An Approach to Wavelet Isomorphisms of Function Spaces Via Atomic Representations

Both wavelet and atomic decomposition techniques are essential tools in the study of function spaces nowadays, but they both have their advantages and disadvantages. The celebrated bridge between both concepts was given by the compactly supported Daubechies wavelets which can be interpreted as atoms. In this paper we deal with the converse direction, that is, we present a fairly general approach how to construct compactly supported wavelets when an atomic decomposition is known already. The main idea is Taylor’s expansion combined with our new, so-called \(\varkappa \)-convergence assumption in the admitted sequence spaces. We finally exemplify our main result and collect some known and new settings where such a wavelet decomposition is obtained, e.g., in spaces of Besov or Triebel–Lizorkin type with a doubling weight.     

Directed Supramolecular Surface Assembly of SNAP‐tag Fusion Proteins

Supramolecular assembly of proteins on surfaces and vesicles was investigated by site‐selective incorporation of a supramolecular guest element on proteins. Fluorescent proteins were site‐selectively labeled with bisadamantane by SNAP‐tag technology. The assembly of the bisadamantane functionalized SNAP‐fusion proteins on cyclodextrin‐coated surfaces yielded stable monolayers. The binding of the fusion proteins is specific and occurs with an affinity in the order of 10⁶ M ^?1 as determined by surface plasmon resonance. Reversible micropatterns of the fusion proteins on micropatterned cyclodextrin surfaces were visualized by using fluorescence microscopy. Furthermore, the guest‐functionalized proteins could be assembled out of solution specifically onto the surface of cyclodextrin vesicles. The SNAP‐tag labeling of proteins thus allows for assembly of modified proteins through a host–guest interaction on different surfaces. This provides a new strategy in fabricating protein patterns on surfaces and takes advantage of the high labeling efficiency of the SNAP‐tag with designed supramolecular elements.     

6π/10π-Electrocyclization of ketene-iminium salts for the synthesis of substituted naphthylamines

An intramolecular 6π/10π-electrocyclization from ketene-iminium salts was developed for the preparation of naphthylamines. Various substituents on the nitrogen, on the aromatic ring, and on the olefin were studied. Tricyclic skeletons were obtained in few steps and good overall yields. The electrocyclization of ketene-iminium salts has been computationally explored by means of DFT calculations and their activation barriers were compared to the parent triene as well as the corresponding dienyl allenes and dienyl ketenes. Electrocyclizations for ketene-iminium salts were shown to be highly exergonic and have much smaller barriers to activation.     

Synthesis and characterization of ionic liquids containing copper, manganese, or zinc coordination cations

Copper-, manganese-, and zinc-based ionic liquids (Cu{NH(2)CH(2)CH(2)OH}(6)[CH(3)(CH(2))(3)CH(C(2)H(5))CO(2)](2) (2), Cu{NH(CH(2)CH(2)OH)(2)}(6)[CH(3)(CH(2))(3)CH(C(2)H(5))CO(2)](2) (3A), Cu{NH(CH(2)CH(2)OH)(2)}(6)[CF(3)SO(3)](2) (3B), Cu{NH(CH(2)CH(2)OH)(2)}(6)[(CF(3)SO(2))(2)N](2) (3C), Mn{NH(CH(2)CH(2)OH)(2)}(6)[CF(3)SO(3)](2) (4), and Zn{NH(2)CH(2)CH(2)OH}(6)[CF(3)SO(3)](2) (5)) are synthesized in a single-step reaction. Infrared data suggest that ethanolamine preferentially coordinates to the metal center through the amine group in 2 and the hydroxyl group in 5. In addition, diethanolamine coordinates through the amine group in 3A, 3C, and 4 and the hydroxyl group in 3B. The compounds are viscous (>1000 cP) at room temperature, but two (3C and 4) display specific conductivities that are reasonably high for ionic liquids (>20 mS cm(-1)). All of the compounds display a glass transition (T(g)) below -50 °C. The cyclic voltammograms (CVs) of 2, 3A, 3B, and 3C display a single quasi-reversible wave associated with Cu(II)/Cu(I) reduction and re-oxidation while 5 shows a wave attributed to Zn(II)/Zn(0) reduction and stripping (re-oxidation). Compound 4 is the first in this new family of transition metal-based ionic liquids (MetILs) to display reversible Mn(II)/Mn(III) oxidation and re-reduction at 50 mV s(-1) using a glassy carbon working electrode.