Modification of carbon electrodes by vitamin B12-polymers

New types of electroactive polymers consisting of derivatives of vitamin B₁₂ and epoxy resins have been synthesized. Surface modification of carbon (carbon felt or basal plane pyrolytic graphite) has been achieved by thermal curing of the monomers on the electrodes. Electrochemical response from the Co (II)/Co (I) redox couple has been observed from sub-mono to multilayer coverages. The influence of the size of the epoxy spacer on charge propagation in the polymer has been studied. The B₁₂-modified electrodes have been applied to electrosynthesis and electroanalysis: They catalyze the reductive cross-coupling of alkyl halides and activated olefins and they are efficient sensors for alkylating agents.     

Short Syntheses of some ‘Decalin‐1,8‐diones’ and their Derivatives: Breaking the Pretended Symmetry

A cheap synthesis of the so‐called ‘decalin‐1,8‐diones’ started with the conjugate (1,4‐) addition of cyclohex‐2‐en‐1‐one derivatives to the γ‐position of the dilithium derivative (buta‐1,3‐diene‐1,1‐bis(olate)) of crotonic acid. Hydrogenation of these ‘1,4‐γ’ adducts and final cyclization afforded the enol tautomers of decalin‐1,8‐diones. Nucleophilic substitutions at these 3‐oxoenols by NH₃ or primary amines created only monoamino products (namely, 3‐oxoenamines) whose reactions with OPCl₃ yielded dihydro(1,3,2)oxazaphosphinin‐2‐one derivatives. The two regioisomers of a trimethyl‐3‐oxoenamine served as models for the constitutional assignments of the two rapidly interconverting (hence, individually NMR‐invisible), tautomeric trimethyl‐3‐oxoenols. Such methyl substitutions served to break the ‘pretended’ symmetry of ‘decalin‐1,8‐dione’. Hydrazine and 3‐oxoenols furnished oxygen‐free indazole derivatives whose N?H bonds exchanged with t_1/2=ca. 0.00035 s at ca. ?58(9) °C.     

Triphilic pentablock copolymers with perfluoroalkyl segment in central position

Adding perfluoroalkyl (PF) segments to amphiphilic copolymers yields triphilic copolymers with new application profiles. Usually, PF segments are attached as terminal blocks via Cu(I) catalyzed azide-alkyne cycloaddition (CuAAC). The purpose of the current study is to design new triphilic architectures with a PF segment in central position. The PF segment bearing bifunctional atom transfer radical polymerization (ATRP) initiator is employed for the fabrication of triphilic poly(propylene oxide)-b-poly(glycerol monomethacrylate)-b-PF-b-poly(glycerol monomethacrylate)-b-poly(propylene oxide) PPO-b-PGMA-b-PF-b-PGMA-b-PPO pentablock copolymers by a combined ATRP and CuAAC reaction approach. Differential scanning calorimetry indicates the PF-initiator to undergo a solid–solid phase transition at 63°C before the final crystal melting at 95°C. This is further corroborated by polarized optical microscopy and X-ray diffraction studies. The PF-initiator could successfully polymerize solketal methacrylate (SMA) under typical ATRP conditions producing well-defined Br-PSMA-b-PF-b-PSMA-Br triblock copolymers that are then converted into PPO-b-PSMA-b-PF-b-PSMA-b-PPO pentablock copolymer via CuAAC reaction. Subsequently, acid hydrolysis of the PSMA blocks afforded water soluble well-defined triphilic pentablock copolymers PPO-b-PGMA-b-PF-b-PGMA-b-PPO with fluorophilic central segment, hydrophilic middle blocks, and lipophilic outer blocks. The triphilic block copolymers could self-assemble, depending upon the preparatory protocol, into spherical and filament-like phase-separated nanostructures as revealed by transmission electron microscopy.     

Deconvolving compactly supported densities

This paper addresses the statistical problem of density deconvolution under the condition that the density to be estimated has compact support. We introduce a new estimation procedure, which establishes faster rates of convergence for smooth densities as compared to the optimal rates for smooth densities with unbounded support. This framework also allows us to relax the usual condition of known error density with non-vanishing Fourier transform, so that a nonparametric class of densities is valid; therefore, even the shape of the noise density need not be assumed. These results can also be generalized for fast decaying densities with unbounded support. We prove optimality of the rates in the underlying experiment and study the practical performance of our estimator by numerical simulations.      

Wiener-hopf equations for waves scattered by a system of parallel sommerfeld half-planes

A scalar time-harmonic wave (governed by Helmholtz's equation) impinges on N semi-infinite half-planes. The scattered field is sought when first, second, and third-kind boundary conditions or even general linear transmission conditions on the plates ∑_m and their complementary parts ∑ are prescribed. Making use of the Fourier transform a representation formula for H¹ (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)-Wiener–Hopf (WH) system for jumps of the Dirichlet–and Neumann–Cauchy data across the semi-infinite screens ∑_m. The (2N × 2N)-Fourier symbol matrix ??_?? contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)-symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑_m.