The Riesz decomposition of finely superharmonic functions

This paper answers a question of Fuglede about minimal positive harmonic functions associated with irregular boundary points. As a consequence, an old and central problem of fine potential theory, concerning the Riesz decomposition, is resolved. Namely, it is shown that, on certain fine domains, there exist positive finely superharmonic functions which do not admit any positive finely harmonic minorant and yet are not fine potentials.     

Unified Interactive Multiple Objective Programming: An Open Architecture For Accommodating New Procedures

It has previously been shown that nine of the most prominent procedures of interactive multiple objective programming can be considered as special cases of a common procedure called the unified algorithm. In this paper, we show how four additional procedures can be similarly included in the unified approach. Also, the paper presents a procedure-switching matrix that depicts the possibilities for switching from one procedure to another, one iteration to the next, in the unified algorithm if so directed by a user.     

The Lusin-Privalov theorem for subharmonic functions

This paper establishes a generalization of the Lusin-Privalov radial uniqueness theorem which applies to subharmonic functions in all dimensions. In particular, it answers a question of Rippon by showing that no subharmonic function on the upper half-space can have normal limit at every boundary point.

     

Synthesis of substituted cyclohexenyl-based beta-amino acids by ring-closing metathesis

[structure: see text] A versatile ring-closing metathesis (RCM) approach has been developed for the preparation of cis and trans cyclohexenyl-based beta-amino acids that are either unsubstituted (3) or substituted (10 and 12) at the alpha-position.     

Investigation of the Interactions of β‐Peptides with DNA Duplexes by Circular Dichroism Spectroscopy

The interaction of β‐peptides with the DNA duplexes of dA₂₀dT₂₀ and a GCN4‐binding CRE sequence was examined. To gauge the factors that govern these interactions, two β‐pentadecapeptides, 1 and 2 , a β‐dodecapeptide, 3 , three β‐decapeptides, 4 – 6 , three β‐heptapeptides, 7 – 9 , and β‐octaarginine 10 were designed and synthesized. The β‐peptides were conceived to adopt a β‐peptide 3₁₄ helix, in which the side chains at position i and i + 3 are aligned vertically along one side of the helix. The side chains of Lys, Asn, and Arg were positioned such that potential H‐bonding sites were created for a helical conformation to interact with the base pairs of DNA. CD Analysis showed that β‐peptides 1, 2 , and 10 interacted with dA₂₀dT₂₀. In addition, β‐peptides 1 and 2 showed significant interaction with a DNA‐duplex 20mer containing the ATF/CREB recognition sequence for the regulatory protein GCN4. It is impossible, at this stage of the investigation, to make a safe proposal about the actual nature of the interaction of the structures(s) of the complexes, the formation of which is suggested by the CD spectra reported herein.     

Synthesis of 2,5-bis{(diethyl-3′-indolyl)methyl}furan and its N,N′-dimetallated complexes (lithium, sodium and potassium): X-ray crystal structures of 2,5-bis{(diethyl-3′-indolyl)methyl}furan and the polymeric tetrahydrofuran adduct of the dilithiated complex

The synthesis of 2,5-bis{(diethyl-3′-indolyl)methyl}furan by the acid catalysed condensation of 2,5-bis(diethylhydroxymethyl)furan with indole is presented. Dilithium, disodium and dipotassium derivatives are prepared by the reaction of the bis(indole) with n-BuLi, NaH and K, respectively, in the presence of various Lewis bases. The X-ray structures of 2,5-bis{(diethyl-3′-indolyl)methyl}furan and the dilithiated derivative (as a polymeric tetrahydrofuran adduct) are reported.     

A Direct Assembly Approach to the Synthesis of N,N′-Bridged Calix[4]pyrroles: The Synthesis of a 1,5-Diazacyclononatriene Locked in a Saddle Conformation

Ring closure of 1,2-bis(1-pyrrolylmethyl)benzene in the acid-catalysed condensation with acetone yields the 1,5-diazacyclononatriene [ O -C₆H₄(CH₂NC₄H₃-2)₂C(CH₃)₂] as the sole identifiable product. The twisted or saddle conformation of the 1,5-diazacyclononatriene, which was confirmed by X-ray crystal structure determination, is conformationally rigid in solution. The conformation of the 1,5-diazacyclononatriene prevents the formation of the target N,N′-bridged calix[4]pyrrole by further acid-catalysed condensation with acetone, the reaction affording unidentified oligomers/polymers instead. The acid-catalysed condensation of 1,3- and 1,4-bis(1-pyrrolylmethyl)benzene with acetone also yields unidentified oligomers/polymers.