Synthesis of Bridged Tetrahydrobenzo[b]azepines and Derivatives through an Aza‐Piancatelli Cyclization/Michael Addition Sequence

Herein, we report the preparation of bridged tetrahydrobenzo[b]azepines, which was accomplished through an aza‐Piancatelli cyclization/Michael addition sequence in a one‐pot fashion from readily available precursors. It is noteworthy that a general method to access these scaffolds was hitherto unprecedented. Additionally, the multifaceted aspects of this process have been exemplified through its application to the synthesis of 2‐azabicyclo[3.2.1]octanes and bridged tetrahydrobenzo[b]oxepines, along with post‐derivatizations.     

Mechanically Interlocked Single‐Wall Carbon Nanotubes

Extensive research has been devoted to the chemical manipulation of carbon nanotubes. The attachment of molecular fragments through covalent‐bond formation produces kinetically stable products, but implies the saturation of some of the C? C double bonds of the nanotubes. Supramolecular modification maintains the structure of the SWNTs but yields labile species. Herein, we present a strategy for the synthesis of mechanically interlocked derivatives of SWNTs (MINTs). In the key rotaxane‐forming step, we employed macrocycle precursors equipped with two π‐extended tetrathiafulvalene SWNT recognition units and terminated with bisalkenes that were closed around the nanotubes through ring‐closing metathesis (RCM). The mechanically interlocked nature of the derivatives was probed by analytical, spectroscopic, and microscopic techniques, as well as by appropriate control experiments. Individual macrocycles were observed by HR STEM to circumscribe the nanotubes.     

The Relationship Between Stock Markets Of Major Developed Countries And Asian Emerging Markets

With the emergence of new capital markets and liberalization of stock markets in recent years, there has been an increase in investors' interest in international diversification. This is so because international diversification allows investors to have a larger basket of foreign securities to choose from as part of their portfolio assets, so as to enhance the reward-to-volatility ratio. This benefit would be limited if national equity markets tend to move together in the long run. This paper thus studies the issue of co-movement between stock markets in major developed countries and those in Asian emerging markets using the concept of cointegration. We find that there is co-movement between some of the developed and emerging markets, but some emerging markets do differ from the developed markets with which they share a long-run equilibrium relationship. Furthermore, it has been observed that there has been increasing interdependence between most of the developed and emerging markets since the 1987 Stock Market Crash. This interdependence intensified after the 1997 Asian Financial Crisis. With this phenomenon of increasing co-movement between developed and emerging stock markets, the benefits of international diversification become limited.     

Toward the Rational Design of Galactosylated Glycoclusters That Target Pseudomonas aeruginosa Lectin A (LecA): Influence of Linker Arms That Lead to Low‐Nanomolar Multivalent Ligands

Anti‐infectious strategies against pathogen infections can be achieved through antiadhesive strategies by using multivalent ligands of bacterial virulence factors. LecA and LecB are lectins of Pseudomonas aeruginosa implicated in biofilm formation. A series of 27 LecA‐targeting glycoclusters have been synthesized. Nine aromatic galactose aglycons were investigated with three different linker arms that connect the central mannopyranoside core. A low‐nanomolar (K_d=19 nm , microarray) ligand with a tyrosine‐based linker arm could be identified in a structure–activity relationship study. Molecular modeling of the glycoclusters bound to the lectin tetramer was also used to rationalize the binding properties observed.     

Alkaline Earth–Olefin Complexes with Secondary Interactions

Strontium and calcium (alkaline earth: Ae) olefin complexes stabilised by secondary Ae???F?C and β‐agostic Ae???H?Si interactions are presented. Olefin coordination onto the alkaline earths is plain in the solid state, and it is thermodynamically favoured over the coordination of THF. The existence of the Ae???olefin interactions is corroborated by solution NMR data and DFT computations. The coordination mode of the olefin varies with steric effects and, if enforced, olefin dissociation can be compensated by the other non‐covalent interactions, as supported by DFT computations.     

Alkaline‐Earth‐Catalysed Cross‐Dehydrocoupling of Amines and Hydrosilanes: Reactivity Trends,Scope and Mechanism

Alkaline‐earth (Ae=Ca, Sr, Ba) complexes are shown to catalyse the chemoselective cross‐dehydrocoupling (CDC) of amines and hydrosilanes. Key trends were delineated in the benchmark couplings of Ph₃SiH with pyrrolidine or tBuNH₂. Ae{E(SiMe₃)₂}₂ ? (THF)_x (E=N, CH; x=2–3) are more efficient than {N^N}Ae{E(SiMe₃)₂} ? (THF)_n (E=N, CH; n=1–2) complexes (where {N^N}^?={ArN(o‐C₆H₄)C(H)=NAr}^? with Ar=2,6‐iPr₂‐C₆H₃) bearing an iminoanilide ligand, and alkyl precatalysts are better than amido analogues. Turnover frequencies (TOFs) increase in the order Ca<Sr<Ba. Ba{CH(SiMe₃)₂}₂ ? (THF)₃ displays the best performance (TOF up to 3600 h^?1). The substrate scope (>30 products) includes diamines and di(hydrosilane)s. Kinetic analysis of the Ba‐promoted CDC of pyrrolidine and Ph₃SiH shows that 1) the kinetic law is rate=k[Ba]¹[amine]⁰[hydrosilane]¹, 2) electron‐withdrawing p‐substituents on the arylhydrosilane improve the reaction rate and 3) a maximal kinetic isotopic effect (k_SiH/k_SiD=4.7) is seen for Ph₃SiX (X=H, D). DFT calculations identified the prevailing mechanism; instead of an inaccessible σ‐bond‐breaking metathesis pathway, the CDC appears to follow a stepwise reaction path with N?Si bond‐forming nucleophilic attack of the catalytically competent Ba pyrrolide onto the incoming silane, followed by rate limiting hydrogen‐atom transfer to barium. The participation of a Ba silyl species is prevented energetically. The reactivity trend Ca<Sr<Ba results from greater accessibility of the metal centre and decreasing Ae?N_amide bond strength upon descending Group 2.     

Approximation by Algebraic Integers and Hausdorff Dimension

The paper computes the Hausdorff dimension of sets of real numberswhich are close to infinitely many real algebraic integers ofbounded degree. It also investigates the distribution of realalgebraic integers of bounded degree, which are proved to beevenly spaced.     

Organic cross-linked electropolymers as supported oxidation catalysts: poly((tetrakis(9,9'-spirobifluorenyl)porphyrin)manganese) films

Anodic oxidation of free base and manganese complexes of tetraspirobifluorenylporphyrins leads to the coating of the working electrode by insoluble electroactive poly(9,9'-spirobifluorene-free and manganese porphyrin) films which electrochemical behavior and physicochemical properties are described. After removal from the electrode, the manganese-complexed polymers were evaluated as catalysts for the oxidation of alkenes by iodobenzene diacetate or iodosylbenzene. The results show that the reactions proceeded very efficiently at room temperature with good yields. The electrosynthesized polymer catalysts can be recycled by simple filtration and reused even up to the eighth cycle without loss of activity and selectivity. These results represent an important improvement over those previously described for manganese-porphyrin-catalyzed epoxidation reactions.     

Sharp phase transition theorems for hyperbolicity of random groups

We prove that in various natural models of a random quotient of a group, depending on a density parameter, for each hyperbolic group there is some critical density under which a random quotient is still hyperbolic with high probability, whereas above this critical value a random quotient is very probably trivial. We give explicit characterizations of these critical densities for the various models.