application of it in impulse noise removal.     

Transition-metal-promoted or -catalyzed exocyclic alkyne insertion via zirconacyclopentene with carborane auxiliary: formation of symmetric or unsymmetric benzocarboranes

Reactions of Cp(2)Zr(μ-Cl)(μ-C(2)B(10)H(10))Li(OEt(2))(2) with alkynes R(1)C≡CR(2) gave as insertion products zirconacyclopentenes incorporating a carboranyl unit, 1,2-[Cp(2)ZrC(R(1))═C(R(2))]-1,2-C(2)B(10)H(10) (1). Treatment of 1 with another type of alkyne R(3)C≡CR(4) in the presence of stoichiometric amounts of NiCl(2) and FeCl(3) or a catalytic amount of NiCl(2) afforded symmetric or unsymmetric benzocarboranes. The regioselectivity was dominated by the polarity of the corresponding alkynes. These reactions could also be carried out in one pot, leading to the equivalent of a three-component [2 + 2 + 2] cycloaddition of carboryne and two different alkynes promoted by transition metals. A reaction mechanism was proposed after the isolation and structural characterization of the key intermediate nickelacycle. These results show that nickel complexes are more reactive than the iron ones toward the insertion of alkynes but that the latter do not initiate the trimerization of alkynes, making the insertion of activated alkynes possible. This work also demonstrates that a catalytic amount of nickel works as well as a stoichiometric amount of nickel in the presence of excess FeCl(3) for the reactions. Such a catalytic reaction may shed some light on the development of zirconocene-based catalytic reactions.