Characteristic functional of a probability measure absolutely continuous with respect to a Gaussian Radon measure

Let μ and μ₁ be probability measures on a locally convex Hausdorff real topological linear space E. C. R. Baker (Lecture Notes in Mathematics No. 109, pp. 33–44, Springer-Verlag, Berlin/New York, 1979) posed the problem of characterizing the absolute continuity of μ and μ₁ by their characteristic functionals. The aim of this paper is to give an answer to this problem in the case where μ is a Gaussian Radon measure. A Fourier transform shall be defined, the inversion formula established, and then a necessary and sufficient condition given for μ₁ to be absolutely continuous with respect to μ based on the characteristic functional. As applications, for the convolution $\text{μ}{}_1\text{= μ1v}$, where v is a Radon measure on E, we shall give some concrete sufficient conditions on v for $\text{μ1v ? μ}$.     

Turn-on circularly polarized luminescent (CPL) molecular system realized by thermo-driven Newman–Kwart rearrangement reaction from CPL-silent O- to CPL-active S-thiocarbamate groups at peripheral position of 1,1′-binapthyl rings

Although chiral 1,1′-binaphthalene-2,2′-diyl-O,O-bis(N,N-dimethylthiocarbamate) (1) revealed no circularly polarized luminescence (CPL) signals, Newman–Kwart rearrangement of O-thiocarbamate groups at 1 yielded clear CPL signals from 1,1′-binaphthalene-2,2′-diyl-S,S-bis(N,N-dimethylthiocarbamate) (2), which acts as a CPL-gen molecule.     

Investigation for the cyclization efficiency of linear tetrapeptides: Synthesis of tentoxin B and dihydrotentoxin

Investigation of the cyclization efficiency of N-methyl linear tetrapeptides using a molecular modeling study and chemical synthesis is described. The linear peptide with two N-methyl groups, MeAla-Leu-MePhe-Gly, forms γ-turn like conformation with the amine at N-terminus and the carbonyl at C-terminus in closer proximity to give the desired cyclic tetrapeptide, dihydrotentoxin. In addition, synthesis of tentoxin B by the combination of Fmoc solid-phase peptide synthesis and cyclization in solution phase has been reported. An unusual amino acid, an L-N-methyl-β-hydroxyphenylalanine derivative, which was assembled on solid support, was prepared from ethyl cinnamate. Cyclic tetrapeptide formation and cleavage of benzyl ether were optimized with DIPCI/HOBt/DIPEA and Et₃SiH/Pd(OH)₂, respectively.     

Fluctuating Carbonaceous Networks with a Persistent Molecular Shape: A Saddle‐Shaped Geodesic Framework of 1,3,5‐Trisubstituted Benzene (Phenine)

A saddle‐shaped macromolecule has been synthesized. The molecule was designed as a geodesic saddle with 1,3,5‐trisubstituted benzene (named phenine) as the fundamental unit. The phenines were woven into a polygonal framework that was composed of 168 sp²‐hybridized carbon atoms. The saddle‐shaped structure with unique symmetry showed atypical conformational changes. The biaryl linkages in this molecule had a small energy barrier for rotation, and these structural fluctuations resulted in seven ¹H NMR resonances representing 84 aromatic hydrogen atoms. Nevertheless, the overall saddle shape of the molecule was persistent, and the “up” and “down” orientations of phenine moieties circulated to give average ¹H resonances. The structural characteristics of this molecule, including the anomalous entropy‐driven dimerization, may deepen our understanding of defect‐rich graphitic sheets.